Tiling: Difference between revisions
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m (is any infinite Penrose tiling three-colorable?) |
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(some notes for collaborative study) | (some notes for collaborative study) | ||
[https://noisebridge.net/images/c/c2/Gardner_PenroseTilings1-1977.pdf | [https://noisebridge.net/images/c/c2/Gardner_PenroseTilings1-1977.pdf 2 chapters from Martin Gardner's book "Penrose Tiles to Trapdoor Ciphers"] | ||
''is this still unproven?'' -> <pre> | |||
A Penrose tiling can, of course, always be colored with four colors so | |||
that no two tiles of the same color share a common edge. Can it always be | |||
colored with three? It can be shown, Conway said, from the local isomorphism | |||
theorem, that if any Penrose tiling is three-colorable, all are, but so far | |||
no one has proved that any infinite Penrose tiling is three-colorable.</pre> | |||
[[Category:Math]] | [[Category:Math]] | ||
Revision as of 15:42, 2 January 2015
(some notes for collaborative study)
2 chapters from Martin Gardner's book "Penrose Tiles to Trapdoor Ciphers"
is this still unproven? ->
A Penrose tiling can, of course, always be colored with four colors so that no two tiles of the same color share a common edge. Can it always be colored with three? It can be shown, Conway said, from the local isomorphism theorem, that if any Penrose tiling is three-colorable, all are, but so far no one has proved that any infinite Penrose tiling is three-colorable.