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For questions about mathematical tiling.

20 votes

Polyomino that can tile itself

As John S. Adair commented, the relevant keyword is rep-tile. Wikipedia provides a partial answer to your second question (shapes other than polyominoes); it cites a paper by Viorel Niţică, "Rep-tiles …
Timothy Chow's user avatar
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9 votes

Tiling the plane with pairwise non-congruent rational triangles

This is overkill for your question, but in Carl Pomerance's paper, On a tiling problem of R. B. …
Timothy Chow's user avatar
  • 82.6k
20 votes

Can a row of five equilateral triangles tile a big equilateral triangle?

He has found a tiling of an equilateral triangle for the heptiamond case, but does not know what the smallest such triangle is. It seems that Reid has never published these results. …
Timothy Chow's user avatar
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13 votes

Is there mathematical significance to the LaGuardia floor tiles?

For those who can't quite see the underlying hexagonal tiling mentioned in David Speyer's comment, I have highlighted part of it below. Please excuse my crude digital editing skills. . …
7 votes
Accepted

Partitioning a rectangle into different isosceles triangles

As Noam Elkies has observed, any acute non-isosceles triangle can be tiled by three pairwise non-congruent isosceles triangles, by connecting each vertex to the circumcenter. There are lots of ways t …
Timothy Chow's user avatar
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16 votes
Accepted

Non-enumerative proof that, in average, less than 50% of tiles in domino tiling of 2-by-n re...

For every tiling of a $2\times (n-2)$ strip I'll need two horizontal dominoes for case (1) and two vertical dominoes for case (2); this is a tie. … But for case (3), I need two horizontal dominoes and only one vertical domino for each tiling of a $2\times (n-3)$ strip. So I'm going to need to buy more dominoes from Harry than from Victoria. …
Timothy Chow's user avatar
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3 votes

An "incomplete" tiling?

If you're hoping for a nice formula, or for a fast algorithm that gives you the number exactly, then you're probably out of luck. You're asking for the coefficients of the matching polynomial of a gri …
Timothy Chow's user avatar
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