On Miles Mathis' Claim π = 4 (in any/all "kinematic" situations).

(For external links, please remove the space unless/until mods fix for new user). The external links are now active.
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Edit: 2022/09/28

Update(s):

1-Page proof
' On a Proof π ≠ 3.14159... '
uploaded to vixra here.

11-Page paper
' On the Use of an Inverse Square to Solve for Pi with Exactitude '
can be found here.
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Herein briefly addresses & seeks to resolve Miles' claim π = 4 "in any/all kinematic situations", thus concerns:

http://milesmathis.com/pi.html
http://milesmathis.com/pi2.html
http://milesmathis.com/pi3.html
http://milesmathis.com/pi7.pdf
http://milesmathis.com/square2.pdf
etc.

False basic underlying assumptions of Western science (short-list):

• 1. π is "defined" as the ratio c/d ...
  

...false.

π as c/d discriminates against 2r/(c/4) wherein 2r describes a right angle instead of a flat diameter:



2r/(c/4) = 8r/c

& viz. Miles' integration:



if/when 8r/c is set in equality with √(2√5+2)/2
c and r resolve:

c = 16r / √(2√5+2)
r = c√(2√5+2) / 16

& if we plug the "approximated" value of π in/as c in the first equality:

π = 16r / √(2√5+2)
r ≈ 0.49952094...

∴ the radius of the "approximated" value of π is not (even) a rational number (!) It is must be precisely 1/2.
The circle whose diameter is 2r = 1 relates to the square s² = 1 via 4 right angles.

This is how/why the outstanding Riemann hypothesis (hence RH) problem exists: the zeta function assumes a/the incorrect value of π.


See 11:55 here:
https://www.youtube.com/watch?v=d6c6uIyieoo&t=715s

Concerning that very question "for which s does ζ(s) = 0?" the answer is none.
There can not be an s for ζ(s) = 0 because in order for ζ(s) = 0, the real element
(ie. the real radius of a real circle) must necessarily be precisely 1/2.
The RH falsely assumes a π of 3.14159... the radius of which is ≈ 0.49952094... and not 1/2.

As such, the RH is invariably true - it can not not be. The real element r = 1/2 is the real radius of a real circle.

The Clay Institute should use the $1M prize to set up an experiment measuring a real circle.
That $1M experiment would teach them more about physics than the $4 000 000 000+ LHC
as it clarifies the nature of the relation between space & time such to unify them via. 1 = Φ(π/4)².

• 2. π was "proven" "transcendental" by Lindemann in 1882...
  

...false.

The "approximated" π of 3.14159... was proven transcendental, because it is.
It doesn't have a rational geometry associated with it ie. no intrinsic symmetries.
The problem is: π is not 3.14159... but the otherwise discrete ratio 4/√Φ.
One can't prove π is transcendental because it is not transcendental. It is a root of:

x⁴ +16x² - 256

thus is geometric.

Anyone who believes "π is transcendental" is unfortunately in a deep slumber (one I wish them to wake from).
Overcoming this π (ie. Riemann hypothesis) problem is a great (and most importantly) unifying "step" forward.
It may not happen the way people want/expect, but it must happen for the same the reason r = 1/2:
as (accordingly to) a natural consequence.

• 3. π was calculated to be between 3 1/7 and 3 10/71 ...
  

...false.

A deficiency is introduced by exhaustive "approximation" methodologies & affects both upper- and lower-limits to the same degree.
That is: 3 and 1/7 is actually 3 and 1/7 minus the deficiency hitherto unaccounted for (for being unconscious of it).
There is no need for such limits if/when it is possible to calculate something precisely. It is possible to precisely calculate a circumference.
One needs to use the right tools, such as a discrete 2π rotation which composes the curve instead of a googleplex of straight lines.

.
Welcome jfmeyer.

Wow, you’ve written a paradigm shifting geometrical Pi paper that can increase humanity’s mathematical awareness and improve the accuracy of world technology. Pi is actually a function of Phi, the golden ratio. Φ = (1 +√5)/2 = 1.61803… . The erroneous transcendental approximation of Pi, π = 3.14159… should be replaced with

π = 4/√Φ = 3.14460…

After a brief review of your posts, paper and Harry Lear’s Measuring Pi Squaring Phi web site, I began copying and verifying many of your formulas/numbers in excel. I would need to study the proofs and your paper further (i.e. the Kepler triangle looks fascinating), but your great diagrams, use of basic math and clear explanations already have me convinced Pi is a function of phi. For example, I’m surprised pi is a root of the quadratic equation X^4 + 16X^2 – 256 = 0; which only works when x=pi=4/√Φ.

Finding a real, unique, time/space kinematic solution to Pi sounds like a real (and irrational) possibility we are interested in, please pardon my levity. If I recall correctly, in a recent pi paper Miles also briefly mentions the four points shared by the circle and square; essentially saying that the two functions agree over the limits of the quarter circle(?) – I’d need to find the actual quote.

Improving the accuracy and measurement of Pi beyond the third decimal place is a great achievement, but your news may not be getting the attention and welcome it deserves, nor from Miles either(?), he may have declared Pi’s extinction a bit too early. Well, frustration at the mainstream and geometric Pi is the norm around here, I think your paper can definitely make a difference.

P.S. I believe a proper kinematic solution must include an object's axial rotation while traveling along the circle circumference. In your paper, How to Properly Measure a Circle https://vixra.org/pdf/2010.0100v1.pdf you show a diagram with the line ABCD rotating about the center of the circle/square. Another rotation needs to be added since point D is axially spinning. I'm not the first to point out that that second rotation takes time and energy.  
.

LongtimeAirman wrote:.
Welcome jfmeyer.

Wow, you’ve written a paradigm shifting geometrical Pi paper that can increase humanity’s mathematical awareness and improve the accuracy of world technology. Pi is actually a function of Phi, the golden ratio. Φ = (1 +√5)/2 = 1.61803… . The erroneous transcendental approximation of Pi, π = 3.14159… should be replaced with

π = 4/√Φ = 3.14460…

After a brief review of your posts, paper and Harry Lear’s Measuring Pi Squaring Phi web site, I began copying and verifying many of your formulas/numbers in excel. I would need to study the proofs and your paper further (i.e. the Kepler triangle looks fascinating), but your great diagrams, use of basic math and clear explanations already have me convinced Pi is a function of phi. For example, I’m surprised pi is a root of the quadratic equation X^4 + 16X^2 – 256 = 0; which only works when x=pi=4/√Φ.

Hello LongtimeAirman (& others): first and foremost my appreciation for much: the fixed links in the OP & for then taking the time to read/consider. I also appreciate the feedback & implore any/all suggestions re: improving upon the paper esp. for the sake of clarity.

If unclear as-is, the implications extend beyond mathematics, as therein is shown the equality of the integer "1". This equality crucially clarifies the nature of the relationship between space and time as being merely (though importantly) multiplicative reciprocal aspects of motion. This ultimately means that reciprocity (as a fundamental mechanic) underlies kinematics. It goes then without saying: reciprocity is not only a "mathematical" principle, it is also a behavioural/ethical one wherein any/all motion(s) (viz. s/t) has a reciprocally related corresponding energy constituency (viz. t/s) whose "product" is always "1" (viz. s/t x t/s = 1). This "1" describes the kinematic condition s/t = 1 as being light (ie. a photon) whence Miles' Charge Field spin-stacking begins from. The "particular" configuration(s) of spin(s) gives us "particles" which build up into atoms/molecules etc. and it all reduces back to (ie. emerges from) this "1". Reciprocity is implied by the nature of the relation between line and curve such to serve as the underlying fulcrum balancing (ie. unifying) gravity and charge.

The most important realization Western science can make at this time is (in) recognizing (such to appreciate & practically utilize) this underlying reciprocity mechanic. It transforms approaches to not only mathematics but all science incl. of living/being. For example, it provides a real/scientific basis for such ethical guidance(s) as "do not do unto others as you would not have them do unto you" and "you reap what you sow" etc. Such principles can be found to be scientifically sound/supported by being of reciprocal nature. It is not a coincidence Miles' Charge Field is missing this mechanic - if one is themselves unconscious of reciprocity, they will not consciously work it into their field equation(s) such to then account for their own local distortion(s). It is very important to be able to do this such to avoid mistaking ones' own local field for the greater.

LongtimeAirman wrote:Finding a real, unique, time/space kinematic solution to Pi sounds like a real (and irrational) possibility we are interested in, please pardon my levity. If I recall correctly, in a recent pi paper Miles also briefly mentions the four points shared by the circle and square; essentially saying that the two functions agree over the limits of the quarter circle(?) – I’d need to find the actual quote.

The kinematic solution is already given: √Φ = √(2(1+√5))/2 is a/the scalar base of motion (with apologies if this was/is somehow not clear).

I will briefly (crudely) demonstrate how/why this is.

Let's focus on these 4 points shared by the circle & square as they naturally exist within a unit square centrally symmetrically about an origin o:

The diagonal of the unit square is equal to precisely √2. Half of √2 is the reciprocal of √2 viz. 1/√2 = √2/2.
Importantly: the area of the s = 1/√2 square (above shaded blue) is s² = 1/2 and thus equal to the radius of the r = 1/2 circle circumscribing it.
This implies the radius of a circle is equal to an internal square, the same the 4 points constructs while/as they rest on perpendicular axes.

Now let us see how/why the golden ratio relates to the r = 1/2 circle, as to be seen: (√5 + 1) / 2 is an operation performed axially.
There is a visualization exercise that can be performed involving simultaneously performing this operation about all axes.

Begin with a √5 diameter circle centrally symmetrically placed about an origin o in/of the square s² = 1/2:


Now collapse the circle towards the origin. Note each "point" on the circumference travels a distance of √5/2:


Now expand the circle back to a √5 diameter circle. Note each "point" on the circumference has now travelled a distance of √5:
(this is the same as (if) each "point" on the circumference were to transit the diameter of the circle simultaneously)


Now continue travelling for an additional +1 unit in all directions such to satisfy √5+1:


Finally, collapse the circle by precisely 1/2 of the total distance travelled such to satisfy (√5+1)/2:


One finds themselves on/as the circumference of the r = 1/2 circle implying Φ describes the surface of this same circle.
Now by taking the square root of Φ, one is actually raising Φ to the radius of 1/2 viz. Φ^1/2 = √Φ.
This √Φ solves for the origin o because each axial Φ is referencing the very centre/origin via the square (root).
This is how/why the Giza pyramid is build with a height of √Φ: it is the "origin".
That is: each discrete unit of space has √Φ as its origin. It is (at) the origin of any/all kinematic(s).

LongtimeAirman wrote:Improving the accuracy and measurement of Pi beyond the third decimal place is a great achievement, but your news may not be getting the attention and welcome it deserves, nor from Miles either(?), he may have declared Pi’s extinction a bit too early. Well, frustration at the mainstream and geometric Pi is the norm around here, I think your paper can definitely make a difference.

The underlying problem resides on the doorstop of human consciousness itself, as most human beings are still presently bound to/by their false basic underlying assumptions/beliefs they have absorbed through the nonsense of Western science. I know Miles is probably focused on moving/situating however it is indeed true that he was too quick to declare π extinct. Nonetheless, the relation to 4 should be obvious: circle and square share 4 common axial points. For this reason alone, π can not be "transcendental".

LongtimeAirman wrote:P.S. I believe a proper kinematic solution must include an object's axial rotation while traveling along the circle circumference. In your paper, How to Properly Measure a Circle https:// vixra.org/pdf/2010.0100v1.pdf you show a diagram with the line ABCD rotating about the center of the circle/square. Another rotation needs to be added since point D is axially spinning. I'm not the first to point out that that second rotation takes time and energy.  
.

I am unsure as to how you are seeing/extrapolating a "second rotation" - there is only one rotation occurring about the origin.
Point D only travels due to the single rotation of AD about the origin, however A, B, C and D are themselves relatively motionless with respect to one another.
The rotational motion about the origin (which indiscriminately applies to A, B, C and D) is afforded in-whole by a single square operation viz. Φ→Φ².

Another way of looking at this is by taking the square root of each axial r = 1/2 such to find + 1/√2 and - 1/√2 as each a 45-degree rotation viz. (2)45 = 90.
Because this occurs both quarterly and simultaneously, only one rotation (ie. square operation) is needed to capture all 360 degrees.
This would include the 360 degrees captured by point D which we are concerned with.

If this does not make sense and/or you still see a "second rotation" please advise.

.
I suspect the world is far more likely to accept π=4/√Φ than the charge field, that is, I might expect to see π = 3.14460… announced in my lifetime. I would have been happy to discover that pi phi relationship anywhere, but to find it here is especially nice. I hope Miles sees fit to address the subject.

I’m slowly going through your information. l’ll need to know more, including better understanding your reply/explanation before possibly bringing up that second rotation again.

Does the ‘origin’ refers to the entire WXYZ diagram? The unit square, along with the origin 0 centered inside, and inscribed r=1/2 circle and 1/√2 square, along with the four common points on two perpendicular axes? The diagram seems like a real mathematical device. Can’t wait till I know why one adds 1 by 1/2 extensions, excetera.  

And then there’s "Reciprocity". I believe “Reciprocity” is demonstrated by the relationship between phi and pi in the origin diagrams. Reciprocity is more than just a mathematical multiplication of inverses resulting in 1. Here, 1 is light, the photon particle, and reciprocity is the relationship between time and space which enables the proton's motion. The reciprocity between the line and curve in the origin diagram is the same as that balancing gravity and charge. Reciprocity should be the basis of human interaction. It all sounds somewhat metaphysical, and I'm most keen on getting the physics correct. I definitely need to work on my understanding.

Thanks for making the axial operation demonstration, showing how moving the 4 common points Φ distance ( Φ = (√5 + 1)/2 ), from starting positions on the r = √5 circle, through the origin to the opposite side of the r = √5 circle, then adding one more unit before dividing the total distance traveled by two. That operation lands the four common points onto the r=1/2 circle. My question is, why does the operation start on the r=√5 circle?

Jfmeyer wrote. "The Giza pyramid is constructed with such a height of √Φ".
Does that mean the ancient Egyptians knew π=4/√Φ? Care to elaborate?
.

LongtimeAirman wrote:I suspect the world is far more likely to accept π=4/√Φ than the charge field, that is, I might expect to see π = 3.14460… announced in my lifetime. I would have been happy to discover that pi phi relationship anywhere, but to find it here is especially nice. I hope Miles sees fit to address the subject.

The sooner the better: overcoming this π problem overcomes millennia of human ignorance. There is a lot of "gravity" associated.
And yet this is not all, for there exists further related "barriers" of Western science: understanding the nature of "time", for one.

The equality π=4/√Φ implying 1 = Φ(π/4)^1/r wherein r = 1/2 predicts a/the unified "field" however Miles is still missing the reciprocity mechanic implied therein (upon which his own "charge field" must/does operate).
If a body recycles "charge" with some particular impedance(s), it causes a local/relative surrounding "field of charge" in relation to, ahem, a Relatively "uncharged" state wherein any/all light is otherwise unimpeded.
Charge can then be described as "spin-stacking" such to consequently cause a particular velocity less than c. However, I note that this is strictly a "mechanical" description and not a full (or even "theoretical") explanation.

Miles' charge field, like General Relativity, presently can not explain any root/cause of any/all motion. It could do this if it solved for a universal origin of any/all projective coordinates. This will ultimately clarify dark matter/energy as well.
Miles has reached a lot of people about the fudging: even from Newton to Einstein, fudge upon fudge. Collectively, they operate in the field of fudge product development, manufacturing & marketing of lots of fudges. It's been this way for a long time.
We can induce an explanation now: it is (all) a natural consequence(s) of any/all failure(s) of science to properly challenge basic underlying assumptions incl. any/all substance of "beliefs" based upon them.
Human motive(s)/action(s) based in/on false assumptions happen to apply directly to the relative charge/gravity ratio of a conscious (or not) moving body. This includes bodies of science.

Western science is approx. up-to 5% conscious (for not knowing 95% of the total universe, as the same measure reflects their own local ignorance).
I'm using their numbers, you see. I'm just interpreting the data such that it reflects the reality: Western science is precisely that ignorant.

The "charge field" conception is not incorrect, but it is incomplete. In present form, it risks discriminating against another valid state(s) of being "uncharged".
The binary of "charged" & "uncharged" discretely precedes any/all "kinematic" motive(s), as only if/when they are not equal would light precede any/all matter.

LongtimeAirman wrote:I’m slowly going through your information. l’ll need to know more, including better understanding your reply/explanation before possibly bringing up that second rotation again.

If one imagines a circle centrally symmetrically plotted on a 2D x & y plane:

one can assign a 3rd dimension z by allowing the origin of coordinates to be a scalar "motive" of some constant (such as c).
One can then imagine the origin z travelling as a light ray at velocity c with x and y remaining relatively fixed.
If one were also travelling at c just behind in the same z direction, the circle remains in fixed proximity.
Treating z as a real "depth" & solving for z is thus equivalent to solving for a/the scalar root of motion (as it concerns c).

LongtimeAirman wrote:Does the ‘origin’ refers to the entire WXYZ diagram? The unit square, along with the origin 0 centered inside, and inscribed r=1/2 circle and 1/√2 square, along with the four common points on two perpendicular axes? The diagram seems like a real mathematical device. Can’t wait till I know why one adds 1 by 1/2 extensions, excetera.

Yes to all, however note the origin o, is not 0 (zero). If the origin is "0" the graph will be based on nothing.

When mathematicians/physicists set their own x & y origin to "0" they are essentially "freeze-framing".
The problem with this in applied math & physics is: nature is not a freeze-frame. Nature is moving.

As above: we solve for z (ie. the origin) as √Φ.

wherein the curve between each 4 pairs of (2r) squares is precisely equal to the reciprocal of √Φ viz. 1/√Φ.
So Miles is half-correct to state π = 4 but √Φ is still the missing "in any/all kinematic situations" base upon which 4 rests.

LongtimeAirman wrote:And then there’s "Reciprocity". I believe “Reciprocity” is demonstrated by the relationship between phi and pi in the origin diagrams. Reciprocity is more than just a mathematical multiplication of inverses resulting in 1. Here, 1 is light, the photon particle, and reciprocity is the relationship between time and space which enables the proton's motion. The reciprocity between the line and curve in the origin diagram is the same as that balancing gravity and charge. Reciprocity should be the basis of human interaction. It all sounds somewhat metaphysical, and I'm most keen on getting the physics correct. I definitely need to work on my understanding.

The physics alone is important because it grounds reality (though Western science would have us believe physics is actually non-physical). Whatever laws do exist will invariably reflect in/as the observable. What matters is how conscious the observation is (&/or is not). Approaching a curve with n-gons is not a conscious endeavour, as one can/will max out (to) the precision afforded by the methodology. Not challenging basic underlying assumptions causes such barriers where none would otherwise exist. In other words: the barriers of Western physics are all in accordance to/with their own false basic underlying assumptions. These assumptions exist because Western scientists are largely unconscious, with consciousness implying trying/testing/falsifying theories by falsifying their most basic underlying assumptions.

Reciprocity is the basis of human interaction regardless of how conscious one is (and/or not). What we inhale, trees exhale (& vice versa) thus reciprocity is present even in/at the level of breathing. To deny reciprocity would be to deny ones own breath (and, say, wear a mask). From even a strictly mechanical standpoint: the other half of our lungs are the trees surrounding us. This mechanic needs to be at the forefront of Western science.

It sounds metaphysical because it is at least half: the laws that govern the physical are the very same that govern the "metaphysical". The expression "as above, so below" is invariably mechanically correct - these are not two separate things (as neither are space & time), they are just one phenomena. What is beyond words is the simultaneity of the two. It doesn't matter if one looks from the bottom-up or the top-down, it is the same fundamental structure/principle. The nature of this structure is hard-coded into the properties of the photon.

For example, place a sphere centrally symmetrically in x, y and z. One can make use of a quaternion 1, i.j.k.
Light occupies the scalar "1" having a velocity c. The i. j. k. are "degrees of freedom".
These degrees of freedom are fundamentally polar: + and - for "charge", for example,
whose magnitude(s) can discretely be speed- and/or spin-based.

LongtimeAirman wrote:Thanks for making the axial operation demonstration, showing how moving the 4 common points Φ distance ( Φ = (√5 + 1)/2 ), from starting positions on the r = √5 circle, through the origin to the opposite side of the r = √5 circle, then adding one more unit before dividing the total distance traveled by two. That operation lands the four common points onto the r=1/2 circle. My question is, why does the operation start on the r=√5 circle?

I return in kind the very same thanks afforded: my own sentiments for your considerate regard.

There is not any r=√5 circle involved (whose diameter would be 2√5), the circle we begin on is d=√5 or r = √5/2.
If you intended the latter: in my own discussions with "mainstream" mathematicians, they can not grasp what you have already demonstrated.
The question is taken to be concerning the reason/need for beginning on the √5 diameter circle.

In short: the reason being the irrational √5 is the integral "common ground" to both Φ and Φ².

We are squaring Φ because we are measuring the discrete 2π that can & does emerge via. Φ² as it relates to (ie. through) √5.

See how the geometric difference between Φ and Φ² is precisely the diameter (2r) of the r = 1/2 circle wherein 2r = 1?
So the operation Φ → Φ² nets us one perfect r = 1/2 circle, the circumference of which we can precisely calculate
without any/all need for exhaustive "approximation" methods. There is no real need/inclining to ever "approximate" π.

We thus must begin & end with the real geometry of √5 (attained by the doubling of the unit square).
We can & must do this because √5 is itself the irrational "ground" carrying the irrational π throughout the square: beginning to end.

In more depth - recall from the paper:

(π+π√5)/2π= Φ
(3π+π√5)/2π = (Φ + 1) = Φ²

& notice √5 is fixed on a static 2π base. So we both began & ended on a base of 2π.
The mathematicians will say "but π can be any variable here, such as x+x√5/2x = Φ).
If we are not a priori assuming a particular value of π, it must be treated as an "unknown" constant.
Assuming we don't know what the correct answer is - the "variable" can be filled by the constant we find.
That is what it means to not "assume" something. You don't assume x is a variable if/when it is not.
π is not a variable. It is a discrete ratio (and it is not even c/d, but 8r/c).
It is that x CAN equal π that is important. We let π be an "unknown" & measure.

In doing so, we are allowing the "square" operation to discretely produce 2π in relation to a known geometric √5 and +1.
To properly measure the emergent circle, we must use the real geometry implied by the involved related integers.
One of the integer coefficients is 1. The other is √5. The 2 merely implies a halved sum of these (ie. 1/2 + √5/2).

If we are going to measure the circle that emerges as a natural consequence of a square, it must all relate back to the real geometry of √5.
So we must know the real underlying geometric relations between 1 (ie: √2) and √5 first, as these are the real constituents of the square.
So our only choices for measuring is beginning with 1 or beginning with √5, as these are the geometric "ground" into the real number system.
They define the integrity to which all other numbers in geometric relation must scale to/from.
This approaches the degree(s) to which Relatively is not necessarily true beyond a certain point.
The problem is in the "charged body" having no practical means to observe beyond the gravitational limit of their own local/relative "field of charge".
It is unaccounted for because Einstein did not know how to measure a circle, thus his (mis)understandings of "time" via. a single privileged clock.
Stephen J. Crothers has raised such objections (& others) for some time now & most of his analysis is absolutely correct.
Miles today is closer than Einstein was, but Einstein's failure wasn't in his intelligence, it was in his improper account of his own short-sightedness.

We can perform the operation (1+√5)/2 or (√5+1)/2 in either direction, but nonetheless √5 is the integral here because it is the real geometric part of Φ.
If there is only one √5, and this √5 is contained in/as the geometry implied by (1+√5)/2, we have to ground in it & stick to it.

LongtimeAirman wrote:Jfmeyer wrote. "The Giza pyramid is constructed with such a height of √Φ".
Does that mean the ancient Egyptians knew π=4/√Φ? Care to elaborate?
.

The designers of the Giza pyramid certainly did. π as 4/√Φ was/is the "capstone" of it, if you will.
However I would not be so quick to assume they were designed by the ancient Egyptians.
It may be the case that the Egyptians inherited the plateau while/as not fully appreciating the knowledge it embodies.

.
Status update.
Mostly reading, re-reading and pondering. Thanks again, I greatly appreciate learning about this timely and important work relating pi, phi and the unified field along with your personal attention and feedback. The following may indicate to you how far I still need to go.

Geometry.

I can see that the unit square origin diagram can be extended outward 1/2 unit distances in both directions on both main axes. The endpoints of the four diagonals of the resulting two1x2 rectangles describe the diagram’s √5 diameter circle. √5 is a special value, an essential component of phi, Φ, where Φ = ( √5 + 1 )/2. Φ has several unique and interesting properties – i.e. Φ2 = Φ + 1, and π = 4/√Φ.

Next, create another circle one unit radius larger than the √5 diameter circle, the √5 + 2 diameter circle. Φ3 = √5 + 2. The diagram then allows direct comparisons of distances, radii, perimeters, circumferences, areas, Φ,  Φ2,  Φ3 and π and is good for any scale.

Geometry wise, I’m stuck in the following three quotes from How to Properly Measure a Circle.  

“The radius of the circle inscribed in the unit square is equal to the area of the square inscribed therein.”

“We may now obtain the exact circumference of the r=1/2 circle by observing the nature and the relationship between √Φ and π/4.

“ Line and curve are resolutely reciprocally related: 1/√Φ = 4/π
“… from phi’s root is derived pi...”“

I don't quite understand the diagram comparing 1/√Φ and 4/π and showing reciprocal areas yet, still, I believe I can claim I’m beginning to properly appreciate the overall geometry of the diagram. However, as you mentioned, nature is not static, it is in motion, so is the diagram.

Motion.

Granted, given the 2π rotational base, the four common points would make a complete circle around the r=1/2 radius circle after traveling 2π. Operationally, how does motion work? You demonstrated that multiplication by Φ, (√5 + 1)/2 is an axial operation that crosses over the center origin. Or are you’re saying that multiplication of the ABCD line by Φ rotates the line once around the diagram’s center? Where A1 is moving along the √5 + 2 diameter circle from A1 to A2, B1 moves from its position on the √5 diameter circle, while C1 moves to C2 on the opposite side of the √5 diameter circle.  D1 travels along the r = ½ circle to D2 without ever leaving the circle.  Why does the diagram include points on both sides of the √5 + 2 diameter circle but only one side of the √5 diameter circle? Why is the C point included.

jfmeyer wrote. "The question is taken to be concerning the reason/need for beginning on the √5 diameter circle".
Airman. That was my intended question, thanks for the correction and √5 discussion.  
jfmeyer wrote. "In short: the reason being the irrational √5 is the integral "common ground" to both Φ and Φ²".

"We are squaring Φ because we are measuring the discrete 2π that can & does emerge via. Φ² as it relates to (ie. through) √5".

"See how the geometric difference between Φ and Φ² is precisely the diameter (2r) of the r = 1/2 circle wherein 2r = 1?"
Airman. Yes.

jfmeyer wrote. "So the operation Φ → Φ² nets us one perfect r = 1/2 circle, the circumference of which we can precisely calculate .…"
Airman. As I said above, I’m stuck here. Does multiplication by Φ indicate an axial distance or a rotation of line ABCD once around the diagram’s center?

//////\\\\\////\\\//\//\\\////\\\\\//////

jfmeyer wrote. "As above: we solve for z (ie. the origin) as √Φ.
wherein the curve between each 4 pairs of (2r) squares is precisely equal to the reciprocal of √Φ viz. 1/√Φ.
So Miles is half-correct to state π = 4 but √Φ is still the missing "in any/all kinematic situations" base upon which 4 rests."
and
jfmeyer wrote.  "If one were also travelling at c just behind in the same z direction, the circle remains in fixed proximity."
Airman. I haven’t made any sense of the need of of solving for z at the origin, √Φ – aside from calculating the height of the great pyramid. I intend to.

\\\\\\/////\\\\///\\/\\///\\\\/////\\\\\\

jfmeyer wrote. "The equality π=4/√Φ implying 1 = Φ(π/4)^1/r wherein r = 1/2 predicts a/the unified "field" however Miles is still missing the reciprocity mechanic implied therein (upon which his own "charge field" must/does operate)."
Airman. At present, I’m far from appreciating the shortcommings of the “charge field”. I don’t see a formula with Φ(π/4) to the 1/r power. Is ^ a typo? On the other hand, the last formula included in How to Properly Measure a Circle, (bolded in the text), is: 1 = Φ(π/4)2. Of course if r=1/2 then 1/r = 2. Is this the formula that predicts the unified field?  
.

LongtimeAirman wrote:.
Status update.
Mostly reading, re-reading and pondering. Thanks again, I greatly appreciate learning about this timely and important work relating pi, phi and the unified field along with your personal attention and feedback. The following may indicate to you how far I still need to go.

The appreciation is also mine: I intend for all of this to culminate into a practical understanding of what can only be described as the same "unified field" you mentioned.

LongtimeAirman wrote:Geometry.I can see that the unit square origin diagram can be extended outward 1/2 unit distances in both directions on both main axes.

Thus the extension/operation is indiscriminately distributed along the x & y axis in all axial directions: +x, -x, +y, -y.
All axial directions implies 4x90degrees apart from origin.
This is very important because this property relates directly to the structure/nature of the photon.

LongtimeAirman wrote:The endpoints of the four diagonals of the resulting two1x2 rectangles describe the diagram’s √5 diameter circle. √5 is a special value, an essential component of phi, Φ, where Φ = ( √5 + 1 )/2. Φ has several unique and interesting properties – i.e. Φ2 = Φ + 1, and π = 4/√Φ.

√5 is very important indeed: it is the "ground" or "reference" for any/all related geometry. It places proper geometric perspective in/around the unit square.
The √5 diameter circle comes from the diagonal of the 2x1 "double" unit square whose own vertices are thus ON the √5 diameter circle.

Miles needs to understand this in order to unify his "charge" field.

He is missing the other half of the field. The other half is accessed through the "in any/all kinematics situations" base of √Φ which links us back to & through √5.
√5 is even more special than this once you add the other half in.

LongtimeAirman wrote:Next, create another circle one unit radius larger than the √5 diameter circle, the √5 + 2 diameter circle. Φ3 = √5 + 2. The diagram then allows direct comparisons of distances, radii, perimeters, circumferences, areas, Φ,  Φ2,  Φ3 and π and is good for any scale.

Yes, however remember we are doing so already having travelled a distance of √5.
So if we say there are 360 points on the √5 diameter circle, each point travels to its own opposite.
That way, each point has travelled precisely √5 provided they each travelled in a straight line.
So there is a real motion involved, beginning with a linear distance travelled of √5.

Through the lens of the three "powers of phi" we see the underlying geometry as it applies in any/all scales.
Hence how/why having the wrong value of π is of great significance: it means we aren't even looking at the circle from the correct perspective.
We then use the diagonals of the unit square to construct an x and y axes, recalling:



wherein by squaring the blue, one attains the red viz. s = 1/√2 thus s² = 1/2 = r
That is: all circles contain the square they themselves circumscribe.
The r = 1/2 circle circumscribes the square s² = 1/2. The magnitudes are equal.
This is how/why "gravity" is a function of radius alone - it relates to/from an area(s) in 2D and/or volume(s) in 3D.

LongtimeAirman wrote:Geometry wise, I’m stuck in the following three quotes from How to Properly Measure a Circle.  

“The radius of the circle inscribed in the unit square is equal to the area of the square inscribed therein.”

The radius of the circle whose d = 2r = 1 has a radius of 1/2.
The perfect square whose side s = 1/√2 squared is s² = 1/2,
thus r = s² = 1/2 wherein the r = 1/2 circle circumscribes the square s²:

LongtimeAirman wrote:“We may now obtain the exact circumference of the r=1/2 circle by observing the nature and the relationship between √Φ and π/4.

“ Line and curve are resolutely reciprocally related: 1/√Φ = 4/π
“… from phi’s root is derived pi...”“

I don't quite understand the diagram comparing 1/√Φ and 4/π and showing reciprocal areas yet, still, I believe I can claim I’m beginning to properly appreciate the overall geometry of the diagram. However, as you mentioned, nature is not static, it is in motion, so is the diagram.

Recall (√5 + 1) / 2 brings us to the circumference of the r = 1/2 circle from any/all direction.
We want the square root of this because we need to "roll back" the square we performed Φ→Φ² to get +2π/2π.
If/when we do so, the golden ratio travels axially inward as if in anside-out square:

LongtimeAirman wrote:Motion.

Granted, given the 2π rotational base, the four common points would make a complete circle around the r=1/2 radius circle after traveling 2π. Operationally, how does motion work?

Space and time are multiplicative reciprocal aspects of motion & thus are practically equivalent to one another. They are not two separate/autonomous phenomena.
Operationally, motion is naturally implied by the square (& root) operation(s) while existing in up to 3 scalar dimensions (xyz and/or ijk).
The square implies a bi-directional 45-degree rotation(s) & is naturally normalized to the speed of light. That is: the "speed" of light is also a "rate" of squares & roots.
We have to be careful here because mathematics can only see/describe the "quantity" of light, not the "quality" of it. This can't be captured with mathematics quite yet.

LongtimeAirman wrote:You demonstrated that multiplication by Φ, (√5 + 1)/2 is an axial operation that crosses over the center origin. Or are you’re saying that multiplication of the ABCD line by Φ rotates the line once around the diagram’s center?

The ABCD line is nothing but a topology which rests on top the real geometry such to reliably "find" the circumference of the r = 1/2.
Once point D finds the r = 1/2 circumference, all we care about from that point on is the rotation. ABC have served their purpose.
Point D relates to the s² = 1/2 square in 4 axial locations while simultaneously being on the circumference of the r = 1/2 circle.
Not only that, their magnitudes are equal. That is: all area(s) s² have an associated r describing a radius of a circle.
What I intended to demonstrate was the difference between Φ² (the square of Φ) and Φ is a rational & discrete 2π with integer difference of 1.
We may use this 2π as a "full rotation" afforded by the square Φ→Φ², hence we allow point D to rotate 2π about an origin composing the r = 1/2 circle.
This means whatever π is, 2π had to pass through 1.618... and 2.618... with nothing lost/added. The measure is thus "precise" to 0 degree(s) of error.

LongtimeAirman wrote:Where A1 is moving along the √5 + 2 diameter circle from A1 to A2, B1 moves from its position on the √5 diameter circle, while C1 moves to C2 on the opposite side of the √5 diameter circle.  D1 travels along the r = ½ circle to D2 without ever leaving the circle.  Why does the diagram include points on both sides of the √5 + 2 diameter circle but only one side of the √5 diameter circle? Why is the C point included.

The diagram is intending to indicate that this operation is carried out simultaneously in each quarter.
The problem with attempting to convey this without motion (ie. animation) presents itself & apologies offered for it being hard to follow. I am planning a re-write & working on something more visual.
One may break the circle into a single quarter & understand this quarter has 4 layers occurring simultaneously as two pairs of reciprocating motion(s). It is upon this base any/all motion can/does occur.

LongtimeAirman wrote:jfmeyer wrote. "The question is taken to be concerning the reason/need for beginning on the √5 diameter circle".
Airman. That was my intended question, thanks for the correction and √5 discussion.  
jfmeyer wrote. "In short: the reason being the irrational √5 is the integral "common ground" to both Φ and Φ²".

"We are squaring Φ because we are measuring the discrete 2π that can & does emerge via. Φ² as it relates to (ie. through) √5".

"See how the geometric difference between Φ and Φ² is precisely the diameter (2r) of the r = 1/2 circle wherein 2r = 1?"
Airman. Yes.

jfmeyer wrote. "So the operation Φ → Φ² nets us one perfect r = 1/2 circle, the circumference of which we can precisely calculate .…"
Airman. As I said above, I’m stuck here. Does multiplication by Φ indicate an axial distance or a rotation of line ABCD once around the diagram’s center?

The axial distance is already contained in Φ as r + √5/2 wherein r = 1/2.
One can also view the denominator '2' in/of (1+√5)/2 as 1/r wherein r is again 1/2.
In either case, the radius is already present in Φ prior to any/all multiplicative operations.

Now we define the base as 2π viz. (π√5+π)/2π squared (π√5+π+2π)/2π
which forces the addition of 2π to be "in-between" 1.618... and 2.618...
because we know Φ² = (Φ + 1) and we know we added 2π.
This 2π is described by the motion of point D according to the "square" s² = 1/2 = r

LongtimeAirman wrote://////\\\\\////\\\//\//\\\////\\\\\//////

jfmeyer wrote. "As above: we solve for z (ie. the origin) as √Φ.
wherein the curve between each 4 pairs of (2r) squares is precisely equal to the reciprocal of √Φ viz. 1/√Φ.
So Miles is half-correct to state π = 4 but √Φ is still the missing "in any/all kinematic situations" base upon which 4 rests."
and
jfmeyer wrote.  "If one were also travelling at c just behind in the same z direction, the circle remains in fixed proximity."
Airman. I haven’t made any sense of the need of of solving for z at the origin, √Φ – aside from calculating the height of the great pyramid. I intend to.

The value taken at z (reciprocally) relates directly to each c/4 (thus π/4), thus in order to know the latter we must know the former.
As the image implied above: we solve for the origin z by taking the square root of the golden ratio.
About all four: +x, -x, +y, -y an inward axial collapse occurs until z (as √Φ) which is whence 2 = 4(1/2) = 4r = 1/r if/as r = 1/2.
The √Φ origin is what reciprocally relates to π/4 via. 1/√Φ = π/4.

Any/all applied mathematics (ie. physics) that does not allow the origin to be √Φ is not real physics.
√Φ is the kinematic base of motion: it "grounds" into the 3 scalar dimensions of motion as they apply to space & time.
What x is to space, y is to time and z is to the scalar kinematic base of motion. This base is ultimately grounded in 1 = Φ(π/4)²
which implies a unified field as/in relation to light.

LongtimeAirman wrote:\\\\\\/////\\\\///\\/\\///\\\\/////\\\\\\

jfmeyer wrote. "The equality π=4/√Φ implying 1 = Φ(π/4)^1/r wherein r = 1/2 predicts a/the unified "field" however Miles is still missing the reciprocity mechanic implied therein (upon which his own "charge field" must/does operate)."
Airman. At present, I’m far from appreciating the shortcommings of the “charge field”. I don’t see a formula with Φ(π/4) to the 1/r power. Is ^ a typo? On the other hand, the last formula included in How to Properly Measure a Circle, (bolded in the text), is: 1 = Φ(π/4)2. Of course if r=1/2 then 1/r = 2. Is this the formula that predicts the unified field?  
.

Yes - as you stated, if r = 1/2 then 1/r = 2 or a "power" of 2.
Note by arguing 1 = Φ(π/4)^1/r wherein r = 1/2, r then describes a real radius of a real circle.
One can then assign this real radius of a real circle to the radius of a photon and spin-stack the rest of the physical universe thereupon.
However note: "charge field" discriminates against there being an "uncharged field" so we'll have to account for that after.

.

Comparing images from jfmeyer’s paper How to Properly Measure a Circle
https://vixra.org/pdf/2010.0100v1.pdf left side, to equal area square and circle
(but unequal perimeters) on the right from Miles’ paper Squaring the Circle, part 2.  
http://milesmathis.com/square2.pdf

I cannot say I understand most of it, you be the judge, Squaring the Circle, part 2 * appears
to contain some pertinent discussion. Please consider adding it to the list of Miles Mathis’ ‘kinematic
pi reference links’ at the top of this thread.

jfmeyer wrote. Thus the extension/operation is indiscriminately distributed along the
x & y axis in all axial directions: +x, -x, +y, -y.
All axial directions implies 4x90degrees apart from origin.
This is very important because this property relates directly to the structure/nature of
the photon.

Airman. To the four extensions +/-x and +/-y in the planar orthogonal axial directions,
agreed. I assume we may or may not consider the third orthogonal z axis as well.
The photon. I believe the photon can be centered in the phi origin diagram. How do two
orthogonal planar axes relate to the structure/nature of the photon?

jfmeyer wrote. √5 is very important indeed: it is the "ground" or "reference" for
any/all related geometry. It places proper geometric perspective in/around the unit square.
The √5 diameter circle comes from the diagonal of the 2x1 "double" unit square whose own
vertices are thus ON the √5 diameter circle.
Miles needs to understand this in order to unify his "charge" field.
He is missing the other half of the field. The other half is accessed through the "in
any/all kinematics situations" base of √Φ which links us back to & through √5.
√5 is even more special than this once you add the other half in.

Airman. I consider your origin diagram as a great improvement over the traditional notion
of an origin (the intersection of three axes). The 1, √5 and (√5 + 2) diameter circles are
scaled to the object’s unit square through the unique value of phi, which allows us to
easily perform or demonstrate rotations or root/power operations as well as show pi is a
function of phi.
As I understand it, the “unified field” encompasses gravity and the charge field. Motion
at the speed of light is a given.

You believe there is a unique property of phi associated with motion which Miles needs to
find in order to definitively “prove” that kinematic pi = 4, just as you’ve shown that
pi = 4 /√Φ. At the bottom of this post, you also state “This base is ultimately grounded
in 1 = Φ(π/4)²”.

jfmeyer wrote. Through the lens of the three "powers of phi" we see the underlying
geometry as it applies in any/all scales.
Hence how/why having the wrong value of π is of great significance: it means we aren't even 
looking at the circle from the correct perspective.
We then use the diagonals of the unit square to construct an x and y axes, recalling:
wherein by squaring the blue, one attains the red viz. s = 1/√2 thus s² = 1/2 = r
That is: all circles contain the square they themselves circumscribe.
The r = 1/2 circle circumscribes the square s² = 1/2. The magnitudes are equal.

This is how/why "gravity" is a function of radius alone - it relates to/from an area(s) in
2D and/or volume(s) in 3D.

The radius of the circle whose d = 2r = 1 has a radius of 1/2.
The perfect square whose side s = 1/√2 squared is s² = 1/2,
thus r = s² = 1/2 wherein the r = 1/2 circle circumscribes the square s²:

Airman. Thanks again for your patience. This is making complete sense. The first time I
read your paper I had no trouble understanding that inscribed square s = 1/√2 has an area
s^2 = 1/2 which is equal to the radius of the circle inscribed in the unit square. I
interpreted that as a metaphysical statement. One should not allow comparisons between a
one dimensional length (radius) and a two dimensional area (sq units). The 1/2 is a
mathematical coincidence. I wasn’t asking you to show that particular equality, but I’m
glad you did. Given your additional excellent diagrams and further descriptions, I agree.
This is the unit square’s inscribed r=1/2 circle and that circle’s inscribed s = (1/√2)
square. Absolutely, the magnitudes are equal, there’s nothing metaphysical about it.
Linking that fact to the explanation/interpretation that “"gravity" is a function of
radius alone” is a very interesting interpretation.

jfmeyer wrote. Recall (√5 + 1) / 2 brings us to the circumference of the r = 1/2
circle from any/all direction.
We want the square root of this because we need to "roll back" the square we performed
Φ→Φ² to get +2π/2π.
If/when we do so, the golden ratio travels axially inward as if in an inside-out square:

Airman. Ok, the division inverted me too but I think I’ve got it, you “solved” for phi
at z=0 to be √Φ by taking
the square root of the golden ratio. I think I see that each quarter circle arc length
equals c/4 = π/4 = 1/√Φ.

jfmeyer wrote. Space and time are multiplicative reciprocal aspects of motion
& thus are practically equivalent to one another.
They are not two separate/autonomous phenomena.
Operationally, motion is naturally implied by the square (& root) operation(s) while existing
in up to 3 scalar dimensions (xyz and/or ijk).

Airman. Space and time as the multiplicative inverses of motion sounds good. I
accept that motion is implied by the root or square operation.

I suppose the phi origin can apply to regular geometry, but given your paper’s Riemann
Hypothesis mentions and your RH youtube video link, I expect both real and complex
numbers too. The paper’s diagram, “f(x) = x^4 + 16x^2 – 256” clearly includes the
phi-based unit square/origin diagram including √5 and √5 + 2 diameter circles. I guess
the image show the Riemann series converging to the roots +/- 4/√Φ +/- 5.088078598i?
That might make a good animation. Is there one green line or four?
Is the line reciprocating in any way? Up or down, and left or right? I’d suggest that
image needs a description.
 
I must ask, can you tell us what the effect of converting pi to 4/√Φ has on the RH, and
would it qualify you to win the one million dollar prize?

jfmeyer wrote. The ABCD line is nothing but a topology which rests on top the
real geometry such to reliably "find" the circumference of the r = 1/2.
Once point D finds the r = 1/2 circumference, all we care about from that point on is the
rotation. ABC have served their purpose.
Point D relates to the s² = 1/2 square in 4 axial locations while simultaneously being ON
the circumference of the r = 1/2 circle.
Not only that, their magnitudes are equal. That is: all area(s) s² have an associated r
describing a radius of a circle.
What I intended to demonstrate was the difference between Φ² (the square of Φ) and Φ is
a rational & discrete 2π with integer difference of 1.
We may use this 2π as a "full rotation" afforded by the square Φ→Φ², hence we allow point
D to rotate 2π about an origin composing the r = 1/2 circle.
This means whatever π is, 2π had to pass through 1.618... and 2.618... with nothing
lost/added. The measure is thus "precise" to 0 degree(s) of error.

Airman. I can follow all that, agreed.

jfmeyer wrote. The diagram is intending to indicate that this operation is carried
out simultaneously in each quarter.
The problem with attempting to convey this without motion (ie. animation) presents itself
& apologies offered for it being hard to follow. I am planning
a re-write & working on something more visual.
One may break the circle into a single quarter & understand this quarter has 4 layers
occurring simultaneously as two pairs of reciprocating motion(s). It is upon this base
any/all motion can/does occur.

Airman. No apologies please, I love a good diagram, just ask anyone. Point C is part of the
formula getting from the √5 diameter circle to the r=1/2 circle, Φ = (1+√5)/2. BC depicts the
distance √5. You've provided many extremely clear diagrams. Good thing too, when I study your
information I found I needed to keep at least one or two of your diagrams open in their own
windows for repeated reference. All phi numbers must be verified to be believed and all your
numbers look good to me.  

Referring to the “approximatly 3.144605511029693144…” diagram
showing a quarter portion of the r=1/2 circle. I see that the value at the top of the quarter’s
right angle equals (√2(1+√5))/2 = √Φ. I also see that the quarter section arc length of
r=1/2 equals 1/√Φ = 2/√2(1+√5) = π/4. The circumference is equal to four such arc
lengths. The large grey arrow down the center of the diagram is simply pointing out that
the two sets of values are reciprocal - is that correct?

Four layers carried on simultaneously? I must keep that in mind.

What exactly are the two pairs of reciprocating motion(s)?

The only thing I can think of is included in Miles’ paper Proof that Pi=4. * A gif shows
how two reciprocating x and y axis motions create a circle.

jfmeyer wrote. The axial distance is already contained in Φ as r + √5/2 wherein
r = 1/2.
One can also view the denominator '2' in/of (1+√5)/2 as 1/r wherein r is again 1/2.
In either case, the radius is already present in Φ prior to any/all multiplicative
operations.

Now we define the base as 2π viz. (π√5+π)/2π squared (π√5+π+2π)/2π
which forces the addition of 2π to be "in-between" 1.618... and 2.618...
because we know Φ² = (Φ + 1) and we know we added 2π.
This 2π is described by the motion of point D according to the "square" s² = 1/2 = r

Airman. Ok. I think I can follow and agree with all that. Is D a single point, or all
four common D points simultaneously?

jfmeyer wrote. The value taken at z (reciprocally) relates directly to each c/4
(thus π/4), thus in order to know the latter we must know the former.
As the image implied above: we solve for the origin z by taking the square root
of the golden ratio.
About all four: +x, -x, +y, -y an inward axial collapse occurs until z (as √Φ)
which is whence 2 = 4(1/2) = 4r = 1/r if/as r = 1/2.
The √Φ origin is what reciprocally relates to π/4 via. 1/√Φ = π/4.

Airman. Agreed.

jfmeyer wrote. Any/all applied mathematics (ie. physics) that does not allow
the origin to be √Φ is not real physics.
√Φ is the kinematic base of motion: it "grounds" into the 3 scalar dimensions of motion
as they apply to space & time.
What x is to space, y is to time and z is to the scalar kinematic base of motion. This
base is ultimately grounded in 1 = Φ(π/4)²
which implies a unified field as/in relation to light.

Airman. You’re making sense to me now.

jfmeyer wrote. Yes - as you stated, if r = 1/2 then 1/r = 2 or a "power" of 2.
Note by arguing 1 = Φ(π/4)^1/r wherein r = 1/2, r then describes a real radius of a real
circle.
One can then assign this real radius of a real circle to the radius of a photon and spin
-stack the rest of the physical universe thereupon.
However note: "charge field" discriminates against there being an "uncharged field" so
we'll have to account for that after.

Airman. How can we help you?


*
http://milesmathis.com/updates.html

PAPER UPDATE, added 11/8/16, Proof that Pi=4. A reader has graciously sent me a gif that
recreates part of the video being suppressed on Youtube and elsewhere, and I have embedded it
in my paper.
http://milesmathis.com/pi7.pdf

The paper’s gif didn’t work for me, Miles redirects to Dragon Face’s vimeo at
https://vimeo.com/189647953

NEW PAPER, added 4/11/20, Squaring the Circle, part 2. I extend this old analysis from 2006,
incorporating my pi=4 findings. I also show you why the circle maximizes area, and what this tells us
about the charge field.
http://milesmathis.com/square2.pdf
.

LongtimeAirman wrote:.

Comparing images...

I cannot say I understand most of it, you be the judge, Squaring the Circle, part 2 * appears
to contain some pertinent discussion. Please consider adding it to the list of Miles Mathis’ ‘kinematic
pi reference links’ at the top of this thread.

It is pertinent (& added).

I understand where Miles was going with it & I agree with its overall direction.
Generally, we need to better understand the nature of the relation between square & circle.
The problem is in first recognizing the circle has its own internal & external square(s), thus
the comparison between the two must begin with the squares the circle is already related to.

For example, the r = 1/2 circle is in relation to two squares: s² = 1/2 and s² = 1.
The circle circumscribes s² = 1/2 & while/as inscribed in the unit square s² = 1.
There are 4 common geometric points relating all three.

LongtimeAirman wrote:I assume we may or may not consider the third orthogonal z axis as well.
The photon. I believe the photon can be centered in the phi origin diagram. How do two
orthogonal planar axes relate to the structure/nature of the photon?

We must consider the third orthogonal z axis if motion is involved.
The z axis can take a scalar magnitude such as a "speed" c, as you say, the photon.

The two orthogonal axes composes the domain(s) to which any/all pairs of particular (+/-) polarities may be discretely confined (to).

The nature of the relation between each pair is antithesis: one is the polar opposite of the other,
thus they balance as-is. All physical structure(s) is based in/on this same underlying axis.

LongtimeAirman wrote:You believe there is a unique property of phi associated with motion which Miles needs to
find in order to definitively “prove” that kinematic pi = 4, just as you’ve shown that
pi = 4 /√Φ. At the bottom of this post, you also state “This base is ultimately grounded
in 1 = Φ(π/4)²”.

Yes, with "in any/all kinematic situations" being satisfied by √Φ viz. 4/√Φ = π.

LongtimeAirman wrote:Thanks again for your patience. This is making complete sense. The first time I
read your paper I had no trouble understanding that inscribed square s = 1/√2 has an area
s^2 = 1/2 which is equal to the radius of the circle inscribed in the unit square. I
interpreted that as a metaphysical statement. One should not allow comparisons between a
one dimensional length (radius) and a two dimensional area (sq units). The 1/2 is a
mathematical coincidence. I wasn’t asking you to show that particular equality, but I’m
glad you did. Given your additional excellent diagrams and further descriptions, I agree.
This is the unit square’s inscribed r=1/2 circle and that circle’s inscribed s = (1/√2)
square. Absolutely, the magnitudes are equal, there’s nothing metaphysical about it.
Linking that fact to the explanation/interpretation that “"gravity" is a function of
radius alone” is a very interesting interpretation.

It is both physical & metaphysical: it indiscriminately applies to both, as fundamentally the same law governs both.
That the magnitudes are equal is an actual "coincidence" in every practical sense of the word
because at r = 1/2 = s² the area of a square discretely relates to the radius of a circle.
Implied: a real radius of a real circle is afforded by the real area of a real underlying square.

LongtimeAirman wrote:Ok, the division inverted me too but I think I’ve got it, you “solved” for phi
at z=0 to be √Φ by taking
the square root of the golden ratio. I think I see that each quarter circle arc length
equals c/4 = π/4 = 1/√Φ.

Precisely.

LongtimeAirman wrote:Space and time as the multiplicative inverses of motion sounds good. I
accept that motion is implied by the root or square operation.

Yes & this is why the inverse square law exists - motion is subject to/of such root & square operations.

LongtimeAirman wrote:I suppose the phi origin can apply to regular geometry, but given your paper’s Riemann
Hypothesis mentions and your RH youtube video link, I expect both real and complex
numbers too. The paper’s diagram, “f(x) = x^4 + 16x^2 – 256” clearly includes the
phi-based unit square/origin diagram including √5 and √5 + 2 diameter circles. I guess
the image show the Riemann series converging to the roots +/- 4/√Φ +/- 5.088078598i?
That might make a good animation. Is there one green line or four?
Is the line reciprocating in any way? Up or down, and left or right? I’d suggest that
image needs a description.

Complex analysis is attempting to accomplish what the rationals & irrationals already do.
As such, the real element of 1/2 applies to broad-spectrum complex analysis, as you intuit.
The "imaginary" i.j.k allows for recursive redistribution of magnitudes into 3 scalar dimensions of motion
as they relate to a/the real element. This allows "real" & "imaginary" to cross in one shared geometry
with the latter able to capture spin.

The "crux" of it all (yes pun) is the r = 1/2 = s² property in/at the unit square.

The lines in the image were/are not meant to be of any practical significance beyond modelling the RH "pole".

LongtimeAirman wrote:I must ask, can you tell us what the effect of converting pi to 4/√Φ has on the RH, and
would it qualify you to win the one million dollar prize?

The raw magnitude of the problem is incomprehensible - the mathematicians have no idea how big of a problem the RH problem actually is/implies.
I know it is considered the biggest unsolved problem in mathematics, but the magnitude of it can not be realized until the root of the problem is known.

The RH problem exists because human beings do not know how to properly measure a circle.

That is the underlying problem the RH is pointing at & is the problem now millennia old.
It underlies (as a common denominator) any/all human ignorance/suffering/death over the same period.

That said, the correct value of π certainly shows how/why the hypothesis can not not be true (ie. by "necessity").
It does so by approaching the problem from the top-down rather than bottom-up,
clarifying what the "real element" even is: a real radius of a real circle.

As for the prize: I am more worried about an even deeper problem being unsolved at such high cost.
The RH problem happens to be the best possible vehicle to globally address such a problem as π.
The correct value of π solves much more than the RH problem, as the solution to unity is in the best interest of science at this time.

LongtimeAirman wrote:Referring to the “approximatly 3.144605511029693144…” diagram
showing a quarter portion of the r=1/2 circle. I see that the value at the top of the quarter’s
right angle equals (√2(1+√5))/2 = √Φ. I also see that the quarter section arc length of
r=1/2 equals 1/√Φ = 2/√2(1+√5) = π/4. The circumference is equal to four such arc
lengths. The large grey arrow down the center of the diagram is simply pointing out that
the two sets of values are reciprocal - is that correct?

Yes. This is because each c/4 is being referenced by the origin of the the unit square via. 2r right-angled radii:

√Φ = √(2√5+2)/2 → 1/√2 → 2/√(2√5+2) = π/4

viz.
kinematics = 2r → reciprocal  → c/4

So line and curve are reciprocally related such that time & space are multiplicative reciprocal aspects.
This means there exists reciprocity between all radii (bodies) & their corresponding circumferences (orbits).
This further implies "time" and "space" are not two independent/autonomous phenomena, but one.

LongtimeAirman wrote:What exactly are the two pairs of reciprocating motion(s)?

Mechanically, they are like two ends of a seesaw with reciprocity at the fulcrum.
The two ends can be occupied by any binary, such as up/down, +/- etc.

However, the photon (ie. light) demands considerations of both physical and non-physical properties, as
light relates information(s) in the form of binary(s) as they apply to any/all subjugate binaries incl. physical & not.
It is a mistake for anyone incl. Western science to assume existence is confined to the "physical". It is not.

LongtimeAirman wrote:The only thing I can think of is included in Miles’ paper Proof that Pi=4. * A gif shows
how two reciprocating x and y axis motions create a circle.

Indeed - there are many ways reciprocity applies & each are as valid as the next.
Different models have different applications, but the principle is universally applicable.

LongtimeAirman wrote:Ok. I think I can follow and agree with all that. Is D a single point, or all
four common D points simultaneously?

It is both for ultimately describing the entire circumference of the circle.
Because the relation exists about all 360 degrees simultaneously, the value it takes immediately reflects such inclusion.
So point/square/circle/sphere D is satisfied by (√5+1)/2 because "2" is the reciprocal of the radius it is describing.

LongtimeAirman wrote:How can we help you?

Anything in the way of helping to instigate a global correction to π is where there is need of help - not (only) for me, but for all of humanity.
There is no better vehicle for such a correction to occur than the RH - the real prize is not $1mil but the enrichment of all lives.

The RH problem is like a finger pointing at a problem the depths of which Western science hasn't yet understood.
The paper is like a finger pointing at the deeper underlying problem: our human civilization does not know
how to properly measure a circle & thus serves as a practical measure of how unconscious the planet is.
With a resolution, the reciprocity principle is compelled to take precedence as preceding relativity:

e = MC² < Relativity
16 = Φπ² < Reciprocity
1 = Φ(π/4)² < Unified Field

wherein 16 = Φπ² rationally precedes e = MC². Einstein didn't solve for it because he didn't know how to measure a circle.

Here is a screen cap of desmos showing (√5+1)/2 precisely describing a point (0, 1/2) on the circumference of the r = 1/2 circle.

We plot 4 points along the y axis.
(0, -√5/2) describes one half diameter of the √5 diameter circle from point A to origin.
(0, √5/2) describes the other half diameter of the √5 diameter circle from origin to point B.
(0, √5/2 + 1) describes the space between -√5/2 and √5/2 plus a rational & discrete "1".
(0, AC/2) finds x & y coordinates (0, 1/2).

This is proof the operation (√5+1)/2 if/when performed axially
adequately describes the circumference of the r = 1/2 circle.

.

I believe there are a couple of errors in your last post.
1. In the desmos diagram "wherein AC/2=(5+1)/2 = Φ". Change 5 to √5.
2. Change sentence from That is: … A "beings” to A “begins”.
3. 2nd diagram. BC = 1, that's clear enough from the diagram. 2nd line from the top.  Change from “BC = √5 + 1” to “AC = √5 + 1”,
Your (√5+1)/2 diagram with rotating points is clearer than these two (√5+1)/2 diagrams.

/////\\\\///\\/\//\\\////\\\\\

I agree that geometric pi, Πg = 4/√Φ, thank you very much. Even better, we can just replace the old 3.14159… value with the new 3.1446055… . Another good reason for the 3.14159’s extinction.

I also agree that kinematic pi, Πk = 4 and that, as you’ve pointed out, the relationship between Πg and Πk needs to be formally
proven. Miles can certainly come up with an elegant proof; but pardon me Sir, I believe, so can you.  

Do you have any objections or suggestions in trying to apply your phi based origin in here?

In Squaring the Circle, part 2 Miles wrote.

The square has a much larger area, but as a matter of kinematics it has the same circumference as the circle.  Both
circumferences are 8r.  That is to say, if you treat the circumference as a distance that has to be traveled by a real body, the distances are equal.  It will take the same time to travel the circle as the square.

 

Below, I’ve transferred Miles’ red unit square and blue inscribed circle of equivalent kinematic distances/time traveled onto the phi based origin’s r=1/2 circle.


How might we depict the motion of an object traveling along the 1/2 radius circle a, b, c, d?

jfmeyer wrote.

We must consider the third orthogonal z axis if motion is involved.
The z axis can take a scalar magnitude such as a "speed" c, as you say, the photon.

The two orthogonal axes composes the domain(s) to which any/all pairs of particular (+/-) polarities may be discretely confined (to).

The nature of the relation between each pair is antithesis: one is the polar opposite of the other, thus they balance as-is. All physical structure(s) is based in/on this same underlying axis.

Airman. For the first two orthogonal axes there are a few parametric alternatives to choose from. Let’s use Wikipedia’s cos and sin
equations for a circle, https://en.wikipedia.org/wiki/Parametric_equation. I’m changing the radius from 1 to r, and adding r in front
of cos(t) and sin(t), where r = 1/2.

x^2 + y^2 = 1,  x^2 + y^2 = r^2,
(x,y) = (r cos(t), r sin(t))   for 0 <= t <= 2πg.

Now we need to include motion. The blue quarter circle arc length is 1/√Φ. The total r=1/2 circumference isΠ g.. .

1/√Φ = Πg/4
(1/√Φ)*4/Πg = 1

A Kinematic multiplier which can be used to convert the geometric length - Πg curves into the  kinematic Πk distances.

Πk = 4/Πg
tk = 4/tg
We may then calculate the object’s actual kinematic position on the r=1/2 circle as a function of time t. Time is the z axis. Or calculate the object’s position as a function of the object’s forward and orthogonal sideways velocities.

Does that sound reasonable?
.

LongtimeAirman wrote:.

I believe there are a couple of errors in your last post.
1. In the desmos diagram "wherein AC/2=(5+1)/2 = Φ". Change 5 to √5.
2. Change sentence from That is: … A "beings” to A “begins”.
3. 2nd diagram. BC = 1, that's clear enough from the diagram. 2nd line from the top.  Change from “BC = √5 + 1” to “AC = √5 + 1”,
Your (√5+1)/2 diagram with rotating points is clearer than these two (√5+1)/2 diagrams.

/////\\\\///\\/\//\\\////\\\\\

Thanks & apologies - fixed the desmos & removed the latter entirely.
Further apologies for the delay in response.

LongtimeAirman wrote:I agree that geometric pi, Πg = 4/√Φ, thank you very much. Even better, we can just replace the old 3.14159… value with the new 3.1446055… . Another good reason for the 3.14159’s extinction.

For practical purposes, a π of 3.14159... is indeed useless if/as given the correct 4/√Φ...
However I think it should endure to serve as the best example (or perhaps even "case study") proving the fundamental need/necessity of science to incessantly challenge basic underlying assumptions.
I can't really stress this point enough: the only reason Western science is in the situation it is owes to their ongoing failure(s) to do so & at such great cost(s).

LongtimeAirman wrote:I also agree that kinematic pi, Πk = 4 and that, as you’ve pointed out, the relationship between Πg and Πk needs to be formally
proven. Miles can certainly come up with an elegant proof; but pardon me Sir, I believe, so can you.

Between analysis & math, I only use the latter for the sake of the former & am not accustomed to the formal "language" of institutionalized math, unfortunately.
I could thus use the help of mathematicians to put all of this into a/the language other mathematicians can understand. I'm not best suited for that, for many reasons.

Concerning Πg & Πk: they may appear as two if/when relativistic perspective is introduced, as in: one is looking from the bottom-up & the other top-down.
Both are thus "valid" but they are still ultimately directed towards one subject/object (with this "oneness" being the unifying factor) thus let s/t = 1.

If/when s/t = 1, this is simply the default "unity" condition wherein gravity & charge are both "polar" constituents of a unified field.
Gravity is moving inward while/as the default scalar expansion of space (ie. the universe) is moving outward.
These two appear as polar opposites however they also mediate that which is subject to/of.

Let 1 be unity & find its roots.
√1 = +1, -1
+1 = is unity (ie. implies zero impedance)
-1 = is not unity (ie. implies non-zero impedance)

wherein -1 is then subject to/of the recursive x.y.z or i.j.k dimensions (ie. cyclic time-based "physicality")
& wherein 1 + (-1) ≠ "0" but = √Φ as the geometric "origin" of any/all space, hence the height of Giza as √Φ.
Implies: all gravitating bodies are simultaneously subject(s) to/of a scalar expansion of +1 from within
& the gravitational contraction of -1 from without. Simultaneity of the two is the mediating factor.

π is thus naturally normalized to the "speed" of light c & thus naturally in relation to any/all acceleration(s) associated with gravity.
That is: the "waveform" of light is naturally captured in/as/by 1=Φ(π/4)² & therein both expansion & contraction reciprocates over a common magnitude.
For example: if/when a body breathes in & out their chest expands & contracts, thus breathing (ie. life) itself relies on a process of sustained reciprocation.
Obviously this suggests the "proof" of reciprocity is in it predicting breathing bodies, but most scientists are unconscious even of their own breath.

LongtimeAirman wrote:Do you have any objections or suggestions in trying to apply your phi based origin in here?

No to the former & yes to the latter, however the latter requires challenging mainstream perspectives in a major way.

Presently, Western science assumes the 3 dimensions normally associated to "space" applies not to "time".

Why?

Is it because we merely "relatively" observe time as (if) a linear "arrow"?
Suppose it is simultaneously both linear and circular.
Suppose Einstein couldn't properly account for "time" because he didn't know how to properly measure a circle.
This endeavour would be important if "time" has anything whatever to do with circles. Well, does it?
The planet is spinning on its axis relative to a central sun, thus so are any/all bodies on it as they concern the sun, a source of c, or "light".
Suppose the 3d normally associated only to "space" actually precedes any/all considerations of space & time entirely.
This allows any/all s³/t motion to have a corresponding t³/s energy constituency whose motion(s) are in 3 scalar dimensions (x.y.z or i.j.k).

Find the product of 3d speed & energy:
(s³/t)(t³/s)=(st)²
a square of "spacetime".

Apply the square of "spacetime" to unity:
(st)² = 1 = Φ(π/4)²
s = 1/t, -1/t
t = 1/s, -1/s

This produces four symmetrical reciprocals whose numerators are naturally normalized to unity (thus π is normalized to c).
From here, both space and time can be afforded up-to 3 dimensions (ultimately they are not two separate/autonomous phenomena).
From one relative perspective, motion occurs in/as space over "time". From another equally valid perspective, energy occurs in/as time over "space".
Why should one be more valid than the other? They are both observing the very same from two "relatively" different perspectives.

This "cube of time" mechanic acts as (if) a contracting sphere centrally symmetrically about a body.

In this image, inward gravity occurs at the poles & energy is channelled outward as "charge" from the equator.
This model also predicts the overall charge impedance of a body causes its own surrounding gravitational boundary.
That is: if a body has zero impedance, it has no gravitational boundary & satisfies the unity condition in any/all "spacetime" configurations.
If a body has non-zero impedance(s), those impedance(s) define the surrounding gravitational boundary (of that same body).
All physical bodies have a gravitational boundary as well as an electromagnetic boundary (though the latter is not only a "physical" boundary).

LongtimeAirman wrote:In Squaring the Circle, part 2 Miles wrote.

The square has a much larger area, but as a matter of kinematics it has the same circumference as the circle.  Both
circumferences are 8r.  That is to say, if you treat the circumference as a distance that has to be traveled by a real body, the distances are equal.  It will take the same time to travel the circle as the square.

 
Below, I’ve transferred Miles’ red unit square and blue inscribed circle of equivalent kinematic distances/time traveled onto the phi based origin’s r=1/2 circle.


How might we depict the motion of an object traveling along the 1/2 radius circle a, b, c, d?

In order to depict it, we first have to extract the underlying cause of it & simply allow the square to "just 'cause" it as a natural consequence.
The paper states the circle is a natural product of a square. That is: the difference between Φ² & Φ is the additional 2π in-between 2.618... and 1.618...
It further finds the curve to be a natural consequence of reciprocity viz. 1/√Φ = π/4 wherein the reciprocal of a linear magnitude is equal to a quarter circumference.
This linear magnitude is the z axis' constancy of c (geometrically √Φ). We can thus allow z to be a source of photon emission(s) in any/all 360-degrees (as to follow).

Recall we found the equality r = 1/2 = s² which relates the area of the square to the radius of the circle circumscribing it.
Miles may have been misinterpreting the geometry to state "both circumferences are 8r" such to support his π = 4 conclusion.
The circumference of the circle is not technically "equal" to 8r, it is in relation to 8r. That is: one discrete 2r per c/4.
The most important aspect of the integration is: by involving "time" the association of 2r to c/4 arises instead of 2r as a flat diameter.
Miles merely did not know to incorporate the natural kinematic base of √Φ which, as we should see, is already naturally normalized to c or the speed of light.
That is: the mere presence of it implies motion. All one has to do is include it in the math - it is practically the "on" switch for (the) light (of the universe).

So to address your question about depicting motion travelling along circle abcd,
the reciprocally related motions giving rise to that curve precedes the full circle.
So we have to go one layer deeper to a quarter & find where that curve is even coming from.
In other words, we must look deeper at a quarter circle wherein 2r is confined to a right angle.

LongtimeAirman wrote:jfmeyer wrote.

We must consider the third orthogonal z axis if motion is involved.
The z axis can take a scalar magnitude such as a "speed" c, as you say, the photon.

The two orthogonal axes composes the domain(s) to which any/all pairs of particular (+/-) polarities may be discretely confined (to).

The nature of the relation between each pair is antithesis: one is the polar opposite of the other, thus they balance as-is. All physical structure(s) is based in/on this same underlying axis.

Airman. For the first two orthogonal axes there are a few parametric alternatives to choose from. Let’s use Wikipedia’s cos and sin
equations for a circle, https://en.wikipedia.org/wiki/Parametric_equation. I’m changing the radius from 1 to r, and adding r in front
of cos(t) and sin(t), where r = 1/2.

x^2 + y^2 = 1,  x^2 + y^2 = r^2,
(x,y) = (r cos(t), r sin(t))   for 0 <= t <= 2πg.

Now we need to include motion. The blue quarter circle arc length is 1/√Φ. The total r=1/2 circumference is Πg.. .

If 2r is allowed to describe a right angle, each 2r is in relation to c/4.
This implies the ratio 2r/(c/4) = 8r/c & s/t constitutes motion.

See this image:


implying c = 4πr²
if/when π = 8/√(2√5+2)
and r = 1/2.

Therefor if we allow √Φ = s/t then:
t = 2s/√(2√5+2) wherein if t = 2r = 1 then s = √Φ
s = t√(2√5+2)/2 wherein if s = 2r = 1 then t = 1/√Φ = π/4
∴ space and time are (multiplicative) reciprocal aspects of motion.
r = c√(2√5+2)/16 wherein if r = 1/2 then c = π = 8/√(2√5+2).

LongtimeAirman wrote:1/√Φ = Πg/4
(1/√Φ)*4/Πg = 1

A Kinematic multiplier which can be used to convert the geometric length - Πg curves into the  kinematic Πk distances.

Πk = 4/Πg
tk = 4/tg
We may then calculate the object’s actual kinematic position on the r=1/2 circle as a function of time t. Time is the z axis. Or calculate the object’s position as a function of the object’s forward and orthogonal sideways velocities.

Does that sound reasonable?
.

Does it work? Can you employ it to measure the circumference of the r = 1/2 circle if given a scalar time t on the z axis?
Geometrically, this scalar time t is a function of √Φ & describes the radial distance travelled by a photon(s) per discrete unit t.
This radial distance thus creates a discrete/definite boundary (ie. the circumference of a circle defined by a radius).

You may have to distribute √Φ over 2 perpendicular radii so √Φ/2 per r in/of 2r in relation to c/4. This means 2(√Φ/2) = 2r = √Φ is in relation to 2(c/8 ) = c/4 = 1/√Φ.
This way, for every r = √Φ/2 there exists one c/8, thus Miles' c = 8r (in)equality gives us a c of 2√(2√5+2) = 5.08807859... which is only meaningful if on a base of π:
2√(2√5+2) / 8/√(2√5+2) = Φ = 1.618... hence his entire "charge field" is missing the crucial base of kinematics afforded by the unification of Φ & π via. 16 = Φπ².

.
jfmeyer wrote. Apologies - fixed the desmos & removed the latter entirely.
Further apologies for the delay in response.
Airman. Please don’t hesitate pointing out my errors, most especially on diagrams.
I’m the one who needs to apologize for delays, I keep re-reading without understanding.
I'll catch on eventually. Please don’t stop presenting your ideas waiting for me to keep up,
there are plenty of readers who can.

jfmeyer wrote. For practical purposes, a π of 3.14159... is indeed useless if/as given
the correct 4/√Φ...
However I think it should endure to serve as the best example (or perhaps even "case
study") proving the fundamental need/necessity of science to incessantly challenge basic
underlying assumptions.
I can't really stress this point enough: the only reason Western science is in the situation
it is owes to their ongoing failure(s) to do so & at such great cost(s).
Airman. Keeping transcendental Pi around might serve as a good abject historical
lesson if mathematicians/scientists can show proper consideration and good judgment. I
remember when I believed they did, but they don’t appear to question their assumptions much
anymore.
I basically agree with you but I think "Science" has been largely taken over by various special
interests so I can't blame it for today's bigger problems verging on violence, including
growing anti-science sentiment, the denial of facts and growing disinformation.

jfmeyer wrote. Between analysis & math, I only use the latter for the sake of the former &
am not accustomed to the formal "language" of institutionalized math, unfortunately.
I could thus use the help of mathematicians to put all of this into a/the language other
mathematicians can understand. I'm not best suited for that, for many reasons.
Airman. I don't imagine I could come up with a Space/time phi-based kinematic proof, but
it sounds like a fine idea. I'm more the engineer type, able to use math and tools to design
and build things and happy to work at creating new problems or solutions.

Any help from mathematicians or other charge field stalkers out there is welcome.  

jfmeyer wrote. Concerning Πg & Πk: they may appear as two if/when relativistic perspective
is introduced, as in: one is looking from the bottom-up & the other top-down. Both are thus
"valid" but they are still ultimately directed towards one subject/object (with this "oneness"
being the unifying factor) thus let s/t = 1.
Airman. Letting s/t =1 is straightforward enough but saying Πg & Πk only differ from a
bottom-up or top-down relativistic perspective threw me when I first read it and every time
since. As you can tell, I don't properly understand Relativity. I suppose the kinematic proof
will likely identify the oneness between kinematic and geometric Pi's.  

jfmeyer wrote.
If/when s/t = 1, this is simply the default "unity" condition wherein gravity & charge are
both "polar" constituents of a unified field.
Gravity is moving inward while/as the default scalar expansion of space (ie. the universe) I
s moving outward.

These two appear as polar opposites however they also mediate that which is subject to/of.
Airman. "Inward gravity and outward space". The concept of duality or polar opposites aside,
here and in your following description and diagram, you indicate inward gravity. I believe Miles’
best explanation for gravity (and the unified field) is his Expansion theory. According to which,
the earth’s gravitational acceleration is equivalent to earth doubling its radius every 19 minutes.  
S=(1/2)*at^2 m, s=6,378,000 m, a= 9.8 m/s, t=√(2*s/a)=1141 seconds or 19
minutes.
All matter - photons, electrons, neutrons and protons - in the universe is expanding at the
same rate. See Miles’ Third Wave series. In Part 1 Miles shows that “mass, inertia and
gravity are all shown to be equivalent, reducible to the same motions”*. Follow that up with
The Perihelion Precession of Mercury **, where as Einstein proved curved space by
plotting Mercury’s position during a solar eclipse, Miles proves his Expansion theory.

Before I depart inward gravity, its safe to say Miles is very interested in a charge based
explanation for gravity. The math works but the idea of rapidly expanding matter and
universe that ends when the surface velocity of the proton reaches lightspeed is too much
for most people to accept. I'm good with expansion theory now but it took me a few years
to accept it. Anyway, Miles asked if anyone had any charge based gravity ideas. We worked
at it here a bit, but no joy.  
Later in this post jfmeyer wrote. “This model also predicts the overall charge impedance
of a body causes its own surrounding gravitational boundary”.
Airman. That sounds like a possible charge based explanation of gravity to me.

jfmeyer wrote. “This produces four symmetrical reciprocals whose numerators are naturally
normalized to unity (thus π is normalized to c)”.
Airman. Time and distance, s/t = 1. Spacetime squares, inversly unified space time axes
(+/- 1/s, and +/- 1/t) normalized to c and "cube of time" mechanic all sounds good and
amazing. Do you have a single source index document listing all these phi based origin facts
and interpretations? If not I'll be forced to start one myself.

jfmeyer wrote. In this image, inward gravity occurs at the poles & energy is channelled
outward as "charge" from the equator.
This model also predicts the overall charge impedance of a body causes its own surrounding
gravitational boundary.
That is: if a body has zero impedance, it has no gravitational boundary & satisfies the unity
condition in any/all "spacetime" configurations.
If a body has non-zero impedance(s), those impedance(s) define the surrounding
gravitational boundary (of that same body).
All physical bodies have a gravitational boundary as well as an electromagnetic boundary
(though the latter is not only a "physical" boundary).  

Airman. The time and space diagram looks very interesting, given the inverted axes
its hard to imagine how it works, getting closer to the origin with increasing space or time(?)
crossing the unit circle boundary. I don't see how 1 or -1 implies impedence or not, but I'll
accept it for now.
I already called attention to the gravity as an impedance to emitted charge sentence.
Why do you show charge emitted from the body's equator and gravity inward toward the
poles? Would the diagram be valid if we replaced the incoming gravity such that the
diagram would show only incoming polar and emitted equatorial charge?  

Airman wrote. How might we depict the motion of an object traveling along the 1/2
radius circle a, b, c, d?

jfmeyer wrote. In order to depict it, we first have to extract the underlying cause of it
& simply allow the square to "just 'cause" it as a natural consequence.
The paper states the circle is a natural product of a square. That is: the difference between
Φ² & Φ is the additional 2π in-between 2.618... and 1.618...
It further finds the curve to be a natural consequence of reciprocity viz. 1/√Φ = π/4
wherein the reciprocal of a linear magnitude is equal to a quarter circumference.
This linear magnitude is the z axis' constancy of c (geometrically √Φ). We can thus
allow z to be a source of photon emission(s) in any/all 360-degrees (as to follow).  
Airman. I was good until the last two sentences, where I got lost. I suppose the z axis
can be the source for a 3D spherical emission of 4 sterradians?

jfmeyer wrote. Recall we found the equality r = 1/2 = s² which relates the area of the
square to the radius of the circle circumscribing it.
Miles may have been misinterpreting the geometry to state "both circumferences are 8r"
such to support his π = 4 conclusion.
The circumference of the circle is not technically "equal" to 8r, it is in relation to 8r. That
is: one discrete 2r per c/4.
The most important aspect of the integration is: by involving "time" the association
of 2r to c/4 arises instead of 2r as a flat diameter.
Miles merely did not know to incorporate the natural kinematic base of √Φ which, as
we should see, is already naturally normalized to c or the speed of light.
That is: the mere presence of it implies motion. All one has to do is include it in the math
- it is practically the "on" switch for (the) light (of the universe).
Airman. "All one has to do is include it in the math - it is practically the "on" switch
for (the) light (of the universe)." again, sounds amazing. Are you selling anything?
I agree with your reasonable argument that it is inaccurate to say the kinematic
circumference is equal to 8r, when it is completely accurate to say the quarter r=1/2
circle's circumference is 2r.

jfmeyer wrote. So to address your question about depicting motion travelling along circle
abcd, the reciprocally related motions giving rise to that curve precedes the full circle.
So we have to go one layer deeper to a quarter & find where that curve is even coming from.
In other words, we must look deeper at a quarter circle wherein 2r is confined to a right angle.
Airman. I follow you.

jfmeyer wrote. If 2r is allowed to describe a right angle, each 2r is in relation to c/4.
This implies the ratio 2r/(c/4) = 8r/c & s/t constitutes motion.
Airman. " & s/t constitutes motion"? Are you saying 8r is distance and c - the circumference,
is time?

jfmeyer wrote. See this image:

implying c = 4πr²
if/when π = 8/√(2√5+2)
and r = 1/2.
Airman. Agreed. That's a good diagram.

jfmeyer wrote. Therefor if we allow √Φ = s/t then:
t = 2s/√(2√5+2) wherein if t = 2r = 1 then s = √Φ
s = t√(2√5+2)/2 wherein if s = 2r = 1 then t = 1/√Φ = π/4
∴ space and time are (multiplicative) reciprocal aspects of motion.
r = c√(2√5+2)/16 wherein if r = 1/2 then c = π = 8/√(2√5+2).
Airman. Agreed.  

LongtimeAirman wrote:1/√Φ = Πg/4
(1/√Φ)*4/Πg = 1

A Kinematic multiplier which can be used to convert the geometric length - Πg curves into the
kinematic Πk distances.

Πk = 4/Πg
tk = 4/tg
We may then calculate the object’s actual kinematic position on the r=1/2 circle as a function
of time t. Time is the z axis. Or calculate the object’s position as a function of the object’s
forward and orthogonal sideways velocities.

Does that sound reasonable?

jfmeyer wrote. Does it work? Can you employ it to measure the circumference of the
r = 1/2 circle if given a scalar time t on the z axis?
Geometrically, this scalar time t is a function of √Φ & describes the radial distance travelled
by a photon(s) per discrete unit t.
This radial distance thus creates a discrete/definite boundary (ie. the circumference of a circle
defined by a radius).
Airman. In my pi simulation the main motion mechanism amounted to the ratio: distance
traveled s is to 4 as the angle traveled a is to 2pi radians, s/4 = a/2p without any problems.
But as usual, you're giving me plenty more to think about.  

jfmeyer wrote. You may have to distribute √Φ over 2 perpendicular radii so √Φ/2 per r in/of 2r
in relation to c/4. This means 2(√Φ/2) = 2r = √Φ is in relation to 2(c/8 ) = c/4 = 1/√Φ.
This way, for every r = √Φ/2 there exists one c/8, thus Miles' c = 8r (in)equality gives us a c
of 2√(2√5+2) = 5.08807859... which is only meaningful if on a base of π:
2√(2√5+2) / 8/√(2√5+2) = Φ = 1.618... hence his entire "charge field" is missing the crucial base
of kinematics afforded by the unification of Φ & π via. 16 = Φπ².
Airman. There's more information than I can currently grasp, thanks for doing a fine job patiently
explaining it all. I'll keep studying it. Any ideas on how we might proceed?


*
171.  The Third Wave: a Redefinition of Gravity, Part I.  http://milesmathis.com/third.html
No curved space, no force at a distance, no force-carrying particle. Gravity is explained here
simply in terms of straight-line motion. Mass, inertia and gravity are all shown to be equivalent,
reducible to the same motions. 9pp

**
58. The Perihelion Precession of Mercury.  http://milesmathis.com/merc.html A long critique of the
historical problem, showing the major errors of Einstein and others. 32pp.
.

I was referred to jfmeyer by Airman in the pi=9 latest paper thread.

I compute that a diameter of 1000.95985x3.14159 is equal to 3144605.455.
My eyes are telling me that the Lear wood circle diameter must be measured so as to be as precise as possible. I will now go rewatch the video.
at 1:19 of the second video we see that the 500 mm mark does not line up with this pencil line. I don't know if this is because of paralax, or what, but it is more than a tenth of a mm off.

I usually myself use a protocol, I decide based on the width of the tick mark of my tape measure to either standardize a measurement off the side of the tick mark closest to zero, the side farthest, or approximate the middle. Does he explain a protocol?

Edit: on reading https://vixra.org/pdf/2010.0100v1.pdf
I run into a terminological problem. On page 4 "the real geometric square" is hard to define so as to follow along. I also note that in the diagram D is what is being incessantly drawn along the circle, but in the fraction to the top left, we get ab=1 which I think is true, bc=squareroot of (5) which is true, but under that we just get d, which is maybe set equal to 2. But it can't equal 2 I think, not in this diagram. We also get Phi in the corners of an inscribed square, not sure why. Under the diagram we get D=phi, but for me D is a point, it would be on the circle yes, but we don't know where that point is yet, and a point cannot have a length, and neither ad nor dc are 2 or phi. What am I missing?

Edit2: D is on the midpoint of the line sweeping, a line of length 1+sqr(5), but how do we know that? If we get the length bd then its over. But we don't know bd. reading.... bd seems to (sqt(5)-1)/2. I'm taking a break. Thanks for reading :)

edit Doing the caluculation, bd=1/phi , I think that clarifies it now.

LongtimeAirman wrote:I basically agree with you but I think "Science" has been largely taken over by various special
interests so I can't blame it for today's bigger problems verging on violence, including
growing anti-science sentiment, the denial of facts and growing disinformation.

There are some long-standing ideological "belief" systems which imbue certain pre-existant texts as being "divinely" authoritative. That is: there is no higher authority than what is written in such texts.
Such ideologies underlie the various manufactured "special interest" groups militarily pursuing unscientific "authority as truth" rather than scientific "truth as authority" (in accordance with their ideological beliefs).

In other words: such special interest groups perceive (thus act) up-to 180-degrees upside-down such to make falsity into truth & truth into falsity etc.
Miles talks about this inversion principle re: "Project Chaos" but his own "Charge Field" can't scientifically predict it without the inverse properties afforded by reciprocity
(I have a model of the photon which clearly predicts the cause of such polar inversion(s) as it relates to any/all relative perception, but is largely off-topic.
I may propose this model elsewhere on the forums at a later time if there is any/enough interest).

For now, in the context of π, "transcendental" & "geometric" represent the two "poles" of such inversion.
In general, Western science is inverted at & from this very point on.
They falsely assume π is "proven" "transcendental" while/as geometric.
A correction to π is practically equivalent to a corrective "pole reversal"
which inverts an already-inverted pole back to proper calibration.
A π of 4/√Φ is naturally calibrated to the rational terminating & irrational non-terminating numbers.
An "approximated" π of 3.14159... is catastrophically decalibrated & thus inevitably breaks down over time
(as human civilizations historically do). I argue an incorrect π predicts such gradual break-downs over time.

LongtimeAirman wrote:I don't imagine I could come up with a Space/time phi-based kinematic proof, but
it sounds like a fine idea. I'm more the engineer type, able to use math and tools to design
and build things and happy to work at creating new problems or solutions.

Any help from mathematicians or other charge field stalkers out there is welcome.

I recently came up with a better way to relate motion on the z-axis to motion along the circumference of the r = 1/2 circle.
If one takes 4 Keppler triangles and places their right-angled vertex on the original x & y intercept (as z):

one can imagine a photon motioning relative from z up to s back down through z down to t and back up to z & rinse/repeat.
These 4 discrete positive distance motions √Φ are the reciprocal of each corresponding c/4 = π/4.

So as one is travelling a "linear" velocity of √Φ (such as a light ray might),
the equivalent "circular" motion is the reciprocal of the velocity of the ray.

LongtimeAirman wrote:Letting s/t =1 is straightforward enough but saying Πg & Πk only differ from a
bottom-up or top-down relativistic perspective threw me when I first read it and every time
since. As you can tell, I don't properly understand Relativity. I suppose the kinematic proof
will likely identify the oneness between kinematic and geometric Pi's.  

You are not alone - not even Einstein properly understood Relativity because he didn't properly understand time (hence his confusion with clocks).
See here for Mr. Stephen J. Crothers discovering how/why Einstein unknowingly violates his own "no privileged observer" principle:
https://www.youtube.com/watch?v=6zWy6_Mog70


The perspective I am speaking of precedes any/all notions of Relativity, the former being false from/at any/all "privileged" points.
If/when two opposite perspectives are both looking at the very same object/subject, they are both indiscriminately valid.
For example, s/t and t/s as speed & energy resp. are two opposite perspectives of the same phenomena of motion.
Πg & Πk are like this: the latter k is the kinetic/kinematic energy causing the geometric g effect we see.
The nature of the relation between them (ie. uniting them) is reciprocity: (t/s x s/t) have a common product 1.

LongtimeAirman wrote:"Inward gravity and outward space". The concept of duality or polar opposites aside,
here and in your following description and diagram, you indicate inward gravity. I believe Miles’
best explanation for gravity (and the unified field) is his Expansion theory. According to which,
the earth’s gravitational acceleration is equivalent to earth doubling its radius every 19 minutes.  
S=(1/2)*at^2 m, s=6,378,000 m, a= 9.8 m/s, t=√(2*s/a)=1141 seconds or 19
minutes.

We can't place aside apparent duality or polar opposition in any kinematic and/or geometric universe, as such is integral.
This is part of the point I am making with regards to physical kinematics and/or motion: it is necessarily polar.
That does not mean the "universe" as a whole is necessarily polar or "charge"-based, but physicality is.
For example, if you imagine a spherical object and apply a magnitude (say 4) to it from two opposite directions
& then begin subtracting from one side, the other side causes a motion proportional to the loss of the other side:

Here, relative motion is caused by any one side being unequal to the other (thus because "time" whence "gravity").

So the earth is expanding outward, but it does so against the inward acceleration caused by gravity (as a consequence of time).
These two velocities expansion +g and gravity -g share the same magnitude but are polar opposites & thus create a "field" inhabited by "charged" bodies.
Any difference (if present) is present in/as physical manifestation(s) occurring in/as cyclical motion(s) over "time". Time is thus a circle-of-all-circles.
This would predict upside-down/unconscious civilizations to perceive time as a linear "arrow" rather than being of cyclic nature, as time is.
Indeed, this is what we are slowly learning: that (the arrow of) time is an illusion (albeit a very persistent one) because it is not an arrow, but a circle.

If we took all the gravity away, all matter would fly apart at the speed of light (which naturally happens outside any/all gravitational boundaries).
If we took all the expansion away, all matter would collapse to a single "point" (which Western science believes whence a "Big Bang").
The "Big Bang" model thus assumes a primordial absence of such an expansion... which is a very big assumption.
It is a very big assumption because the alternative is there having never once been a single discrete "beginning" of expansion.
One could generalize this as a steady-state universe wherein so-called "Big Bangs" are subject to/of cyclical nature (ie. more than one).

So there is indeed an "equivalent" motion as if the earth is expanding... it is so because it is expanding.
But it is also simultaneously collapsing according to the inward acceleration caused by gravity.
Note: the acceleration afforded by gravity has the capacity to exceed c, whereas c is always c.
We see this occur with so-called "black holes" wherein matter breaks the light barrier owing to gravity overtaking c
(akin to speed breaking the sound barrier) & is eventually recycled back into manifestation via. vehicles such as quasars.

LongtimeAirman wrote:All matter - photons, electrons, neutrons and protons - in the universe is expanding at the
same rate. See Miles’ Third Wave series. In Part 1 Miles shows that “mass, inertia and
gravity are all shown to be equivalent, reducible to the same motions”*. Follow that up with
The Perihelion Precession of Mercury **, where as Einstein proved curved space by
plotting Mercury’s position during a solar eclipse, Miles proves his Expansion theory.

This same scalar rate of expansion is contingent on the constancy(s) of Φ and π via. 1 = Φ(π/4)².
However, both expansion & gravitation are incessantly simultaneous within any gravitational boundary.
This is true for any/all systems of aggregates incl. solar systems.

Western science is incredibly ignorant of these boundaries & their properties.

There are inversive principles that apply to these boundaries, such as IoR lensing (index of refraction).
Basically: once perception/observation reaches the gravitational boundary of a body, the lens inverts
& it is therefrom as if looking through the wrong end of binoculars such to see close phenomena as far away.
This happens if/when we look outside of the gravitational boundary of our own galaxy.
Everything that appears really, really far away is actually not & the distances & speeds are all off accordingly.

I thus disagree overall that Einstein ever "proved" curved space, as space is not independent of time (& Relativity even suggests this).
It is rather the math that is curved (as Miles states), not the actual space itself (as I state). We can model the behaviour with curved math.
What is actually happening involves curved time just as much as curved space, as space and time are one cohesive phenomena.

A gravity-centric universe is only ever 1/2 of the equation, as it discriminates entirely against the expansion-centric universe counter-part.
In this way, Relativity can only ever account for up-to 1/2 (currently: 5%) of the universe because it can't see the other half without the reciprocal relation.

LongtimeAirman wrote:Before I depart inward gravity, its safe to say Miles is very interested in a charge based
explanation for gravity. The math works but the idea of rapidly expanding matter and
universe that ends when the surface velocity of the proton reaches lightspeed is too much
for most people to accept. I'm good with expansion theory now but it took me a few years
to accept it. Anyway, Miles asked if anyone had any charge based gravity ideas. We worked
at it here a bit, but no joy.  
Later in this post jfmeyer wrote. “This model also predicts the overall charge impedance
of a body causes its own surrounding gravitational boundary”.
Airman. That sounds like a possible charge based explanation of gravity to me.

There is technically no "charge"-based explanation for gravity because gravity is the inverse of "uncharged" expansion.
The outward expansion rate of space between bodies outside of each others' gravitational boundaries naturally tends towards c.

This expanding region of space is the "uncharged" field as it has only one direction: "out". Gravity is the polar "in" direction reversal
as a natural consequence of charge impedance(s), the same causing the gravitational boundary of the body concerned.

LongtimeAirman wrote:Time and distance, s/t = 1. Spacetime squares, inversly unified space time axes
(+/- 1/s, and +/- 1/t) normalized to c and "cube of time" mechanic all sounds good and
amazing. Do you have a single source index document listing all these phi based origin facts
and interpretations? If not I'll be forced to start one myself.

No, however I can direct you to where these were discovered & discussed (please pm if interested).

LongtimeAirman wrote:The time and space diagram looks very interesting, given the inverted axes
its hard to imagine how it works, getting closer to the origin with increasing space or time(?)
crossing the unit circle boundary. I don't see how 1 or -1 implies impedence or not, but I'll
accept it for now.
I already called attention to the gravity as an impedance to emitted charge sentence.
Why do you show charge emitted from the body's equator and gravity inward toward the
poles? Would the diagram be valid if we replaced the incoming gravity such that the
diagram would show only incoming polar and emitted equatorial charge?

1 implies the expansion tending towards c. This is the default condition outside a gravitational boundary whose equiv. vector is "out" in all directions.
-1 implies the recursive i.j.k 3 scalar dimensions over t which capture any/all not c. That is: all particular time-based physicality.
1 would refer to the state of being "unimpeded" while/as -1 allows s³/t to capture & describe any/all bodies' 3D motions over time.

I showed gravity at the poles & charge at the equator because it is only a 2D depiction - I only have 2 degrees of freedom there.
In 3D, gravity is inward from all directions & expansion is outward in all directions & they are mutually simultaneous.
"Charge" is the "difference" between the two & is according to the particular charge of the body as it channels light.

Incoming gravity is not to be confused as "charge". Charge is a property of a body, not a field.

LongtimeAirman wrote:I was good until the last two sentences, where I got lost. I suppose the z axis
can be the source for a 3D spherical emission of 4 sterradians?

The z-axis alone is 1D thus can only represent a linear magnitude. However, a linear magnitude is all that is needed to describe a sphere if given an origin and 3D.
That is: the magnitude is indiscriminately distributed in all directions from the point such to define a circular/spherical boundary.
The z-axis can thus be a source of a scalar "rate of expansion" and/or "rate of contraction" & simultaneously both if subject to ± polarity.

LongtimeAirman wrote:"All one has to do is include it in the math - it is practically the "on" switch
for (the) light (of the universe)." again, sounds amazing. Are you selling anything?
I agree with your reasonable argument that it is inaccurate to say the kinematic
circumference is equal to 8r, when it is completely accurate to say the quarter r=1/2
circle's circumference is 2r.

I'm not selling anything (outside of challenging basic underlying assumptions).
Note c/4 is not 2r directly but is the reciprocal of the 2r original intersect.

LongtimeAirman wrote:" & s/t constitutes motion"? Are you saying 8r is distance and c - the circumference, is time?

8r alone is referring to a timeless length, not a time-based distance.
The c emerges upon the introduction of time giving us a ratio 8r/c satisfying s/t (=velocity) and/or t/s (=energy).
We let there be equality between 8r/c & √Φ because these coincide at the origin of the r = 1/2 circle:

√Φ = t/s = √(2√5+2)/(1/r) → (1/r)/√(2√5+2) = s/t = π/4 if/as r = 1/2, for example.

LongtimeAirman wrote:There's more information than I can currently grasp, thanks for doing a fine job patiently
explaining it all. I'll keep studying it. Any ideas on how we might proceed?

I suppose it depends on what one means to accomplish.

3rd doorman wrote:I was referred to jfmeyer by Airman in the pi=9 latest paper thread.

Hello & welcome, thanks for joining the discussion.

3rd doorman wrote:I compute that a diameter of 1000.95985x3.14159 is equal to 3144605.455.

Are you assuming π = 3.14159...? Because I am arguing in reality, it does not.
I argue the π of 3.14159... has a real radius of 0.49952094... and not 1/2, as assumed.
This deficiency reflects the resolution limit of any/all approximation methodology(s) using polygons.
I argue a real radius of 1/2 gives rise to a real circumference 3.1446055... as Harry's measure shows.

The problem with the polygon approach is in the need for it to "approximate" a fixed radius while itself having a variable one.
It can/will never resolve the real radius of 1/2 because the proximity between origin & surface is never such a constant with an n-gon.
Only by beginning & ending directly on the circumference of the circle can one measure it with precision. The paper does this.

3rd doorman wrote:My eyes are telling me that the Lear wood circle diameter must be measured so as to be as precise as possible. I will now go rewatch the video.
at 1:19 of the second video we see that the 500 mm mark does not line up with this pencil line. I don't know if this is because of paralax, or what, but it is more than a tenth of a mm off.

As you mentioned, what is important is the measure of the diameter being precisely 1000mm.
A real circle of 1000mm diameter will have a real circumference greater than 3144mm.

3rd doorman wrote:I usually myself use a protocol, I decide based on the width of the tick mark of my tape measure to either standardize a measurement off the side of the tick mark closest to zero, the side farthest, or approximate the middle. Does he explain a protocol?

Note the difference between the "approximated" π predicting a circumference of ~3141.6mm & the "precise" π predicting a circumference of ~3144.6mm being a matter of a full 3mm.
A (1/10)mm discrepancy is trivial with respect to such a wide margin as 3mm. All we need to do is measure a circumference greater than 3141.6mm anywhere outside of margin of error(s).
I do not know whether or not he explains his protocol to such fine detail, but his measure suggests he went through reasonable effort to be accurate to within 1mm.
In any event, by beginning & ending directly on the circumference of an r = 1/2 circle, the circumference can be measured as a precise ratio 8 / √(2√5+2) ≈ 3.14460...
...the number 3.14159... is the closest a polygon(s) can ever get which maxes out at the thousandth decimal place.

3rd doorman wrote:Edit: on reading https://vixra.org/pdf/2010.0100v1.pdf
I run into a terminological problem. On page 4 "the real geometric square" is hard to define so as to follow along.

If you look at a unit square as follows:

the "real geometric square" s² = 1/2 has sides s = 1/√2. If one folds the corners of a unit square inward along these 4 s = 1/√2 lines,
one divides the area of the unit square by half. Further, the area of the square s² = 1/2 is equivalent to the radius of the circle r = 1/2,
hence s² = 1/2 = r is an extremely important equality: it relates a real radius to the real area of a real square.

3rd doorman wrote:I also note that in the diagram D is what is being incessantly drawn along the circle, but in the fraction to the top left, we get ab=1 which I think is true, bc=squareroot of (5) which is true, but under that we just get d, which is maybe set equal to 2. But it can't equal 2 I think, not in this diagram.

Point D is technically AC/2 which is equal to (√5+1)/2 delivering us to an (x, y) of (0, 1/2). See here:


See how A is plotted at (0, -√5/2) and B is plotted (0, √5/2), thus AB = √5.
See how C is plotted at (0, √5/2 + 1) thus AC = √5 + 1.
See how D emerges at (0, 1/2) according to AC/2 while/as equal to (√5 + 1)/2.
Now rotate AC about the origin & find D incessantly coincide with the circumference of the r = 1/2 circle.
We can measure this circumference without any/all need for "approximation" & find 8/√(2√5+2) = 4/√Φ.

The entire circumference of the r = 1/2 circle is described by the operation (√5 + 1)/2 performed from any/all 360 degrees, including at the vertices of the inscribed square, hence:

3rd doorman wrote:We also get Phi in the corners of an inscribed square, not sure why.

because (√5 + 1)/2 simultaneously describes the entire circumference of the r = 1/2 circle as well as the 4 vertices of the s² = 1/2 square inscribed therein.
Those vertices have a proximity of 1/2 from the origin just as the radius of the circle does. Thus (0, 1/2) & (1/2, 0) & (0, -1/2) & (-1/2, 0) are 4 discrete points
on which both the r = 1/2 circle and the square s² = 1/2 reside.

3rd doorman wrote:Under the diagram we get D=phi, but for me D is a point, it would be on the circle yes, but we don't know where that point is yet, and a point cannot have a length, and neither ad nor dc are 2 or phi. What am I missing?

Both AD and CD are (√5 + 1)/2 = Φ whereas AC is 2Φ.

Ok wow! I think I overlooked your reply and was editing my previous post, sorry, I'll just make a new post from now on. Also, I've had to look up transendental numbers, kepler triangles, even reciprocal, so my math is playing catch up but with that in mind I'll try and honor your efforts and put forth some effort of my own on that catch up!

Thanks for your response so far!

"Note the difference between the "approximated" π predicting a circumference of ~3141.6mm & the "precise" π predicting a circumference of ~3144.6mm being a matter of a full 3mm."

Ok, looking at my math, I for sure mixed up the decimal point. But I think my point still stands. 3.14159 is in meters so let me use 1.000 to stand for 1 meter.
Let me demonstrate two calculations, and double check them with your own calc.
1.00095985 x old pi = a number close to, just under new pi is my thesis.
or as I calculate now
1.00095985 x 3.14159 = 3.144605455 which is not your new pi of
= 3.14460551xxx but is close
1.002 x 3.14159 = 3.14787318

So mismeasuring all diameters by 1mm seems to be significant.
2mm overshoots, and 3mm overshoots even more. I went to the trouble because I suspect measuring error, not as much as 3mm in every diameter though.

1/10mm is not enough, you are correct. But I only mentioned the misalignment at the center, there are other "visual" phenomenon I witnessed in the video, and limits to what his setup can display, it may be useful to estimate the actual error. I certainly have some suggestions to improve its "visual" presentation with the goal being to demonstrate a lack of measurement error.

Forgive me but none of this impinges on your phi work. My comments there should be considered as how I experience "disclarity" in my ability as I try to follow along.
I'm out of time so I'll have to continue again soon.

So I reviewed the video. I'm trying to believe no measurement error has taken place, but my doubt creeps in. The goal of the presentation is to remove the doubts of the audience, but I guess I am holding out.

The first video is an ad. Not a problem per se, but the audience is going to see its an ad, and that time will not contribute to holding the viewer. Many people like myself will skip it, I decided to watch most of it, I don't see why it was included.

I have made circles before, my technique was make a hole that is snug around a screw, let that be the center or point of rotation and feed it through the saw once the screw is secure in a baseplate. His techinque with the sweep of the compass is similar. I made a decent aluminum circle on a bandsaw. Its edge was still rough, and I took the time to also sand it, while still on the rotator, and ended getting a very uniform cylinder, because the circle has thickness. I took care to make a a right angle at the edge, and to make the edge consistent, but it was only 1/8 inch so there were limits. The way I tested this was while on the rotator, I affixed a pencil in a vise, so that it could draw a circle just inside the edge. I then measured with my eye as it was rotated quickly and saw that the distance between my pencil mark and the edge did not wiggle and waver in size.

I've also had circles, and then had to find the center. I used the compass techiniqe and an engineers square that had a center finder attatchment. So anyway, how does he find his center, how does he find his diameter, it is not stated, but if his diameter is off, his center is off.

The beam compass sweeps. Obviously we have to trust him that his compass stays at center and has no slop, meaning he tightens down its screws so the needle stays in one place and cannot change its angle. Lets assume this is true, but admit he doesn't give us that "visually". We don't get to monitor the center of the compass and it can roll right out and then back in to a hole made by its pointy tip. I've seen it happen when a force is applied laterally to the compass needle.

Now to the video. The compass sweep starts at 3:12. Look closely at the edge of the wood. Does that look like a polished aluminum edge, for sure no. I see variation on the top edge. The top is tan, the side of the cylinder is whiter, Look closely! Zoom in, I see portrusions from the white contrasting with the carpet, I see white on the wrong side of the compass! Indeed its tip seems to point right at the edge, but this edge hasn't even been sanded it seems, it appears to be a raw routed cylinder side. I want to certify that the edge is consistent but I'm not even aligned correctly and so it appears the cylinder side is maybe not consistent with the edge. Having only one camera eye, and parallax complicated the entire viewing experience, his hand held setup has limitations.

At 3:32 the compass needle appears inside the edge for sure more than .2mm. The compass sweep runs till 4:21. Watch it again and again, notice how he moves too quick, notice how the white outer edge has little portrusions, notice how the compass tip at times seems in the tan area, and sometimes points into the white area. He actually says its indicating 500mm when the video is to the best of my interpretation, not showing 500mm, but over 500mm in the realm of .5mm or more.

At this point I've lost faith in my experimenter. There are errors of around .5 mm in that radius says the compass, there are portusions of around .5 mm from the cylinder side, all leading to a larger circufrence when a tape is laid over that surface. Every portrusion makes a kind of polygonal estimating error just like archimedies but from the outside. Everywhere that compass doesn't just align with the edge, but where the side ends up being larger in functional diameter under the tape brings us closer to my diameter of 1.0009596 meters. Could it average out to .5 per radi? No I think.

Lastly, the act of wrapping a metal tape around this cylinder edge is where the real mystery begins. Miles has said wrapping a string around a cylinder is fine, but when you then straighten out the string, a fundamental change has taken place. I don't know! Its here my theoretical understanding gets foggy. But here is one thing I can say, strings stretch, and when wrapped around a cylinder it lays on its outside surface, but length is measured using an axis through its cross section, I can't certify there is no archimedies polygonal error creeping in between those two states of the string, and so I remain fascinated with all this. A metal tape stretches way less, but still has an outer edge and a apparent tension axis that is passing through the cross section of the material. The circumfence of this tension axis is fundamentally larger in radius by 1/2 the thickness of the tape, so we could have been shown the thickness of the tape in one location at least, several would be better, running it through a rolling micrometer would have been nice.

He used the numbers facing inward toward the cylinder edge. fine. He then obscures the reading of the tick marks, not so fine. This experiment involves me seeing the zero mark next to another tick mark, but we don't get that. He could have sacrificed his unsanded raw circle and cut a notch out so we could see. I would be proud to have a table of birch with such an experimental notch cutout, it only has to be about a 3mm deep wedge shape.

Another point of faith, that the tape traces a plane parallel with the circle top, that the tape doesn't sag anywhere. We are not given this assurance. How does he prevent sag? It for sure would occur even with a metal tape but the metal tape would be resistant. Still, it MUST be parallel, I don't get to see how parallel, and thus doubt creeps in.
Finally, he could have taken another measurement with the numbers facing out, and with a notch reading hole we could have seen the calibration between the two sides when its convex or concave. This would show that only one side was calibrated for wrapping type measurements.

All this leaves me with doubts I cannot resolve. If there is a total error that approaches .5mm per radius, we could get a completely distinct value of pi here. Check out 5:10. That circle edge could be portruding past the 1000mm tick mark by as much as 2/10 of a mm. Putting all theoretical work on Phi aside, this experimenter has not earned my faith. I have to assume error may be creeping in where I cannot even think it would.

You yourself mention we should spend large sum of money to measure a circle! Just look at the visible portrusions on that cylinder edge, I could have improved this experiment with sandpaper and 10 minutes! Your theoretical work and his deserve better, but obviously making such a video is time consuming expensive and presents real limitations, not to be mean but we have to overcome such limitations if its to be useful.

Man, your drawings and diagrams are awesome Thanks. Having read through them they are clearer than the paper. keplers triangles somehow eluded me so better late than never to hear about them! Also fold overs, circle resizings, I was failing to follow along with your steps. The more I understand it the more I want to see it routed in birch for a front door to my house, if only there was a machine that could do it....

kidding aside, I still misunderstand all the implications. The unit circle just seems like magic pretty much, so a 1 meter table is iconic. The black measuring tape is great, I love his drawing, with maybe the same or a different proof on it. But his center is mysterious, If its parallax, monocularity, or the center is just not a defined shape on a defined grid, at least not in the video. Well shucks. but I very much want to believe he is being careful and rigorous, this is the second pi challange I can't get around. Does it really not matter? I can do this experiment at home, just not at one meter, and my measuring tape is different.

Foam Board Circle 2 cut by NT Rotary Circle Cutter
its the number 6 video at the link above ending in /pi-measurement
3:22 we get an edge to ruler shot, and at 3:42 I see a side to center measurement, but I cannot see the center in an unambiguous way, and at the table side the edge was aligned with the left side of the tick mark? So read this one also from the left side of the tick mark? 500.5mm

Knowing that I don't know the math to estimate error in all these situations, but have a decent eye and experience making and measuring, Is driving me up a wall. I can't afford an NT rotary, circle cutter! I would have to make a beam compass out of my AXE!!!. And the weight of the geometrical analysis makes it even harder to stay impartial, If its true, or true enough for me, or a challenge I never end up understanding it still is hard to put down. Kepler right triangles and the unit circle! Cooool. AND the giza pyramidl, I'm charged up.

.
3rd doorman, I'm surprised at your apparent "expertise", and your critique of Mr. Lear's one meter diameter circle construction sounds completely valid. I'm delighted you seem as amazed with the phi-based origin as I am.
If you cannot build a 1m diameter birch circle, maybe you can build four r=1/2 m quarterbirch circles?!  

jfmeyer, Of course mainstream science needs to recognize the charge field; but everyone should be taught your phi-based origin in elementary school, the easiest first step to a better world.    
.

Thanks Airman, for the compliment. I think I already made a mistake somewhere, when I forgot where to put the decimal place. I think my comments were more toward the video, and the methodology presented.

I cannot build anything at the moment.

As far as the paper https://vixra.org/pdf/2010.0100v1.pdf, I mentioned that "real geometric square" is hard to define. I guess I owe it to him to read over his comments before I make further comments on it.

3rd doorman wrote:
I compute that a diameter of 1000.95985x3.14159 is equal to 3144605.455.

"Are you assuming π = 3.14159...? Because I am arguing in reality, it does not.
I argue the π of 3.14159... has a real radius of 0.49952094... and not 1/2, as assumed.
This deficiency reflects the resolution limit of any/all approximation methodology(s) using polygons.
I argue a real radius of 1/2 gives rise to a real circumference 3.1446055... as Harry's measure shows.

The problem with the polygon approach is in the need for it to "approximate" a fixed radius while itself having a variable one.
It can/will never resolve the real radius of 1/2 because the proximity between origin & surface is never such a constant with an n-gon.
Only by beginning & ending directly on the circumference of the circle can one measure it with precision. The paper does this."

I just copy and pasted, forgive me for not formatting it properly.

To jfmeyer. I asserted was that a diameter of 1000.95985 x (old pi approximation) = a number close to new pi.
I think you have to admit it does not discuss polygons or how that approximation was generated.




"As you mentioned, what is important is the measure of the diameter being precisely 1000mm.
A real circle of 1000mm diameter will have a real circumference greater than 3144mm."

Once again you assert new pi. But what I was saying was that it appeared that a measurment error was in effect. You don't address what I am calling an apparent measurement error, and I'm not sure why. Obviously the video is not yours, but what I am saying is that it does not measure precisely in a way that comes through on the video, in fact it seems to be off and I have estimated it to be off by something like .1mm.

"Note the difference between the "approximated" π predicting a circumference of ~3141.6mm & the "precise" π predicting a circumference of ~3144.6mm being a matter of a full 3mm.
A (1/10)mm discrepancy is trivial with respect to such a wide margin as 3mm. All we need to do is measure a circumference greater than 3141.6mm anywhere outside of margin of error(s).
I do not know whether or not he explains his protocol to such fine detail, but his measure suggests he went through reasonable effort to be accurate to within 1mm.
In any event, by beginning & ending directly on the circumference of an r = 1/2 circle, the circumference can be measured as a precise ratio 8 / √(2√5+2) ≈ 3.14460...
...the number 3.14159... is the closest a polygon(s) can ever get which maxes out at the thousandth decimal place."

Yes I noticed that the difference is a bit over 3mm. You are referring to your paper again, but in fact I was talking just about the video.

An error of .1mm on a radius leads to +.62mm to the circum calculation.
An error of .1mm on a diameter leads to +.31mm to the calculation. We might see 3144.9mm instead of the value you see in the video. Using the vernier scale I think it would be quite non-trivial to overlook a diameter or radius mismeasurement of .1mm. Your paper cannot correct for error in the video, the errors in the video will still be there and will result in the video not supporting your paper's conclusion.

I, 3rd doorman wrote
"I run into a terminological problem. On page 4 "the real geometric square" is hard to define so as to follow along."
This is feedback on your paper. It is not clear what sqaure you are referring to. You say its referring to s2. Consider making that clear in your paper.

In your diagram above addressing my question on "the real geometric square" I find further disclarity. You use ssquared and then re use it on another object, give it values of 1 and 1/2, and label a side as just s, yes I understand what is happening, I can keep all the squares sorted. But your LABELLING is bring a barrier to that.

I'm used to using compass and straight edge and I can build a unit square, inscribe a circle, and inscibe a square in that circle using just those tools. Is using just those tools what you mean by "real geometric"?

3rd doorman wrote:
We also get Phi in the corners of an inscribed square, not sure why.

because (√5 + 1)/2 simultaneously describes the entire circumference of the r = 1/2 circle as well as the 4 vertices of the s² = 1/2 square inscribed therein.
Those vertices have a proximity of 1/2 from the origin just as the radius of the circle does. Thus (0, 1/2) & (1/2, 0) & (0, -1/2) & (-1/2, 0) are 4 discrete points
on which both the r = 1/2 circle and the square s² = 1/2 reside.

Your thesis could be true, but I would still object to the phi symbols being there.


3rd doorman wrote:
Under the diagram we get D=phi, but for me D is a point, it would be on the circle yes, but we don't know where that point is yet, and a point cannot have a length, and neither ad nor dc are 2 or phi. What am I missing?

Both AD and CD are (√5 + 1)/2 = Φ whereas AC is 2Φ.

Sorry, you are not answering my question. D is not AD nor CD. I think just floating a D under that representation of phi is confusing. D is a point, D[=phi] makes no sense whatsoever. Go put what you just wrote IN YOUR PAPER, and explain how you arrived at it because I had to figure it out for myself and I am not pleased that I had these D statements around to confuse me. D[=phi] is not true here, and I suspect will never be true here, it should be removed unless your intention is to confuse people.

3rd doorman wrote:I just copy and pasted, forgive me for not formatting it properly.
To jfmeyer. I asserted was that a diameter of 1000.95985 x (old pi approximation) = a number close to new pi.
I think you have to admit it does not discuss polygons or how that approximation was generated.

The same "old pi approximation" method(s) both implicitly & explicitly concerns polygons, as the very same was employed to derive the number 3.14159... in the first place.
By contrast, I am arguing it is possible to precisely measure a curve with 0 need/inclining for "approximation" (thus margin of error) & derive a precise result.
This is the important point the paper makes: "without the need/inclining for approximation".

3rd doorman wrote:Once again you assert new pi. But what I was saying was that it appeared that a measurment error was in effect. You don't address what I am calling an apparent measurement error, and I'm not sure why...

Because it's irrelevant: neither I nor you participated in the measure & the video is merely in support of other findings
contingent on the aforementioned: it is possible to measure a circle without "approximating" it.
Doing so produces the result 8/√(2√5+2) which is not an "approximation" but a precise ratio. This ratio is arrived at
using only the "real" numbers (and their roots) viz. 1, 2, 3, 4, 5... √1, √2, √3, √4, √5... etc. and a single square operation Φ→Φ².
There is nothing else needed to measure a circle, as the square operation produces the very 2π rotation which constructs the r = 1/2 circle.

Even supposing/assuming Harry did make a non-trivial error(s): it doesn't prove anything one way or the other. We need a more accurate measure regardless.

See the following image beginning from the top-left:

From the top-left, 1/16 is equivalent to 1/4².
By removing the square, one is effectively quadrupling the area viz. (1/4)/(1/4²) = 4. This is as (1/16)→(1/4).
Now one may remove another square from 4 via. 1/√4 = 1/2 effectively doubling the area of the quarter.
The powers of phi indicate the entire circumference of the r = 1/2 circle is contained between the squares Φ and Φ².
Note: AD = CD = (√5+1)/2 = Φ.

With the correct value of π, we can now "square the circle":


Here is an obscure video I found online recently which shows the squaring of the circle:
https://www.youtube.com/watch?v=JUoOgqFsFOc

3rd doorman wrote:Yes I noticed that the difference is a bit over 3mm. You are referring to your paper again, but in fact I was talking just about the video.

Harry's video is not the primary piece lending itself to π = 8/√(2√5+2). It supports any/all mathematical derivations absent "approximation".
I already know the tendency for those attached to "transcendental" π to want to conclude the measure is flawed because they don't like the result.
I will simply state this: it is possible to know how not to measure a circle: by "approximating" it. There is precisely 0 (none) need/inclining to do so.

3rd doorman wrote:An error of .1mm on a radius leads to +.62mm to the circum calculation.
An error of .1mm on a diameter  leads to +.31mm to the calculation. We might see 3144.9mm instead of the value you see in the video. Using the vernier scale I think it would be quite non-trivial to overlook a diameter or radius mismeasurement of .1mm. Your paper cannot correct for error in the video, the errors in the video will still be there and will result in the video not supporting your paper's conclusion.

The paper has nothing to do with the video - it is autonomous.

3rd doorman wrote:This is feedback on your paper. It is not clear what sqaure you are referring to. You say its referring to s2. Consider making that clear in your paper.

I always consider making all things as clear as possible, but I only had 8 pages of real estate in the paper.
It was intended to be short & with brevity comes incapacity to address any/all such nuances.
I am nonetheless planning something more large-scale which incorporates the feedback I've received.

3rd doorman wrote:In your diagram above addressing my question on "the real geometric square" I find further disclarity. You use ssquared and then re use it on another object, give it values of 1 and 1/2, and label a side as just s, yes I understand what is happening, I can keep all the squares sorted. But your LABELLING is bring a barrier to that.

You're complaining I used "s" on two completely different squares despite giving each their own area?
The point D confusion I can understand but this is silly nitpicking by comparison.
Next time I will use a little "s" and a big "S" for squares s² = 1/2 and S² = 1 resp.

3rd doorman wrote:I'm used to using compass and straight edge and I can build a unit square, inscribe a circle, and inscibe a square in that circle using just those tools. Is using just those tools what you mean by "real geometric"?

"Real geometric square" means it can be represented geometrically using only the "real" numbers' implied geometries.
For example(s), the square s² = 1/2 is a real geometric square because it has real geometric sides s = 1/√2.
Compass and straight edge can be used to construct "real" geometry because they use the geometric properties of "real" numbers.

3rd doorman wrote:Your thesis could be true, but I would still object to the phi symbols being there.

Not "could be"... is. The entire circumference of the circle is satisfied by (√5+1)/2 if/as performed radially.
This property alone implies the golden ratio can not not be in relation to the circumference of the circle.

3rd doorman wrote:Sorry, you are not answering my question. D is not AD nor CD.

I did answer your question. I told you D is technically AC/2 which invariably reconciles at r = 1/2 radially.
If you simultaneously travel from A to D & C to D with equal start & speed, the two will meet at D after having each travelled Φ.
This means AD = CD = Φ because Φ is precisely what exists between each pair of points, with AC thus being 2Φ or √5+1.

3rd doorman wrote:I think just floating a D under that representation of phi is confusing. D is a point, D[=phi] makes no sense whatsoever.

D is arrived at by way of AC/2 = (√5+1)/2 radially. The "point" D is thus not (only) a point, it is a circumference of a circle.
The radial operation (√5+1)/2 invariably reconciles on the circumference of the r = 1/2 circle which is what D becomes upon a full rotation.
The square operation Φ→Φ² satisfies one full rotation about the origin of coordinates such to produce an additional discrete 2π.

3rd doorman wrote:Go put what you just wrote IN YOUR PAPER, and explain how you arrived at it because I had to figure it out for myself and I am not pleased that I had these D statements around to confuse me. D[=phi] is not true here, and I suspect will never be true here, it should be removed unless your intention is to confuse people.

It depends on how seriously one is looking at it & whether or not one is just looking for something to nit-pick.
The point of ABCD was to show the circumference of the r = 1/2 circle is captured by (√5+1)/2 radially.
Once one has understood this, one can then discard ABCD and focus on D1-4, because they are the most important.
D1-4 defines the "reciprocal lines" s = 1/√2 responsible for allowing us to precisely measure the circumference.
These reciprocal lines form the real geometric square square s² = 1/2 whose area is equal to the radius r = 1/2.

"The same "old pi approximation" method(s) both implicitly & explicitly concerns polygons, as the very same was employed to derive the number 3.14159... in the first place.
By contrast, I am arguing it is possible to precisely measure a curve with 0 need/inclining for "approximation" (thus margin of error) & derive a precise result.
This is the important point the paper makes: "without the need/inclining for approximation".

See, that is what I am calling asserting new pi. My thesis here is: I"m allowed to talk about old pi, and set up a simple product. I don't think it is too ntipicky to anlayze a circumphence of new pi, and divide it by old pi, with my calculator, and write the value down here in the forum for discussion purposes.

Do you challenge my thesis?

3rd doorman wrote:See, that is what I am calling asserting new pi.

But it's not asserting a "new" π, it is finding the π that already exists naturally because there is only one.
If anything, the "approximated" π is the "new" π which was/is arrived at only by a deficient methodology(s).
If the π of 3.14159... is false (as I argue it is), it was/is itself the "new" π that came on-scene by way of human ignorance.

That is: because human ignorance, therefor "new" π of 3.14159... according to their own ignorant approximation methodology.
This new (albeit millennia-old) "approximated" π is a/the common denominator of the history of millennia of human civilization(s).

If π = 4/√Φ then with or without human consideration, π ≠ 3.14159... but measures as the limitation(s) of those who otherwise believe/endorse it.

3rd doorman wrote:My thesis here is: I"m allowed to talk about old pi, and set up a simple product.

Of course you can & we can compare the two. I found the precise ratio(s) relating radius & circumference of a circle thus:

c = 16r/√(2√5+2)
r = c√(2√5+2)/16

If π = 4/√Φ then when we plug in the approximated/deficient π of 3.14159... in/as c, then r = 0.49952094...
This indicates the circumference of such an approximated π of 3.14159... has not a real radius of 1/2 as assumed, but slightly less.
The difference is slight, granted: but non-trivially so.
Catastrophically: r is irrational in the approximated π. It is hitherto assumed to be a rational & discrete 1/2 which is actually false.
This means a π of 3.14159... can not apply to any kinematic systems esp. those involving rotational motion without loss/error.

That involves all physics. The physical universe uses a π of 4/√Φ just as Miles states π = 4 in any/all "kinematic" situations.
All I am doing is equating "in any/all kinematic situations" to √Φ (& in doing so stating the golden root is the kinematic base of the universe).

3rd doorman wrote: I don't think it is too ntipicky to anlayze a circumphence of new pi, and divide it by old pi, with my calculator, and write the value down here in the forum for discussion purposes.

No, nitpicky is complaining two different squares with unique areas used "s" to indicate "side".
I think it is useful to compare the old π to the correct one: it highlights the blunder(s) of humanity.
It shows how "far off" & why. The reason is relating to the "approximated" vs. "precise" radius.
The only way to ensure a radius of 1/2 is to allow it to apply to all 360-degrees.
One simple rotational motion accomplishes this, the same afforded by Φ→Φ².

Do you challenge my thesis?

No, I endorse it. We should compare the two but not as it ultimately relates back to Harry's physical measure, but any/all measure incl. mathematical.
The arithmetic reflects real geometric progression (as the Keppler triangle does) as it applies to a real geometry using algebraic "polynumerals" such as (√5+1)/2.

Mathematicians have "defined" π as c/d wherein d = 2r. I argue this definition (catastrophically) discriminates against 2r as a right angle such that 8r/c instead of c/2r.
8r/c is found to be the correction ratio to which √Φ as √(2√5+2)/2 applies. This application is impossible with the "definition" being c/2r = c/d.
So my first contention with π = c/d = 3.14159... is the definition, not the actual number. The imprecise number is secondary,
it just happens to be a natural consequence of ignorantly assuming c/d wherein d = 2r. It will always be limited to/by that.
My further contention is the notion that π is somehow "transcendental". It is not, for π as 4/√Φ is a root of x⁴ + 16x² - 256.
Note the value of x such to produce 256 and -256 are 4 and 4i respectively. These are the "real" and "imaginary" elements.
The number 3.14159... is transcendental, yes, because it doesn't have a real, rational radius of 1/2 like 4/√Φ ≈ 3.1446... does.

So again: Miles is "more correct" than mainstream science incl. any/all endorsing of a π of 3.14159... in any/all applied maths/physics.
The physical universe is a universe of motion, thus a "kinematic" π must/does apply. So I'm actually measuring two ignorance(s) here:
mathematicians who erroneously "approximate" π to 3.14159... and Miles not having solved for the "kinematic" base of √Φ.

The deeper problem under all of this is the thoroughly unscientific "belief"-based ideologies that absolutely hate science.
These are the same ideologies behind "Project Chaos" dismantling anything/everything they hate incl. science/academia.
They hate other things too, such as any/all people/nations who do not worship the particular god or idols they worship.
All of this global chaos reduces back into one particular ideological division which is as old as the π "approximation" problem itself.

Such deeper problems needing to be addressed simply can not be so long as Western science fails to challenge such basic underlying assumptions.
The equality 1 = Φ(π/4)² has the capacity to predict precisely what we see as the ontological circumstances facing humanity not only now, but for millennia.
There is an immense body of knowledge to be discovered behind such an equality, not the least of which is the underlying universal principle of reciprocity.
One sole implication of such an equality is itself immense: the equality clarifies the nature of the relation between "space" and "time" as being naught but
multiplicative reciprocal aspects of motion viz. s/t x t/s = 1 = Φ(π/4)^1/r wherein r = 1/2 and is a real radius of a real circle.

All geometry incl. kinematic would then be constructed upon such an equality wherein the real radius of 1/2 scales to/from the real radius of a photon.
So all Miles needs to do is apply this equality to light & he can use the radius of the photon as a/the datum upon which he constructs his charge field.
After all: this radius of 1/2 is the reciprocal "2" in counter-space (ie. the domain after travelling through the origin of coordinates).
That is: if one approaches an origin as a line & travels through the origin, their motion becomes a curve in counter-space.

What √(2√5+2)/2 is to line, the reciprocal 2/√(2√5+2) is to the corresponding curve.
It thus can be said from the "root" of Φ comes π & they are one in/at 1 = Φ(π/4)².

Φ and π are thus the "Adam & Eve" of mathematics, so-to-speak.
What the "root" of Φ is to the "side" of Adam, π is to eve.
1/√Φ = π/4 is the "marriage" of them as one.

These equalities will allow the unification of GR and (so-called) QM with both presently being as irreconcilable as the radii of 0.49952094... and 1/2 are.
The "link" between the two requires a correct π & the two are already naturally in unison by way of the same. The 95% of the universe scientists can't account for
is nothing but a measure of their own unconsciousness. That number will go down (and fast) as human beings become conscious of the underlying reciprocity principle.
The entire physical universe rests on the principle of reciprocity. If not reciprocity, then no physical universe & the same is implied by the very presence of light.

I don't have a lot of free time for the last few years, like I used to before that, so I haven't been able to keep up with this forum or with Miles' science site. But I happened to notice this discussion thread just now and it's kind of interesting. I see it's been going on steadily for over a month now.

Lucky that Airman has interest and takes time to get involved in such discussions. Otherwise, would this thread have gone on beyond one or two posts?

The things I find interesting in this thread so far are: Harry Lear's measurement of a 1 meter circle (I forget if it was radius or diameter); the reciprocal relationship between space and time; J.F. Meyer's name; and his/her apparently knowing more than Miles about this subject relating to Miles' finding that pi = 4 in kinematics.

Has Miles ever mentioned Lear's measurement? I don't think I've heard of it before.

I've heard of the reciprocal relationship between space and time before from books by Dewey P Larsen in the 90s. He said something like a photon is a vibration, a projection of circular motion on a plane surface at a right angle to the plane of the circular motion. He had a lot of interesting info, but I think most of it was wrong. I think I mentioned some of his ideas to Miles about ten years ago, esp. s/t. So J.F., where did you get your idea for s/t from?

J.F., are you Semitic? I recall that Miles has said a few times on his history site that Meyer is a Jewish surname. He seems to suspect that a lot of people with Jewish surnames are involved in major conspiracy. If you seem to know more than Miles on this math topic, I suspect that he might suspect you of being an agent of the conspiracy intent on diverting people from the truth. Jared M joined this forum a few years ago and soon told us about Miles' history site. His findings there interest me a lot and I find most them to be very plausible or probable, but I think Jewish surnames aren't good evidence of malevolent conspiracy. I know several Meyer's in my area near St Louis and I think they're German, not Jewish. I think it's a German surname.

Privately, I shared with him the surnames in my ancestry and he said some of them are conspiracy names, but he admitted there are some in his family tree too. My Grandma who was a child when Woodrow Wilson was president told me that we're related to him and all of our relatives who are related to him voted Democratic for him, even though they were normally Republican. I don't know our exact relationship, but I know there is a Wilson in our family tree who apparently was his first cousin, but I don't know of evidence of that.

I didn't mention that so far on the CuttingThroughTheFog forum that Jared introduced us to, but last year or so the forum owner, Josh, got suspicious of me and said he didn't appreciate my contributions to the forum, so I left, but I came back recently, because I wanted to discuss the Covid BS. But Jared accused me of being a conspiracy agent and some other person there said some of my posts there didn't sound like the same person writing each one. I think some of them are paranoid. But, as long as I don't get censored too much, I want to keep participating, because they come up with a lot of what I think is very important info. And I want to share my findings as well. Some of the people there don't like to hear anyone say Miles is wrong about anything. They're like a cult that defends their guru. Hopefully, they'll outgrow such naivete'. PS, I recognize 3rd Doorman's username here from that forum. Do you think I'm an agent or a normie?

Has anyone here told Miles about the info in this thread? It looks to me like a lot of the info would be worth posting in a paper on his science site.

I hope readers here don't find much of this post to be too off-topic.

LloydK wrote:I don't have a lot of free time for the last few years, like I used to before that, so I haven't been able to keep up with this forum or with Miles' science site. But I happened to notice this discussion thread just now and it's kind of interesting. I see it's been going on steadily for over a month now.

Lucky that Airman has interest and takes time to get involved in such discussions. Otherwise, would this thread have gone on beyond one or two posts?

Hello Lloyd. Indeed thanks to both Airman & 3rd doorman for engaging. Your own comments are also appreciated.

LloydK wrote:The things I find interesting in this thread so far are: Harry Lear's measurement of a 1 meter circle (I forget if it was radius or diameter); the reciprocal relationship between space and time; J.F. Meyer's name; and his/her apparently knowing more than Miles about this subject relating to Miles' finding that pi = 4 in kinematics.

Has Miles ever mentioned Lear's measurement? I don't think I've heard of it before.

I've heard of the reciprocal relationship between space and time before from books by Dewey P Larsen in the 90s. He said something like a photon is a vibration, a projection of circular motion on a plane surface at a right angle to the plane of the circular motion. He had a lot of interesting info, but I think most of it was wrong. I think I mentioned some of his ideas to Miles about ten years ago, esp. s/t. So J.F., where did you get your idea for s/t from?

It was Dewey B. Larson who first postulated space and time as being multiplicative reciprocal aspects of motion & in this, he was/is correct.
I did spend much time analyzing Larson's work (as by trade I am an analyst) & found his physical theory to be superior to General Relativity.
That is not to say it is without problems, like General Relativity, but it has much less catastrophic problems & explains much more.
The correct measure of π confirms the underlying reciprocity principle Larson postulated. He already derived it as a natural consequence by means of induction.

We can now know why: √Φ = √(2√5+2)/2 is subject to inversion via. the reciprocal of √2 viz. 1/√2 in each of four quadrants such to become its multiplicative reciprocal 2/√(2√5+2) = π/4.
Reciprocity is thus the fulcrum existing between a speed- or velocity-based motion s/t and corresponding energy constituency t/s whose product is constantly normalized to 1 (ie. the constancy of light).

Larson also postulated only one universal constant: unity (at s/t = 1).
In April of 2020, e = MC² was solved for as 16 = Φπ² implying unity at 1 = Φπ²/16 = Φ(π/4)².
This equality can only be understood/appreciated if conscious of the π "approximation" problem otherwise concealing it.
Predictably: the π "blunder of millennia" as I call it, will ongoing be underlying any/all barriers to any/all possible GUFTs.
The incorrect π will always prevent any/all unification. This is simply a natural consequence of having the wrong π.

LloydK wrote:J.F., are you Semitic? I recall that Miles has said a few times on his history site that Meyer is a Jewish surname. He seems to suspect that a lot of people with Jewish surnames are involved in major conspiracy. If you seem to know more than Miles on this math topic, I suspect that he might suspect you of being an agent of the conspiracy intent on diverting people from the truth. Jared M joined this forum a few years ago and soon told us about Miles' history site. His findings there interest me a lot and I find most them to be very plausible or probable, but I think Jewish surnames aren't good evidence of malevolent conspiracy. I know several Meyer's in my area near St Louis and I think they're German, not Jewish. I think it's a German surname.

No, I am not Semitic & Meyer is a pseudonym. It is a German name, as you intuit, not a Jewish one. I was born into a Catholic environment but no longer believe in Catholicism.

I am aware of Miles' "Jew" problem. Unfortunately, Miles doesn't actually know what a real "Jew" even is.
If you asked him to explicitly define a "Jew" he would presently give you the wrong answer
because he himself falls for the "it's the Jews!" sentiment (which is really 1400-year-old Islamic propaganda).
He calls people "Jews" who haven't even picked up & read a Torah in their entire lives, let alone worship a god.

What Miles doesn't see is the real Jews who are hiding behind the Torah Jews & have been for 1400 years.
I don't blame him: hardly anyone on this planet sees the real Jew hiding behind the scapegoat Torah Jews. That's how the deception works.
The Torah Jews are merely the state-sanctioned scapegoat of the real Semitic "Jews" who worship a single book (in Arabic, not Hebrew).

Not even Adolph Hitler knew who the real "Jews" were - his ignorance of the same not only costed him the war, but his own life
(when he realized who the real "Jews" were, he shot himself. At that time, he was allied with them because they were deceiving him the entire time).
Once the real "Jews" took control via. Adolph Hitler, they manufactured their genocide machines & everyone who was an "unbeliever" was designated a "Jew" & sent to camps.

So we have a situation wherein real Jews can't account for their own book-worshipping blood-spilling "Jew" nature & instead project the very same onto the rest of the world.

Miles is thus more deceived by the real "Jews" than even he knows.
Unfortunately, so are his readers who entertain his geopolitical views.
His geopolitical commentary does more to protect the real "spooks" than not because he is pointing his finger in the wrong direction, giving the real "Jews" cover.
Miles doesn't realize he is doing this, but that is precisely the quality the real Jews rely on: for one to be unconscious they are inadvertently serving the "cause" of their god.

LloydK wrote:Privately, I shared with him the surnames in my ancestry and he said some of them are conspiracy names, but he admitted there are some in his family tree too. My Grandma who was a child when Woodrow Wilson was president told me that we're related to him and all of our relatives who are related to him voted Democratic for him, even though they were normally Republican. I don't know our exact relationship, but I know there is a Wilson in our family tree who apparently was his first cousin, but I don't know of evidence of that.

Unfortunately, Miles' absurd conspiracies re: geopolitics & races & families has done more harm to many others than not.
All of the families Miles is complaining about have owners. His "Jewish" families are just slaves (ie. "goyim") of the real Jew owners.
The real Jews are not holding a Torah in their hands. That's the 1400-year-old deception one has to see past before anything else.

LloydK wrote:I didn't mention that so far on the CuttingThroughTheFog forum that Jared introduced us to, but last year or so the forum owner, Josh, got suspicious of me and said he didn't appreciate my contributions to the forum, so I left, but I came back recently, because I wanted to discuss the Covid BS. But Jared accused me of being a conspiracy agent and some other person there said some of my posts there didn't sound like the same person writing each one. I think some of them are paranoid. But, as long as I don't get censored too much, I want to keep participating, because they come up with a lot of what I think is very important info. And I want to share my findings as well. Some of the people there don't like to hear anyone say Miles is wrong about anything. They're like a cult that defends their guru. Hopefully, they'll outgrow such naivete'. PS, I recognize 3rd Doorman's username here from that forum. Do you think I'm an agent or a normie?

I don't know what you or others perceive to be "agents" but Project Chaos is conducted by book-worshippers trying to globally subdue "unbelieving" nations & people.
They hate science esp. if it undermines/falsifies their "belief" in their single book and ideal man-idol prophet who they strive to emulate.
They pursue an "us vs. them" viz. "believer vs. unbeliever" war & have been since its inception.

So unless you're doing that, then no.

LloydK wrote:Has anyone here told Miles about the info in this thread? It looks to me like a lot of the info would be worth posting in a paper on his science site.

I hope readers here don't find much of this post to be too off-topic.

The incorrect value of π directly underlies any/all such global conflicts. The problems are not unrelated however we should not go too much deeper into geopolitics here.
I know who the real Jews are and the various strategies they employ to silence/suppress/censor/harass/abuse/accuse/slander. I'll draw example should the gestapo arrive.

So my thesis, that I can divide new pi by old pi, with my calculator, and post the result here in the foum is not being challenged.

Notice I don't define new pi or old pi. Therefore my thesis still stands and your assertion about what is old and what is new is completely irrelevant.

Right?

@Doorman, don't you agree with the OP that Harry Lear's measurement is closest to the correct value of pi?

@EFMeyer, what happened 1400 years ago? I guess I should discuss that privately, since it's probably off-topic here.

3rd doorman wrote:So my thesis, that I can divide new pi by old pi, with my calculator, and post the result here in the foum is not being challenged.

No - there is no reason why it would be.

I would only challenge which of the two is "old" and which is "new" (let alone which is "false" and which is "true").

3rd doorman wrote:Notice I don't define new pi or old pi.

If you leave π undefined, you must then yourself measure a circle from start to finish. I had to & did.
If you come up with 3.14159... I would be able to highlight at what point the deficiency enters the measure.

3rd doorman wrote:Therefore my thesis still stands and your assertion about what is old and what is new is completely irrelevant.

Right?

No.

My assertion about what is old and what is new is completely relevant.

If a π of 3.14159... emerged only recently in place of a preexisting π of 4/√Φ (as the Giza pyramid implies), the former is "new" whereas the latter is "old".
It may be helpful to distinguish the two π's as "approximated" and "precise" given I argue 4/√Φ is "precise" whereas 3.14159... is merely an "approximation".
You can not express the latter as a ratio of integers and/or their roots as you can with the former 8/√(2√5+2) = √(8√5-8 ).

If you wish to argue a π of 4/√Φ is "imprecise" that would be the negation of my own argument (& your victory if proven)
as I know (ie. argue) a π of 3.14159... is just that: "imprecise" & is merely "approximating" what is really 4/√Φ ≈ 3.1446...

LloydK wrote:@Doorman, don't you agree with the OP that Harry Lear's measurement is closest to the correct value of pi?

I know the question is not addressed to me, but I'll comment here for those with preexisting emotional/psychological attachments to a "transcendental" "approximated" π of 3.14159...
The temptation will be to only see what they want to be true (or in this case, false). It is a problem between what is imaginary & what is real (the "real" element always being 1/2).
In this case, one is exhaustively attempting to introduce/assume error(s) in the physical measurement itself such to completely invalidate it (despite it not invalidating the geometry/arithmetic predicting it).

LloydK wrote:@EFMeyer, what happened 1400 years ago? I guess I should discuss that privately, since it's probably off-topic here.

Pm - long story short, "believer vs. unbeliever" became the basis of a global geopolitical state waging perpetual war until there are no more "unbelievers".

right, so whetherit is called new or old pi is relevant. Just not to my thesis. So once again, I'm not even allowed to talk about it unless you define the terms, but expressly, I did not define the terms so you are just changing the subject to "global geopolitical state waging perpetual war" which of course we know makes the value of pi a little this way and little that way, depending on if a bomb is exploding in the middle of your measurement, a bomb of chinese or russian manufacture WOULD be relevant to measurement of pi done to .5 mm per radius.

So we agree on that at least.

LLoyd, no, the lear measurement is pathetic. REALLY. would you like the number and video where he shows us he cannot use a spirit level? I'd like to perform his entire experiment over again, but I certainly cannot afford a multi hundred dollar certifed tape. I DO know how to measure the tension applied to it as different "length" measurements are taken.

At this point any string or metal tape is still a hypothetical object down at the molecular level. I imagine crooked lines, edges of polygons, trillions of them, forming what is assumed or averaged out to be a "line" but within that line are all these spring loaded angles of connection between atoms. The metal tape DOES stretch, just not alot, but additionally it resists clean contact with a routed wood surface. We need an accuracy of .5mm per radius roughly, and 1mm per diameter. Its such a simple calculation that even jfmeyer should be able to discuss. Alas, nits are still nits even when unpicked. right? Why am I picking over this proof anyway?

This image finally catches it for me.
https://i.servimg.com/u/f63/20/34/92/80/mmpi11.jpg
somewhere in "reciprocal" the word and that arrow, the length of a line is definitively in a known ratio to a length of a curve we call the circle, in this case pi/4. Clarification of that little part of the algebraic, geometric, part of the proof could stand to be clarified way further than all of the other constituent parts of the proof.

3rd doorman wrote:right, so whetherit  is called new or old pi is relevant. Just not to my thesis. So once again, I'm not even allowed to talk about it unless you define the terms, but expressly, I did not define the terms so you are just changing the subject to "global geopolitical state waging perpetual war" which of course we know makes the value of pi a little this way and little that way, depending on if a bomb is exploding in the middle of your measurement, a bomb of chinese or russian manufacture WOULD be relevant to measurement of pi done to .5 mm per radius.

I'm not defining any terms & like you I do not "define" π, I'm simply stating if you choose to leave π undefined (as I have & recommend) you have to produce something upon which you base the number 3.14159...
If you don't, you're practically pulling that number out of thin air & it is not based in/on anything at all. Your "thesis" therefor isn't a "thesis" unless/until it is grounded in something (if even theoretical).

If you do not assume the "definition" c/d (wherein d = 2r), that is fine. But you still have to have something tangible to reference implying or indicating π = 3.14159... esp. if it is being compared with another value.
If this were a formal debate, you are essentially attempting to remove any/all substance from your own position such that a true comparison can not be made (which is the opposite of what your "thesis" means to accomplish).

If you want a 1:1 comparison, as I do, you must produce something that indicates and/or implies "...therefor 3.14159..."
and/or simply answer the question "upon what do you base the assertion π = 3.14159...?"

This is a fair question because I can/will answer the same regarding a π = 4/√Φ & the comparison can then be made.

3rd doorman wrote:LLoyd, no, the lear measurement is pathetic. REALLY. would you like the number and video where he shows us he cannot use a spirit level? I'd like to perform his entire experiment over again, but I certainly cannot afford a multi hundred dollar certifed tape. I DO know how to measure the tension applied to it as different "length" measurements are taken.

I think you're projecting a "pathetic" reaction/attitude onto Lear. You're accusing him of so much & now slandering him despite the work he put into the measure (which you didn't & admit you can't/won't).

I do not need the video to argue π = 4/√Φ, it just corroborates. It is predictable those who are averse to the result will take it out on Lear and/or his measure.

3rd doorman wrote:At this point any string or metal tape is still a hypothetical object down at the molecular level.

They are real objects, not hypothetical objects. They have real boundaries beyond which their constituency(s) apply not.

3rd doorman wrote:I imagine crooked lines, edges of polygons, trillions of them, forming what is assumed or averaged out to be a "line" but within that line are all these spring loaded angles of connection between atoms.

That is absurd. What you're describing reflects the polygon "approximation" method rather than a real physical measure.
It's like you're trying to pin the problems associated with the "approximation" method(s) to the real, physical measure instead.
I can as easily say "when I imagine the polygon approximation methods, I imagine crooked lines, edges of polygons forming what is assumed or averaged out to imply a circumference..." etc. and it applies.

3rd doorman wrote:The metal tape DOES stretch, just not alot, but additionally it resists clean contact with a routed wood surface. We need an accuracy of .5mm per radius roughly, and 1mm per diameter. Its such a simple calculation that even jfmeyer should be able to discuss. Alas, nits are still nits even when unpicked. right? Why am I picking over this proof anyway?

I already made it & already discussed it. I already suggested we need a more accurate measure & even suggested the Riemann Hypothesis prize be used to fund it.
I know the equality 1 = Φ(π/4)^1/r wherein r = 1/2 is the "real element" for being the real radius of a real circle.

The Riemann Hypothesis problem only exists because the Zeta function assumes the incorrect value of π which has a "real element" of 0.49952094... hence the non-trivial ζ(s) = 0 has not been found.
Or in other words: the problem exists because humanity has hitherto not known how to properly measure a circle. That's the lesson waiting behind the resolution of the Riemann Hypothesis.

So the Riemann Hypothesis problem and the π problem are the same problem.
Because incorrect π, therefor RH problem. If correct π, RH = true (by necessity)
as implied by the solution to unity above: it necessarily involves the golden ratio.

3rd doorman wrote:This image finally catches it for me.
https://i.servimg.com/u/f63/20/34/92/80/mmpi11.jpg
somewhere in "reciprocal" the word and that arrow, the length of a line is definitively in a known ratio to a length of a curve we call the circle, in this case pi/4. Clarification of that little part of the algebraic, geometric, part of the proof could stand to be clarified way further than all of the other constituent parts of the proof.

You are correct about this: it could be clarified further & will be. However, not in a paper or still image(s). The reason is it involves motion.

What you said is definitely true: the length of a line is definitely in a known (or knowable) ratio to a length of a corresponding curve c/4.
The problem is the "line" is actually on a 3rd z axis & can not even be seen in 2D geometry. A z dimension would be a height off the page.

For example, if you placed the base (of length 1) of a Keppler 1/√Φ/Φ triangle along the diameter of the r = 1/2 circle
wherein x = -1/2 and x = 1/2 are the ends of the base, the 3rd z axis occupies the same point(s) as dimension z (-1/2, 0, √Φ) and (1/2, 0, √Φ).
One has to imagine the z axis as in a 3rd dimension precisely √Φ above and/or below each of the 4 axial points.

From these 4 points the magnitude associated with √Φ travels through the origin via. r√(4Φ) and becomes 1/r√(4Φ) = 1/√Φ per c/4.
So what line is to √Φ, curve is to the reciprocal 1/√Φ such that line and curve are thus reciprocally related (as space and time are).

recalling √5+1/2 = Φ is used to locate the r = 1/2 circle circumference & is now contained in/as the hypotenuse over a base of 1.

.

I hope you don't mind, its just an image, along with the ipycanvas python code that created it, my first jupyter notebook "project". I also posted the image and code in the Periodic Table/jupyter notebook thread.

I was happy to see your last image included the z axis. Unfortunately, ipycanvas is limited in that it can only draw images and does not support 3d plotting.

Please let me know if I need to make any changes or corrections.

Code:


# Draw a phi-based origin

from ipycanvas import Canvas
from math import pi, sqrt

# The plot is square, with extra margin on the right for dimensions.
isquare = 400  # scaling plot to the desired canvas size
center = isquare/2
half = isquare/10 # sized slightly greater than 1+sqrt(5)/2
unit = isquare/5 # the scalar between 1 and the canvas sq's side length
pradius = 0.02*unit  # used for dimensional points
bradius = (sqrt(5)/2)*unit # r=sqrt(5)/2  circle
cradius = (1/2)*(sqrt(5)+2)*unit # r=(sqrt(5)/2)+1  circle

pwidth = isquare+1.6*unit
canvas = Canvas(width=pwidth, height=isquare)

# Grid s = 4.6, with lines every 0.1
canvas.stroke_style = 'gray'
#canvas.set_line_dash  # not used
grid = 4.6
i = 0
while i <= grid:
        canvas.stroke_line(center + (i - grid/2)*unit, center-grid/2*unit, center + (i - 2.3)*unit, center+grid/2*unit)
        canvas.stroke_line(center - grid/2*unit, center-(i - grid/2)*unit, center + grid/2*unit, center-(i - grid/2)*unit)
        i += 0.1

# Clear the grid from the unit square area
canvas.fill_style = 'white'
canvas.fill_rect(center - half, center - half, unit, unit)   

# r=1/2 circle
canvas.fill_style = 'yellow'
canvas.fill_circle(center, center, half)

# Axes
canvas.stroke_style = 'green'
canvas.stroke_line(center-cradius, center, center+cradius, center)
canvas.stroke_line(center, center-cradius, center, center+cradius)

# Remove the yellow from the r=1/2 circle from within the s=1/sqrt(2) square
canvas.fill_style = 'white'
canvas.begin_path()
canvas.move_to(center, center + half)
canvas.line_to(center + half, center)
canvas.line_to(center, center - half)
canvas.line_to(center - half, center)
canvas.fill()

# Unit square
canvas.stroke_style = 'red'
canvas.move_to(center, center + half)
canvas.stroke_line(center - half, center + half, center + half, center + half)
canvas.stroke_line(center + half, center + half, center + half, center - half)
canvas.stroke_line(center + half, center - half, center - half, center - half)
canvas.stroke_line(center - half, center - half, center - half, center + half)
#canvas.stroke_rects(center, center, 2*unit, unit)
# The Last line is no good. The stroke_rects command kept bombing - exceeding the
# Jupyter tab memory. No rectangles - must draw each line separately.

# Draw r=1/2, r=sqrt(5)/2 and r=(sqrt(5)/2)+1 circles
canvas.stroke_style = 'blue'
canvas.stroke_circle(center, center, half) # r=1/2 circle
canvas.stroke_style = 'black'
canvas.stroke_circle(center, center, bradius)  # r=sqrt(5)/2  circle
canvas.stroke_circle(center, center, cradius)  # r=(sqrt(5)/2)+1  circle

# 1/sqrt(0.5) square, D1, D2, D3, D4
canvas.stroke_style = 'black'
canvas.stroke_line(center, center - half, center + half, center)
canvas.stroke_line(center + half, center, center, center + half)
canvas.stroke_line(center, center + half, center - half, center)
canvas.stroke_line(center - half, center, center, center - half)

# Horiz 2x1 rectangles (left and right halves) with sqrt(5) diagonals
canvas.stroke_style = 'black'
canvas.stroke_line(center - half, center - half, center - unit, center - half)
canvas.stroke_line(center - unit, center - half, center - unit, center + half)
canvas.stroke_line(center - unit, center + half, center - half, center + half)
canvas.stroke_line(center + half, center - half, center + unit, center - half)
canvas.stroke_line(center + unit, center - half, center + unit, center + half)
canvas.stroke_line(center + unit, center + half, center + half, center + half)
canvas.stroke_line(center - unit, center - half, center + unit, center + half)
canvas.stroke_line(center - unit, center + half, center + unit, center - half)

# Vert 2x1 rectangles (Top and bottom halves) with sqrt(5) diagonals
canvas.stroke_line(center - half, center - half, center - half, center - unit)
canvas.stroke_line(center - half, center - unit, center + half, center - unit)
canvas.stroke_line(center + half, center - unit, center + half, center - half)
canvas.stroke_line(center - half, center + half, center - half, center + unit)
canvas.stroke_line(center - half, center + unit, center + half, center + unit)
canvas.stroke_line(center + half, center + unit, center + half, center + half)
canvas.stroke_line(center - half, center - unit, center + half, center + unit)
canvas.stroke_line(center - half, center + unit, center + half, center - unit)

# Dimension lines and points
#canvas.fill_style = 'black'
canvas.font = '15px serif'
canvas.stroke_style = 'red'
canvas.fill_style = 'red'
canvas.stroke_line(center, center - cradius, center + cradius + 1.2*unit, center - cradius)
canvas.stroke_line(center, center + cradius, center + cradius + 1.2*unit, center + cradius)
canvas.stroke_line(center + cradius + 1.2*unit, center - cradius, center + cradius + 1.2*unit, center + cradius)
canvas.fill_circle(center + cradius + 1.2*unit, center - cradius, pradius) # point
canvas.stroke_circle(center + cradius + 1.2*unit, center + cradius, pradius) # point

canvas.stroke_line(center + cradius + 0.4*unit, center - bradius, center + cradius + 0.4*unit, center - cradius)
canvas.stroke_circle(center + cradius + 0.4*unit, center - bradius, pradius)
canvas.stroke_circle(center + cradius + 0.4*unit, center - cradius, pradius)

canvas.stroke_line(center + unit, center - half, center + cradius + 0.4*unit, center - half)
canvas.stroke_line(center + cradius + 0.4*unit, center - half, center + cradius + 0.4*unit, center + half)
canvas.stroke_line(center + cradius + 0.4*unit, center + half, center + unit, center + half)
canvas.stroke_circle(center + cradius + 0.4*unit, center - half, pradius)
canvas.stroke_circle(center + cradius + 0.4*unit, center + half, pradius)

canvas.stroke_line(center + cradius + 0.4*unit, center + bradius, center + cradius + 0.4*unit, center + cradius)
canvas.stroke_circle(center + cradius + 0.4*unit, center + bradius, pradius)
canvas.stroke_circle(center + cradius + 0.4*unit, center + cradius, pradius)

canvas.stroke_line(center, center - bradius, center + cradius + 0.6*unit, center - bradius)
canvas.stroke_line(center, center + bradius, center + cradius + 0.6*unit, center + bradius)
canvas.stroke_line(center + cradius + 0.6*unit, center - bradius, center + cradius + 0.6*unit, center + bradius)
canvas.stroke_circle(center + cradius + 0.6*unit, center - bradius, pradius)
canvas.stroke_circle(center + cradius + 0.6*unit, center + bradius, pradius)

canvas.stroke_line(center, center - half, center + cradius + 0.8*unit, center - half)
canvas.stroke_line(center + cradius + 0.8*unit, center - half, center + cradius + 0.8*unit, center - cradius)
canvas.stroke_circle(center + cradius + 0.8*unit, center - half, pradius)
canvas.stroke_circle(center + cradius + 0.8*unit, center - cradius, pradius)

canvas.stroke_line(center, center + half, center + cradius + unit, center + half)
canvas.stroke_line(center + cradius + unit, center + half, center + cradius + unit, center - cradius)
canvas.stroke_circle(center + cradius + unit, center - cradius, pradius)
canvas.stroke_circle(center + cradius + unit, center + half, pradius)

# Dimension text. First remove the red dimension lines where the dimension text will be placed.
# The different colors helped, so I left them in.
#canvas.fill_style = 'black'
#canvas.fill_style = 'red'
canvas.fill_style = 'white'
tlocx = center + cradius + 0.4*unit - 0.15*unit
tlocy = center - cradius + bradius/2 - 0.2*unit
canvas.fill_rect(tlocx, tlocy, 0.3*unit, 0.3*unit)
canvas.fill_style = 'black'
tlocxb = center + cradius + 0.37*unit # + 0.01*unit
tlocyb = center - cradius + bradius/2 + 0.015*unit
canvas.fill_text('1', tlocxb, tlocyb)

#canvas.fill_style = 'cyan'
canvas.fill_style = 'white'
tlocx = center + cradius + 0.4*unit - 0.15*unit
tlocy = center - 0.15*unit
canvas.fill_rect(tlocx, tlocy, 0.3*unit, 0.3*unit)
canvas.fill_style = 'black'
tlocxb = center + cradius + 0.37*unit # + 0.01*unit
tlocyb = center + 0.07*unit # 0.15*unit
canvas.fill_text('1', tlocxb, tlocyb)

#canvas.fill_style = 'yellow'
canvas.fill_style = 'white'
tlocx = center + cradius + 0.4*unit - 0.15*unit
tlocy = center + cradius - bradius/2 - 0.1*unit
canvas.fill_rect(tlocx, tlocy, 0.3*unit, 0.3*unit)
canvas.fill_style = 'black'
tlocxb = center + cradius + 0.37*unit
tlocyb = center + cradius - bradius/2 + 0.115*unit
canvas.fill_text('1', tlocxb, tlocyb)

#canvas.fill_style = 'magenta'
canvas.fill_style = 'white'
tlocx = center + cradius + 0.6*unit - 0.15*unit
tlocy = center - 0.15*unit
canvas.fill_rect(tlocx, tlocy, 0.3*unit, 0.3*unit)
canvas.fill_style = 'black'
tlocxb = center + cradius + 0.2*unit + 0.3*unit
tlocyb = tlocyb = center + 0.07*unit
canvas.fill_text('√5', tlocxb, tlocyb)

#canvas.fill_style = 'green'
canvas.fill_style = 'white'
tlocx = center + cradius + 0.8*unit - 0.15*unit
tlocy = center - cradius + (cradius - half)/2 - 0.15*unit
canvas.fill_rect(tlocx, tlocy, 0.8*unit, 0.3*unit)
canvas.fill_style = 'black'
tlocxb = center + cradius + 0.8*unit - 0.12*unit
tlocyb = center - cradius + (cradius - half)/2 + 0.06*unit
canvas.fill_text('Φ^1=Φ^2-1', tlocxb, tlocyb)

#canvas.fill_style = 'orange'
canvas.fill_style = 'white'
tlocx = center + cradius + unit - 0.15*unit
tlocy = center + half - cradius + (cradius - half)/2 - 0.15*unit 
canvas.fill_rect(tlocx, tlocy, 1.5*unit, 0.3*unit)
canvas.fill_style = 'black'
tlocxb = center + cradius + unit - 0.1*unit
tlocyb = center + half - cradius + (cradius - half)/2 + 0.06*unit
canvas.fill_text('Φ^2=Φ+1', tlocxb, tlocyb)

canvas.fill_style = 'white'
tlocx = center + cradius + 1.2*unit - 0.15*unit
tlocy = center - 0.15*unit
canvas.fill_rect(tlocx, tlocy, 0.3*unit, 0.3*unit)
canvas.fill_style = 'black'
#tlocxb = center + cradius + 1.1*unit
tlocxb = center + cradius + 1.075*unit
tlocyb = tlocyb = center + 0.07*unit
canvas.fill_text('Φ^3=√5+2', tlocxb, tlocyb)

# Image border
canvas.stroke_style = 'black'
canvas.stroke_line(0, 0,pwidth, 0)
canvas.stroke_line(pwidth, 0, pwidth, isquare)
canvas.stroke_line(pwidth, isquare, 0, isquare)
canvas.stroke_line(0, isquare, 0, 0)

canvas


P.S. I replaced the code after making a few corrections and changes - no change to the image.
.

Airman, does JF's info seem worthy of a paper on Miles' science site?

.
Lloyd wrote. does JF's info seem worthy of a paper on Miles' science site?

Airman. The answer can be yes or no. Miles has written several papers on pi, concerning the distance traveled around a curve versus its geometric length. The time it takes to travel around the circle is the same as it takes to travel around the square circumscribing that circle. This has been verified experimentally by Steven Oostijk.

jfmeyer has pointed out that “Miles’ claim π = 4 (in any/all "kinematic" situations)” is yet to be proven mathematically; it would be great if Miles were to do so. jfmeyer is, to some extant, challenging Miles, all well and good. What’s amazing is the fact that jfmeyer is also providing a possible solution in the form of the phi-based origin, a means of linking straight lines and curves through time and space(?). Heck if I know, I certainly haven’t quite grasped reciprocals and duality, but is sure looks interesting. If Miles sees such an answer, it might help change the world, and pi, for the better. In which case writing another paper on the subject is the least he should do.
.

Step 1 claims there's something wrong with saying π = c/d. But if we say that π is not c/d, then we're no longer talking about π, but some other constant, not the one that yields the circumference of a circle given the radius.

Simple intuition reveals that π must be transcendental. An arc and a line segment are essentially different from one another. Each is an element of geometry; neither can be derived from the other. We draw an arc with a compass, a line segment with a straightedge. What is the algebraic relationship between compass and straightedge? There isn't one. Each represents an element of geometry; neither is more fundamental than the other. If π were algebraic, then we would be able to install some gears on a compass, to implement an algebraic formula (one involving the golden ratio or square root of 5 perhaps), and the compass would then draw straight lines. We could try that, but the result would be an approximation of straightness, not straightness as in the shortest distance between two points; that's what the straightedge is for.

Miles already mentioned (http://milesmathis.com/square.html), "What has been proved by Lindemann et. al is that π is transcendental and therefore cannot be measured with absolute accuracy by a compass. This much is true and I therefore have nothing to say against it."

@airman Steven never actually experimented on an object that is traveling the perimeter of a square. I expect the accelerations necessary at the corners would complicate matters.

@garett
Miles also seems to imply that no value can be measured by a compass with absolute accuracy.

Hello Garrett,

garrettderner wrote:Step 1 claims there's something wrong with saying π = c/d. But if we say that π is not c/d, then we're no longer talking about π,

The paper asks the reader to suspend any/all hitherto taken-to-be-true notions of π because c/d is ultimately wrong as a "definition".
This means we don't assume to know what π even is & do not thus confine it to c/d. Thereby we allow 'what if c/d is false?'

As an equality, π = c/d is fine because such a ratio is valid.
One can compare the full circumference of a circle to its 2r diameter.
But as a definition, π is c/d discriminates against 2r per c/4.

The discrimination in/of the definition c/d catastrophically excludes other valid possibilities.

So yes, we are talking about π insofar as being some discrete ratio of radii & circumference. We just don't assume that ratio is c/d.
If you are trying to argue π can only be c/d wherein d = 2r, that is a/the false basic underlying assumption being addressed.

The correct value of π is arrived at by way of finding an algebraic equality between 8r/c and √(2√5+2)/2 with the latter being √Φ.
This means the origin of any/all circles (& squares they circumscribe) is necessarily not "0" but rather arithmetically/geometrically √Φ.
This means the integers 1, 2, 5, etc. and their roots √1, √2, √5 etc. all concern a single central axis & an r = 1/2 circle whose origin is √Φ.
The radius of this single central circle about this single central axis is the real element of 1/2 (confirming the RH is invariably true).

Mathematicians have catastrophically ill-defined π as a c/d ratio because π is composed of 8r, not 2r.
8r is needed in & of 8r/c = √Φ such to solve for r & c. These r and c are precise, not "approximate".

In any event: we are ultimately talking about the real circumference of a real circle whose real radius is 1/2.
The circumference of such a circle is, in reality, greater than 3.1446...
whereas 3.14159... is non-trivially deficient at the thousandth decimal place.

A real 1000mm diameter circle has a real circumference greater than 3141.6mm.
A single tenth of a mm above (within margin of error) implies/proves the deficiency of 3.14159...

Establishment mathematicians can't measure beyond the boundary of their own ignorance(s)
despite this very boundary being the very first thing to ever bother measuring at all. There is nothing else to measure.
By properly measuring a circle (ie. without "approximation" begetting "transcendence") one obtains a discrete 4/√Φ.

Predictably: the incorrect value of π is the most basic underlying "blunder of millennia" holding back Western science.

Humanity has the wrong value of π due to false basic underlying assumptions & deficient "approximation" methodologies.
The paper shows there is precisely 0 need/inclining to ever "approximate" a circle at all & can be measured as a precise ratio.
That ratio is 8/√(2√5+2) = 4/√Φ & is a root of polynomial x⁴ + 16x² - 256 thus π is certainly not "transcendental".

garrettderner wrote:but some other constant, not the one that yields the circumference of a circle given the radius.

The ratio 8r/c allows each c/4 to have 1 discrete 2r as a corresponding right angle, as any/all circles naturally have on any orthogonal axis.
This allows 4 symmetrical quadrants to each discretely contain c/4 in geometric relation(s) to 2r.

Geometry and number are actually not two separate/autonomous things at all: numbers naturally pertain to (ie. imply) geometry.
There is only one correct rational/irrational ratio generally relating line & curve & it is the ratio 4/√Φ.
This relation reflects the integrity of the geometric relations naturally existing between rationals & irrationals.

garrettderner wrote:Simple intuition reveals that π must be transcendental.

It is the other way around: simple intuition absent assumption reveals that π must be algebraic.
Recall r = 1/2 = s² wherein the radius of the r = 1/2 circle is equal to the area of the square it circumscribes.

π can not be "transcendental" if the radius is equal to the area of a real geometric square it circumscribes.
One minimally has 4 points to geometrically describe both the circle and the square simultaneously.

garrettderner wrote:An arc and a line segment are essentially different from one another. Each is an element of geometry; neither can be derived from the other.

They are different while/as complimentary, as in: likeness & image resp.
Curve and line share in/as the same basic relation.
π is derived from the reciprocal root of the golden ratio viz. 1/√Φ = π/4.
Φ and π are thus the Adam & Eve of mathematics, so-to-speak.
Their union is in/at 1 = Φ(π/4)² thus it can not be stated they are "essentially different..." if/when they are essentially one (ie. 1).

garrettderner wrote:We draw an arc with a compass, a line segment with a straightedge. What is the algebraic relationship between compass and straightedge?  There isn't one.

There is one: the real linear radius (ie. proximity) between origin (ie. the needle) & circumference (ie. the pencil).
That measure reflects a/the real angle between the compass' two arms & scales according to the golden ratio
because the golden ratio is the universal scalar. It is the only number in the universe with the properties it has.

garrettderner wrote:Each represents an element of geometry; neither is more fundamental than the other.

That is correct because Φ and π are not two separate/autonomous phenomena.
They are two aspects of the same underlying relation, hence 1 = Φ(π/4)².

garrettderner wrote:If π were algebraic, then we would be able to install some gears on a compass, to implement an algebraic formula (one involving the golden ratio or square root of 5 perhaps), and the compass would then draw straight lines. We could try that, but the result would be an approximation of straightness, not straightness as in the shortest distance between two points; that's what the straightedge is for.

A normal compass is itself composed of two straight edges. That's what you need to compose a curve regardless of how you look at it.

garrettderner wrote:Miles already mentioned (http://milesmathis.com/square.html), "What has been proved by Lindemann et. al is that π is transcendental and therefore cannot be measured with absolute accuracy by a compass. This much is true and I therefore have nothing to say against it."

They all falsely assume π = 3.14159... along with the last two millennia of human civilizations.
I was taught the same number in school & now know how/why it is actually deficient/wrong.

Of course a π of 3.14159... will appear "transcendental" having no integral quarter symmetry as 4/√Φ naturally does.

The circumference of an r = 1/2 circle is 8/√(2√5+2) & this ratio is absolutely precise.
It is approx. 3.1446055... & is not "transcendental" but algebraic.
This is the relation the real physical universe assumes & operates on.

So the imprecisely approximated number 3.14159... is "transcendental" only because it is merely a deficient approximation of what is really an algebraic 4/√Φ.

LongtimeAirman wrote:jfmeyer has pointed out that “Miles’ claim π = 4 (in any/all "kinematic" situations)” is yet to be proven mathematically; it would be great if Miles were to do so. jfmeyer is, to some extant, challenging Miles, all well and good. What’s amazing is the fact that jfmeyer is also providing a possible solution in the form of the phi-based origin, a means of linking straight lines and curves through time and space(?). Heck if I know, I certainly haven’t quite grasped reciprocals and duality, but is sure looks interesting. If Miles sees such an answer, it might help change the world, and pi, for the better. In which case writing another paper on the subject is the least he should do.

Hello - I did see your earlier post & no problems, it is spot on.

Mathematically, π ≠ 4 so Miles couldn't ever prove his assertion. He is missing the kinematic base upon which 4 sits, which is √Φ.
Any/all experiments conducted finding π = 4 similarly fail to recognize & account for the presence of the kinematic base of √Φ.
We may perceive/measure it as 4 for not realizing we are ourselves in/on the very same kinematic base of √Φ.
I argue this is naturally the case in such measures, as humanity is unconscious of what the speed of light is based in/on.
16 = Φπ² preceding e = MC² predicts light is naturally normalized to the circumference of a circle (ie. π).
4/√Φ is the embodiment of the relation between rational & irrational numbers as they cooperatively describe the circumference of a perfect r = 1/2 circle.

Indeed the Φ-based origin is of extreme significance: it practically unites recti- and polar-Euclidean geometries to a common ground.
As it applies to physics, this common ground is light with motion and/or energy as s/t & t/s ratios "relative" to it.
One could consider it the union of space and time as they operate on the shared principle of reciprocity.

That is: the real, physical universe is necessarily Φ-based & 1 = Φ(π/4)² underlies all physics.
It is practically the 1-inch "god" equation Dr. Michio Kaku has been searching for.
1 = Φ(π/4)² predicts reciprocity is the key underlying principle
(applies indiscriminately) governing the "real" physical universe.

The implications of this are profound, yet the global situation is pathetic.
Western science is being destroyed by those who absolutely hate science
esp. as it undermines their own divisive/destructive belief-based religious ideology(s).
I am watching them do this, as I have been for quite some time now.
I am also watching humanity be deceived/destroyed by them, stage-by-stage, piece-by-piece.

Understand those who seek division instead of unity are stooges of Project Chaos - willing or not.
I am on Miles' side in the long run, however he is himself unknowingly deceived by the makers of it.
It is possible to see through all deception(s)/propaganda(s) relating to Project Chaos.

If/when you explicitly know what a thing is, you become immune to any/all deceptions trying to have you believe it is something it is not.
That is the power of knowledge: it builds immunity to what could otherwise be the presence of belief-based deception & ignorance causing suffering.

.

Another phi-based origin, turtle generated.

I’m not suggesting it for everyone, but making a few phi-based origin diagrams has allowed my mind plenty of time to dwell upon it. It just shows us the relationship between the s=1/√2, r=1/2, s=1, r= √5/2 and r=(√5 +2)/2, (circles, squares, and rectangles. Yet, even without considering reciprocity and duality its a pretty amazing diagram, showing an undeniable link between pi and phi. I believe I may have seen images of mandalas based on phi (?).

Thank you Sir. I’m still contemplating the third dimension, time and space, etc.

I was prejudiced against turtle graphics, thinking it was kid stuff. With zero turtle experience I was able to create the output image above in just a few hours – midst the mayhem in my living room. The plot is two dimensional, but one may still draw a third axis to present a 3d image. There are turtle games, so there must be a way to make an interactive √phi-based origin.
.

LongtimeAirman wrote:Another phi-based origin, turtle generated.

I’m not suggesting it for everyone, but making a few phi-based origin diagrams has allowed my mind plenty of time to dwell upon it. It just shows us the relationship between the s=1/√2, r=1/2, s=1, r= √5/2 and r=(√5 +2)/2, (circles, squares, and rectangles. Yet, even without considering reciprocity and duality its a pretty amazing diagram, showing an undeniable link between pi and phi. I believe I may have seen images of mandalas based on phi (?).

Here is a photograph from Google images taken fairly recently (2012) at Nazca, Peru.
The image etched into the ground is over 2000 years old & resembles your own graphs.


Mandalas invariably utilize this basic quadratic symmetry implied by Φ & π but only if/as π = 4/√Φ.
There is no such quadrature in/of a π of 3.14159... thus what LongTimeAirman stated is extremely important.
This geometry shows us the real, geometric relation(s) between key ratios composed of rational & irrational numbers.
The ratio 1/√2 is particularly important because it establishes the geometric "datum" of the rational terminating & irrational non-terminating numbers.
It also defines the side lengths of the square s = 1/2 as it relates to the r = 1/2 circle circumscribing it such that each 1/√2 has a corresponding c/4.
It is in the form (rational) / (irrational) & the rest of the numbers scale to/from here (as afforded by the universal scalar Φ).
As such, any/all further numbers (ie. 2, √5 etc.) will invariably concern 1 & √2 (that is: their integrity will always agree with the latter).

LongtimeAirman wrote:Thank you Sir. I’m still contemplating the third dimension, time and space, etc.

The same thanks is returned in kind for your attention & consideration.

Concerning the third dimension: this is naturally normalized to the so-called "speed" of light. That is: it is simply the rate of causality.
If you compared the s/t distance of √Φ to the equivalent s/t distance of π/4, their product is incessantly 1. This relates to space & time.

In terms of physics, this same property of an incessant product of 1 is satisfied by (s/t x t/s) implying the principle of reciprocity.
Here is a basic model of the relation:



wherein v = s/t can also be a speed. If one imagines the so-called "speed" of light as an incessant square (& root) operation(s),
the speed of light is the fixed rate at which squares & square roots naturally occur & upon which all kinematics (motion) occurs.

As earlier stated: if one thinks of space & time as two separate/independent/autonomous phenomena, one will misconceive.
Like yang & yin, space and time are cooperative aspects composing one whole. To see space and time as anything other than cohesive is thus erroneous.
General Relativity (ie. Einstein) intuited this inextricable link between space & time but has hitherto not been able to explain why it is so.

The explanation is this: space and time are multiplicative reciprocal aspects of motion.
They have no more or less significance than a numerator and a denominator have.

I should also remark: if/as one accounts for motion in both 3D space as well as in 3D time, so-called "time dilation" ceases to exist.
That is: time dilation is an artifact of only assuming/assigning a single dimension to time. In reality, time has the same 3D space has.
This is another example of how false basic underlying assumptions causes debilitating misconceptions behind which Western science is stuck.

LongtimeAirman wrote:I was prejudiced against turtle graphics, thinking it was kid stuff. With zero turtle experience I was able to create the output image above in just a few hours – midst the mayhem in my living room. The plot is two dimensional, but one may still draw a third axis to present a 3d image. There are turtle games, so there must be a way to make an interactive √phi-based origin.

I wouldn't be ashamed to admit the basic relations we are working with is kids' stuff.
As was suggested before me: a young child can & should learn this basic Φ-based geometry.

Unfortunately, we are still waiting on Miles to even confront/address it, despite it underlying his "charge field".
If/as he realizes π = 4/√Φ he will immediately see how it all fits in. It will probably all strike him at once.
The deeper underlying problem here is whether or not he will confront it, or deliberately ignore it.

In the meantime, I am working on a video which finds π beginning from a clean slate.
It will derive the x & y axis from the orthogonal √2 diagonals of the unit square.
I will post it here when complete - I am waiting on a few resources.

.
As usual, plenty to think about, thank you very much, like 3D time to go along with 3D space.

Nazca phi geometry! I needed to get a clearer image.  


Nazca Sun-Glyph image credit: Gilbert de Jong
The Nazca Sun-Star as the Magic Square of Mercury
by Joseph E. Mason
http://blog.world-mysteries.com/science/nazca-lines-enigma-of-the-sun-star-and-cross-mandala/
That site describes a magic square explanation which has nothing to do with phi.

Well, that image is a little better. I had to start plotting the lines, hoping to see if the sun-glyph contained some new phi based essential truth.


I didn’t get very far as there are many differences and deviations between the glyph and my favorite phi geometry image. Actually, I’d need an even better image to plot it properly. I saw somewhere the main site is square, s=180m, divided into a grid of 8x8 s=1/2 squares (each about 22.5m on the side). All the corners of of the s=1/2 squares are defined by “dots”. The s=1/2 squares can also include 4 each, internal edge midpoint adjacent dots. I see the keppler rectangles pattern as a huge structure, each dot is a column which helps hold up the roof, but spans of ten or 20 meters are extremely large. There’s no hint of either the s=1/sqrt(2) square or the r=1/2 circle, but they may have been present in a roof structure. The glyph’s keppler diagonal section endpoints are not on their proper lines. There doesn’t appear to be a r=sqrt(5)/2 circle, and the sun-glyph includes an extra circle between where the r=sqrt(5)/2 circle would be and what appears to be the r=(sqrt(5)+2)/2) circle. The s=180m square includes 3 each, s=1/2 squares per corner, and where are those corners exactly; aligned to the s=4 grid or the tangents to the r=(sqrt(5)+2)/2) circle? There’s another even larger square. Despite all that, it seems fairly evident the sun glyph is based on phi geometry. Please pardon my digression.

Good luck building the phi-based origin from scratch. Check out how these guys do it.
https://www.youtube.com/watch?v=rfl-UCZr2-g

The Mandala of Compassion at Dartmouth
Jan 28, 2011
.

Airman, I guess you remember when we discussed using turtle graphics and other programs for trying to do photon/matter simulations. I haven't messed with turtle for quite a few years, but I liked how simple it was and how complexity could be built up from simple building blocks, so to speak. The main problem I had with it was that it took too long to plot complex things, especially objects in motion. I was an amateur, but pros probably have ways to speed things up a lot.

JF, I tried to interest folks, including Miles, at the "CutFog" forum in this thread, but didn't get anywhere there. I mentioned there that some of the members seem childish in treating Miles like a guru. So the forum owner, Josh, childishly decided to ban me for insulting them. Jared had previously attacked me when I returned to their forum and suggested that the Covid virus was genetically engineered in Wuhan, China. He accused me of being a spook, working for the CIA etc. He and Josh and even Miles seem absurdly paranoid and sure of themselves. They would probably suspect Airman of being in psy ops or something too. They think spooks are trying to divert them from work that might uncover proof of conspiracy. So I can't have scientific discussions with them, which is a shame.

LloydK wrote:JF, I tried to interest folks, including Miles, at the "CutFog" forum in this thread, but didn't get anywhere there.

For no fault of yours: I am not surprised.

LloydK wrote:I mentioned there that some of the members seem childish in treating Miles like a guru.

Indeed, idolatry is childish: such people attach themselves to the hip of others just as children do their mothers.
Interestingly, the underlying phenomena is the same with the idolatrous Abrahamic cults underlying this global war.
The idol-worshippers' psychology is extremely childish: as if they never grew beyond the emotional maturity of a 9-year-old.
I earlier sensed Miles is like a 9-year-old child trapped in a man's body.
He is thus already at odds with himself & needs not any external conflict(s).

LloydK wrote:So the forum owner, Josh, childishly decided to ban me for insulting them.

Please do not take it or anything they say/do personally - insult is never 'a given but 'a taken.
Those who are so easily "insulted" by anything have deeper issues within themselves.
One is ultimately accountable for one's own internal state of being.
Those who believe otherwise tend to justify blaming others.

LloydK wrote:Jared had previously attacked me when I returned to their forum and suggested that the Covid virus was genetically engineered in Wuhan, China.

It was. The deeper question(s) is why? Who ordered it? What is the motive?
Neither Miles nor Josh knows the real answer to these questions.
If they did, they would not behave as irrationally as they do.

It is (now) possible to precisely read & extract a real motive/will/intention of any (non-)motioning body(s) incl. ideological bodies/states.
This follows from any/all motion(s) discretely having a corresponding reciprocally related energy constituency.
Crucially implied by the equality 1 = Φ(π/4)² is the resolute clarification of the "real" & "imaginary" elements.
The solution to unity thus allows/permits one to rationally discern what is real from what is not.

Miles and his entire following collapse at their own not knowing the real underlying motive of "Project Chaos".
They see the damage it is causing (like Hitler did) but are blind as to the real underlying cause (again like Hitler).
Now Hitler was catastrophically deceived by the real "Jews" into believing the Jews are someone other than who they really are.

Miles is similarly deceived, as are most people on the planet.

The war being fought is at least 1400 years old & takes the form "believer vs. unbeliever".
The "believer vs. unbeliever" war is a 100% "Jewish" war perpetuated by book-worshippers.
If one worships a single book while/as dividing humanity in 2, such is the endeavour of a "Jew".

Penetrating & completely seeing through the "great deception" entails knowing
the real "Jews" of this planet are not holding a Torah in their hands, but a Qur'an.
If/when this is known, the global war becomes extremely easy to see & understand.

LloydK wrote:He accused me of being a spook, working for the CIA etc.

He is himself much closer to being a psychologically controlled "spook" than you are (or appear to be).
One thing you will notice about those who become "infected" is: they tend to project their own qualities.
They will unconsciously accuse you/others of what they are themselves guilty of. That's their "infection".
You will find this general pathology underlies Nazism/fascism/socialism as well.
Infected people no longer have the capacity to look at themselves in the mirror (only out/down at others).

LloydK wrote:He and Josh and even Miles seem absurdly paranoid and sure of themselves.

They are absurdly paranoid - that is Miles' own personal illness. He has infected others with it - those who surround him are subject to/of the same.
I was/am glad to have found at least some people on these forums who are not so succumb & can take digs against Miles.

The "sure of themselves" part is only cosmetic: it is because they are unsure of themselves they have to artificially appear as secure.
In reality, they are thoroughly insecure of themselves & this is measurable in/as their inability to bear looking at themselves in the mirror.
As a natural consequence, if they have something nasty buried inside of themselves, it will come out in the form of an accusation against others.

LloydK wrote:They would probably suspect Airman of being in psy ops or something too.

They will see any/all others as what they themselves are. It is like wearing red shades believing the whole world is red.
The world is not red, they see it as red because they can not account for the red of their own lenses through which they perceive.

LloydK wrote:They think spooks are trying to divert them from work that might uncover proof of conspiracy. So I can't have scientific discussions with them, which is a shame.

Ironically: they are themselves diverting from work that actually does imply proof of a conspiracy (to keep humanity ignorant).
They thus do more towards that end by ignoring the equality(s) π = 4/√Φ as it implies 16 = Φπ² preceding e = MC².

The only thing one can do in this situation is observe how Miles' own delusions holds him & his work back.
If he chooses to behave like this, one may as well draw lesson(s) from it & learn how not to change the world.

From his perspective, he sees a delusion of everyone else trying to hold him back even if/as the opposite is true.
Neither I nor anyone else could hold Miles back: he is absolutely capable of doing it all by himself (& that he does).

I know it is not easy to confront any possibility that what humanity has held to be so true for so long is, in fact, not.
If anyone has any (other) ideas to push a global correction to π, please feel free to discuss.
In my opinion, a proof of the Riemann Hypothesis would be the best vehicle.

Riemann Hypothesis (problem):

The real part of every nontrivial zero of the Riemann zeta function is 1/2.

Riemann Hypothesis (solution):

1 = Φ(π/4)^1/r

wherein r = 1/2 is the real radius of a real circle & the "real part" of 1/2.

That is what is hiding behind the correct measure/value of π.
There is no more important correction to possibly occur than π.
It appears Miles will not be of any help/use in this.

Well, JF, I finally have a little time to read and reply. The details of much math are not so interesting to me, so I don't try to comprehend much of it. It's not apparent to me that a global acceptance of n will accomplish much, even if such acceptance was possible. Seems more likely that global acceptance of Jesus' advice to love our neighbors would be more productive. Miles shows that much of science and even math need revising so that should help move humanity in the right direction too, more trivially IMO.

Are you as sure of yourself as you sound? I'm willing to discuss (beneficial influence on the public). I may have time next week.

Does anyone know if Miles has discussed @jmeyers update for:

√Φ = √(2√5+2)/2 → 1/√2 → 2/√(2√5+2) = π/4

Chromium6 wrote:Does anyone know if Miles has discussed @jmeyers update for:

√Φ = √(2√5+2)/2 → 1/√2 → 2/√(2√5+2) = π/4

An update:

It is possible to pinpoint the most deeply embedded false basic underlying assumption giving rise to the deficient 3.14159...
All exhaustive "approximation" methodologies are based on the (false basic underlying) assumption:

given an n-sided polygon (with perimeter p) and corresponding circle (with circumference c),
it is assumed as n increases, p trivially approaches c.

This assumption is not necessarily true (and has endured for approx. 2000 years).

Initially, p does approach c but not indefinitely. There comes a discrete point wherein p actually begins to recede from c.
As such, if "approximating" an r = 1/2 circle, the "approximation" ends up having a radius of, not 1/2 as it should, but slightly less at 0.49952094...

This is catastrophic because the correct value of π as 8/√(2√5+2) correctly assumes a rational, terminating radius of 0.5
whereas the "approximated" π assumes an irrational, non-terminating radius of 0.49952094... and goes on and on and on.

This is ultimately why the "approximated" π is "transcendental" - it is because it has not a terminating real element of 1/2.

Thus the real "crisis in science" is: scientists do not know how to properly measure a circle.

That is the reality (or "real element") underlying the present state of affairs.
The truth is stranger than fiction, only it is not fiction - it is real.

A very basic scientific hypothesis can be formulated & tested:

The "Blunder of Millennia" Hypothesis:
A real circle of 1000mm diameter will measure non-trivially greater than 3141.59mm...
Expected: greater than 3144.60mm.

This hypothesis is testable, thus "scientific" however I do not expect scientists to perform the measure. They are too afraid of the result & the implications.

Too bad, because the solution to e = MC² as 1 = Φ(π/4)² is the 1-inch equation Dr. Kaku is looking for. It all resolves back into unity.
They can/will never find it due to the π problem - they instead negligently refuse to challenge their basic underlying assumptions.

Greetings once again,

It was recently realized the correct value of π can be directly solved for
using the inverse square law:

I = 1/D²

by allowing the positive solution to (x² - x) = 1
as x = (√5 + 1) / 2 to be the intensity scalar I
while/as allowing D to describe the area of a circle πr²
contained in the geometric domain 1 = (x² - x):

x = 1/(πr²)²

recalling the radial application of (√5 + 1) / 2 geometrically contains the area of the r = 1/2 circle:


We therefor let r = 1/2 for being the real geometric radius of the 2r = 1 diameter circle
as geometrically contained inside the domain (x² - x) = 1 (which we let be the numerator)
& as geometrically arrived at by way of the radial application of (√5 + 1) / 2 (which we let be x)
to solve for its circumference (for x invariably & incessantly reconciling r = 1/2 for any/all 360°):

x = 1/(π(1/2)²)²
x = 1/(π(1/4))²
x = 1/(π/4)²
x = 16/π²
π² = 16/x
π = 4/√x
∴ π = 4/√Φ
= 2√(2(√5-1))
≈ 3.1446055...

and given π = 4a as r = 1/2 according to:

a = πr²
a = π(1/2)²
a = π(1/4)
a = π/4
∴ π = 4a

we can (inversely) find the area of the same circle by using 4a instead of π:

x = 1/(4ar²)²
x = 1/(4a(1/2)²)²
x = 1/(4a(1/4))²
x = 1/a²
a = 1/√x
∴ a = 1/√Φ
= √(2(√5-1)) / 2
≈ 0.78615137...

Neither Archimedes nor any mathematician(s) since thought to ask one simple question concerning the use of both
inscribed & circumscribed polygons whose internal angles sum greater than 360° to reconcile a perfect 360° circle:

J.F. Meyer wrote:"...is there a better way?"

Indeed, there is:


One would thus have to practically deny the inverse square law to deny π = 4/√Φ predicted by it.

Finally, with the integers & their roots geometrically intact,
c scales according to r via. the equality(s):

also expressed as:

r = c√(2(√5+1)) / 16

and

c = 4r / √(2(√5-1))

while noting they can be (re-)written in various ways (all equally valid).

These are obtained by correctly solving for the origin of coordinates in/at the centre of the (only) "unit" square according to (x² - x) = 1.
The unit square whose origin is o resolves as 8r/c = √x wherein x = Φ. By setting 4r / √(2(√5-1)) equal to the approximated π of 3.14159...
as arrived at by n > 4 n-gons:

4r / √(2(√5-1)) = (≈π)
r = 0.49952094...

...we obtain what the real radius of a real circle would (really) be if its circumference were, really, 3.14159...
Emphasis on "real" because r = 1/2 = s² is real element for being the real radius of a real circle
as it geometrically circumscres a real square of equal area via. r = 1/2 = s².

As stated earlier: this has implications for the outstanding Riemann Hypothesis.
The problem both exists & persists because Riemann constructed his analysis (falsely) assuming π = 3.14159...
...which means the problem can & will not be solved without π being corrected: it's where the problem begins & ends.

To close, all of the above follows from the affirmative result of
a simple experiment performed to test the following hypothesis:

-J.F. Meyer wrote:'The Blunder of Millennia Hypothesis':
A real circle of 1000mm diameter will have a circumference non-trivially greater than 3141.6mm. Expected: ~3144.6mm.

all lending itself to:

∴
π ≠ 3.14159...
π = 4/√Φ
π² = 16/Φ
16 = Φπ²
E = MC²
1 = Φ(π/4)²

= (x² - x)
such that it naturally contains the universal constancy(s)
of Φ and π together as, not two, but one
thus unification is (now) possible.

Hi jfmeyer,

Just wondering if you ever looked at Miles' "Euler" paper? Got me thinking on how your PI is represented differently than the Manhatten metric for bodies in motion...that is how you see actual
body motion around a circle with PI?
This may be similar to LTAM's question above on PI=4 (in kinematic situations) -- this thread's title.

http://milesmathis.com/euler.pdf