A puzzle: dissect a square into congruent pieces, all touching the center

Re:A puzzle: dissect a square into congruent pieces, all tou... by ColinWright on Wednesday May 25, 2011 @04:34PM (#2585442)

You've found two infinite families and one sporadic solution.

There is another sporadic solution, and the 8 piece solution you've found is not, in fact a sporadic.

And yes, the infinities are uncountable.

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Re:A puzzle: dissect a square into congruent pieces, all tou... by pozorvlak on Thursday May 26, 2011 @08:56AM (#2587551)

puzzles

Oh, right - you can vary the shape of the diagonal lines, provided each "arm" has rotational symmetry about its mid-point.

OK, so we've got three infinite families and the trivial solution (only one piece - is that your sporadic solution?). I think that might be all: each piece can contain 4, 2, 1 or 1/2 of the original square's corners, since (lacuna) all pieces must contain the same number of corners and further subdividing the corners (into 1/3s, say) would mean some pieces don't touch the centre (another lacuna).

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Re:A puzzle: dissect a square into congruent pieces, all tou... by ColinWright on Thursday May 26, 2011 @09:44AM (#2587665)

OK, that's now the set of solutions I've got. You've also gone some way to showing them to be complete.

More to do, though.

And now do it for an equilateral triangle.

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Re:A puzzle: dissect a square into congruent pieces, all tou... by ColinWright on Thursday May 26, 2011 @05:12PM (#2589461)

OK - I've now seen a "solution" with 16 "pieces."

My head hurts.

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Re:A puzzle: dissect a square into congruent pieces, all tou... by vanishing on Wednesday May 25, 2011 @04:43PM (#2585469)

Ah, yes. You can also rotate the 8-fold solution by 22.5 degrees for another solution.

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Re:A puzzle: dissect a square into congruent pieces, all tou... by vanishing on Wednesday May 25, 2011 @04:46PM (#2585482)

Right. As I said, I'm weak in math.

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Re:A puzzle: dissect a square into congruent pieces, all tou... by ColinWright on Wednesday May 25, 2011 @04:58PM (#2585529)

You can't be that weak at what I call math, although your experiences with math education might be unhappy ones. You have found more solutions than I first found - that can't be bad.

Half my life is spent helping people discover that they're good at "proper math" even when they think they're bad at "school math."

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Re:A puzzle: dissect a square into congruent pieces, all tou... by ColinWright on Wednesday May 25, 2011 @04:44PM (#2585476)

Hmm. Don't think so.

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