# Difference between revisions of "Tiling"

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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"] |

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+ | ''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 22:42, 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.