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Results tagged with tiling
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user 135257
For questions about mathematical tiling.
11
votes
Polyomino that can cover an arbitrarily large square but not the entire plane
those $P_x$, namely that $P_x$ only contains placements valid on the cell $x$, we notice that we just proved the existence of a placement that is valid on every single cell of the plane, also known as a tiling …
- 1,016
49
votes
Accepted
Polyomino that can cover an arbitrarily large square but not the entire plane
Now we can construct a tiling as follows: Tile the central $1 \times 1$ square just like the tilings from $S^1$ do, then tile the central $3 \times 3$ square like the tilings from $S^2$ do, and so on. … By our choice of $S^i$, each extension agrees with the previous ones, and we end up with a valid tiling of the entire plane. …
- 1,016