Re: Correction Re: [math-fun] Problem about tiling regular 2n-gon with rhombi
PUZZLE: Given a rhombus tiling of a 2n-gon (so that each polygon edge is a rhombus edge), show that the number of rhombi is determined by n.
As Michael Kleber and George Hart have (perhaps inadvertently) pointed out, I neglected to mention (except in the Subject line) that the 2n-gon is supposed to be regular.
For a straightforward generalization to parallelograms, one need only assume that the 2n-gon is convex and has n pairs of parallel sides.
i think you need to say "n pairs of parallel *and equal* sides". mike
PUZZLE: Given a rhombus tiling of a 2n-gon (so that each polygon edge is a rhombus edge), show that the number of rhombi is determined by n.
For a straightforward generalization to parallelograms, one need only assume that the 2n-gon is convex and has n pairs of parallel sides.
i think you need to say "n pairs of parallel *and equal* sides".
No and no! You just need to assume, as the original puzzle did, that the 2n-gon can be tiled by rhombuses (or parallelograms). As I pointed out before, any parallelogram tiling gives rise to a pairing of (necessarily parallel and equal) edges. --Michael Kleber kleber@brandeis.edu
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