Shelagh ([info]ingaborg) wrote,
@ 2009-07-03 13:44:00
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Martin Gardner query
My Dad has been given a strangely-cut piece of paper folded into a square, which physically simulates a method for remembering Maxwell's Relations (something to do with thermodynamics, don't worry about it).

The problem is that he has posted it to me, and I have unfolded it in a curious fashion, but now cannot refold it - and neither of us knows how to use it anyway.

The kindly scientist who gave it to him said that it was based on an article in "Fun with Maths" by Martin Gardner. Now, while it has a very Martin Gardnerish sort of look (anybody here remember hexaflexagons?) I cannot find any references to a book of that name by Gardner.

The piece of paper is shaped like a square with the corners cut out. It is then folded into a square with four quadrants. You can refold it in various ways to show other panels in the quadrants. No, that probably doesn't make any sense if you haven't seen it.

Anyway, does this ring any bells with anybody? I'd dearly love to find the original reference, and help Dad refold and use it!



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[info]uk_sef
2009-07-03 02:21 pm UTC (link)
Perhaps it wasn't a book at all but a magazine column article. In which case you might have the name of the column (or article) and not the magazine.

I do have a lot of Martin Gardner stuff but that doesn't currently sound familiar enough for me to guess where it might have been - but I know I have trouble guessing where to find other stuff I definitely know was his, let alone things of which I'm unsure.

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[info]omylouse
2009-07-03 02:31 pm UTC (link)
Sounds useful even though I don't really know anything about it! I can cross-post this on my lj & to uber-geeks to see if it rings any bells with them if you like?

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[info]uk_sef
2009-07-03 02:32 pm UTC (link)
PS Can you give me any more magic words which might appear in a chapter heading or describe better what inscription might be on (each side of) the paper so I can spot it flicking through my books? Can you eliminate any books because you have them yourself? I'm feeling rather sick at the moment so I don't have a great deal of enthusiasm.

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[info]ingaborg
2009-07-03 04:00 pm UTC (link)
I have "Mathematical puzzles and diversions" and "More mathematical puzzles and diversions". A quick flick through hasn't found the thing I'm looking for, but it is a bit like a tetraflexagon but the configuration is

xx
xxxx
xxxx
xx

There is a cross cut in the middle so that you effectively have a continuous chain of 12 squares. The whole is then folded into a square that looks like

xx
xx

You can refold it in various configurations.

The inscription won't help you because the point is that this is a novel application to use the device for Maxwell's relations! I think it is sort of a matrix rotation/symmetry thingie.

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[info]uk_sef
2009-07-03 04:28 pm UTC (link)
Now that does seem vaguely familiar. Just checking: are there no diagonal folds?

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[info]ingaborg
2009-07-03 04:30 pm UTC (link)
No, there are not.

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[info]uk_sef
2009-07-03 04:38 pm UTC (link)
Got it! It's in "Wheels, Life And Other Mathematical Amusements" chapter 7.

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[info]ingaborg
2009-07-03 04:41 pm UTC (link)
That's wonderful, thank you! I can request it from the library and check it out in detail. I expect the book will be fun to read too :) :) :)

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[info]ingaborg
2009-07-03 04:42 pm UTC (link)
What's it FOR then???

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[info]uk_sef
2009-07-03 04:47 pm UTC (link)
In that book it was just another tetraflexagon - in which it was easy to get faces 1 to 4 (ie all 4 squares having those numbers) but allegedly harder to get 5 and 6. I'm fairly certain I made and "solved" one way back in the past. I even suspect that EWT & co have one (in their dining room when last seen).

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[info]ingaborg
2009-07-03 04:01 pm UTC (link)
Hmm, the configuration didn't come out right, the xx on top and bottom should be centred. The "Edit post" button seems to have vanished!

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[info]dougs
2009-07-03 04:05 pm UTC (link)
It seems likely that "Fun with Maths" by Martin Gardner is in fact "Mathematical Games" by Martin Gardner, a regular monthly column in Scientific American.

But I've googled on that basis, and come up with nothing.

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