Difference between revisions of "Tiling"

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(notes)
 
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 chapter 7 from Martin Gardner's book "Penrose Tiles to Trapdoor Ciphers"]
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[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>
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A Penrose tiling can, of course, always be colored with four colors so
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that no two tiles of the same color share a common edge.  Can it always be
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colored with three? It can be shown, Conway said, from the local isomorphism
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theorem, that if any Penrose tiling is three-colorable, all are, but so far
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no one has proved that any infinite Penrose tiling is three-colorable.</pre>
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[[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.