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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 …
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. …
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. …
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 …
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. …
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 …