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Results tagged with tiling
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user 3106
For questions about mathematical tiling.
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.
. …
- 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. …
- 82.6k
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. …
- 82.6k
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 …
- 82.6k
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 …
- 82.6k
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. …
- 82.6k
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 …
- 82.6k