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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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 Eric Lafontaine Posts: 1 Registered: 10/2/13
Re: cotpi 69 - Black and white plane
Posted: Oct 2, 2013 2:40 PM

On 2013-10-02 18:17, 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?

I must have missed something?
Place an equilateral triangle anywhere on the plane
Set one of its corners white, another one black
What do you do with the third one?

Next question: what kind of plane makes equilateral triangles impossible?
Assuming of course that "a plane" is infinite, and not constricted in a

--
Éric Lafontaine

Date Subject Author
10/2/13 cotpi
10/2/13 Pubkeybreaker
10/2/13 quasi
10/2/13 Mike Terry
10/6/13 David Bernier
10/6/13 David Bernier
10/6/13 David Bernier
10/6/13 David Bernier
10/6/13 David Bernier
10/6/13 quasi
10/6/13 quasi
10/6/13 David Bernier
10/6/13 David Bernier
10/6/13 quasi
10/6/13 David Bernier
10/9/13 Phil Carmody
10/9/13 David Bernier
10/2/13 Eric Lafontaine
10/2/13 Michael F. Stemper
10/2/13 quasi
10/2/13 quasi
10/2/13 Haran Pilpel
10/2/13 quasi
10/2/13 quasi
10/2/13 Ted Schuerzinger