Martin Gardner

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Martin Gardner

Post by LongtimeAirman on Thu Feb 15, 2018 7:06 pm

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Martin Gardner (October 21, 1914 - May 22, 2010). Taken from one of his many cover images. I don’t know the actual description of the image shown. I chose it because I believe it shows an end-over-end rotation. I guess the question might go like this, rotate two bolts about an axis between the two bolts as shown. Note that the bolts themselves do not spin about an interior axis. If one maintains a steady contact between the two bolts, not allowing any slipping between the threads, what is the resulting horizontal motion?

I’ve always been interested in math. Martin Gardner was my hero. I’d subscribed to Scientific American since ninth grade because of his Mathematical Games section. https://www.scientificamerican.com/media/pdf/Aug2008_Martin_Gardner_Recreational_Mathematics.pdf. I didn’t always understand him, but I sure enjoyed the topics he discussed. Like going through many sheets of graph paper when first plotting Conway’s Game of Life and later programming my own cellular automatons. Oh, and I would read and try to understand at least one other Scientific American article each month.

I have seven or so Martin Gardner paperback books on my shelf – in one the pages have turned orange. Doing a search I see many documents are available.
https://archive.org/search.php?query=creator%3A%22Martin+Gardner%22

Ans. I believe the threads between the two bolts allow free rotation without any resulting horizontal change in position.

P.S. From The Colossal Book of Short Puzzles and Problems by Martin Gardner.
16.12 Twiddled Bolts. Two identical bolts are placed together so that their helical grooves intermesh [Figure 16.10]. If you move the bolts around each other as you would twiddle your thumbs, holding each bolt firmly by the head so that it does not rotate and twiddling them in the direction shown, will the heads (a) move inward, (b) move outward, or (c) remain the same distance from each other? The problem should be solved without resorting to actual test. (I am indebted to Theodore A. Kalin for calling this problem to my attention.)

Answer 16.12—(August 1958) The heads of the twiddled bolts move neither inward nor outward. The situation is comparable to that of a person walking up an escalator at the same rate that it is moving down.
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Last edited by LongtimeAirman on Sat Feb 17, 2018 12:47 am; edited 1 time in total (Reason for editing : Added PS)

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Re: Martin Gardner

Post by Cr6 on Fri Feb 23, 2018 11:58 pm

A bit tricky to wrap one's head around. What happens if Bolt A spins faster than Bolt B?

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Re: Martin Gardner

Post by LongtimeAirman on Sat Feb 24, 2018 1:03 am

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Cr6 wrote. A bit tricky to wrap one's head around. What happens if Bolt A spins faster than Bolt B?

Thanks for asking, I can't say I was good at these things, but I loved them.

I'll give you my best guess. Please note Martin’s instructions are much clearer than mine. He asks that you twiddle the bolts as you might twiddle your thumbs. Your twiddling thumbs form end-over-end rotations with each other; they do not spin, nor do they spin at different rates.

If one changes the problem, and allows the bolts to spin then the bolts will move horizontally inward or outward or both may move sideways. The rate of motion will be the addition of the two spins, since the meshed threads prevent the bolts from spinning independently.
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Re: Martin Gardner

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