Search: keyword:hardsort
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| BP323 |
| Jigsaw puzzle pieces can be assembled into a square vs. jigsaw puzzle pieces cannot be assembled into a square. |
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| BP335 |
| Tessellates the plane vs. does not tessellate the plane. |
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COMMENTS
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EX7152 is an example of a shape than can be stretched in such a way that it no longer tessellates the plane. This is a property that is only exhibited by shapes that tessellate with rotated copies of themselves. - Leo Crabbe, Mar 05 2021 |
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CROSSREFS
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Adjacent-numbered pages:
BP330 BP331 BP332 BP333 BP334 * BP336 BP337 BP338 BP339 BP340
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KEYWORD
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nice, stretch, unstable, math, hardsort, creativeexamples, proofsrequired, perfect, pixelperfect, traditional
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CONCEPT
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infinite_plane (info | search),
tessellation (info | search),
tiling (info | search)
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WORLD
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shape [smaller | same | bigger]
zoom in left (fill_shape)
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AUTHOR
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Aaron David Fairbanks
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| BP344 |
| Shape can tile itself vs. shape cannot tile itself. |
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COMMENTS
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Left examples are sometimes called "rep-tiles."
The tiles all must be the same size. More specifically, all left examples can tile themselves only using scaled down and rotated versions of themselves with all tiles the same size. Right examples cannot tile themselves using scaled down rotated versions of themselves or even reflected versions of themselves with all tiles the same size.
Without the puzzle piece-like shape EX4120 on the right side the current examples also allow the solution "shape can tile with itself so as to create a parallelogram vs. shape cannot tile with itself so as to create a parallelogram." |
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CROSSREFS
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See BP532 for a version with fractals.
Adjacent-numbered pages:
BP339 BP340 BP341 BP342 BP343 * BP345 BP346 BP347 BP348 BP349
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EXAMPLE
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Go to https://oebp.org/files/yet.png for an illustration of how some left-sorted shapes tile themselves. |
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KEYWORD
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hard, nice, precise, notso, unstable, math, hardsort, creativeexamples, proofsrequired, perfect, traditional
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CONCEPT
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recursion (info | search),
self-reference (info | search),
tiling (info | search),
imagined_shape (info | search),
imagined_entity (info | search)
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WORLD
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shape [smaller | same | bigger]
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AUTHOR
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Aaron David Fairbanks
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| BP532 |
| Self-tiling fractal using one size of tile vs. does not tile itself with a single size of itself. |
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| BP853 |
| Prime knot vs. composite knot. |
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| BP860 |
| Finitely many copies of the shape can be arranged such that they are locked together vs. not so. |
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CROSSREFS
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This is a generalisation of BP861.
Adjacent-numbered pages:
BP855 BP856 BP857 BP858 BP859 * BP861 BP862 BP863 BP864 BP865
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KEYWORD
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hard, nice, stub, precise, stretch, unstable, hardsort, challenge, creativeexamples, perfect, pixelperfect
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CONCEPT
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tiling (info | search)
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WORLD
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fill_shape [smaller | same | bigger]
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AUTHOR
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Leo Crabbe
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| BP863 |
| Two shapes can tessellate the plane together vs. not so. |
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| BP1005 |
| The collection of dot clumps has the same numerical property as each of the dot clumps vs. not so. |
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