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Topic: cotpi 69 - Black and white plane
Replies: 26   Last Post: Oct 9, 2013 10:23 AM

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William Elliot

Posts: 1,533
Registered: 1/8/12
Re: cotpi 69 - Black and white plane
Posted: Oct 3, 2013 3:55 AM
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On Wed, 2 Oct 2013, cotpi wrote:

> How can you construct a plane where every point is coloured
> either black or white such that two points of the same colour
> are never a unit distance apart?


You cannot. Let ABC be an equilateral triangle with unit sides.

Pick a color for A, black for example.
Then B and C have to be colored white
and they're at a unit distance. Oh my.




Date Subject Author
10/2/13
Read cotpi 69 - Black and white plane
cotpi
10/2/13
Read Re: cotpi 69 - Black and white plane
Pubkeybreaker
10/2/13
Read Re: cotpi 69 - Black and white plane
quasi
10/2/13
Read Re: cotpi 69 - Black and white plane
Mike Terry
10/6/13
Read Re: cotpi 69 - Black and white plane
David Bernier
10/6/13
Read Re: cotpi 69 - Black and white plane
David Bernier
10/6/13
Read Re: cotpi 69 - Black and white plane
David Bernier
10/6/13
Read Re: cotpi 69 - Black and white plane
David Bernier
10/6/13
Read Re: cotpi 69 - Black and white plane
David Bernier
10/6/13
Read Re: cotpi 69 - Black and white plane
quasi
10/6/13
Read Re: cotpi 69 - Black and white plane
quasi
10/6/13
Read Re: cotpi 69 - Black and white plane
David Bernier
10/6/13
Read Re: cotpi 69 - Black and white plane
David Bernier
10/6/13
Read Re: cotpi 69 - Black and white plane
quasi
10/6/13
Read Re: cotpi 69 - Black and white plane
David Bernier
10/9/13
Read Re: cotpi 69 - Black and white plane
Phil Carmody
10/9/13
Read Re: cotpi 69 - Black and white plane
David Bernier
10/2/13
Read Re: cotpi 69 - Black and white plane
Eric Lafontaine
10/2/13
Read Re: cotpi 69 - Black and white plane
Michael F. Stemper
10/2/13
Read Re: cotpi 69 - Black and white plane
quasi
10/2/13
Read Re: cotpi 69 - Black and white plane
quasi
10/2/13
Read Re: cotpi 69 - Black and white plane
Haran Pilpel
10/2/13
Read Re: cotpi 69 - Black and white plane
quasi
10/2/13
Read Re: cotpi 69 - Black and white plane
quasi
10/2/13
Read Re: cotpi 69 - Black and white plane
Ted Schuerzinger
10/2/13
Read Re: cotpi 69 - Black and white plane
Mark Brader
10/3/13
Read Re: cotpi 69 - Black and white plane
William Elliot

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