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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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 Michael F. Stemper Posts: 122 Registered: 9/5/13
Re: cotpi 69 - Black and white plane
Posted: Oct 2, 2013 3:12 PM

On 10/02/2013 01:40 PM, Eric Lafontaine wrote:
> 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?

That was my reaction, as well.

> Next question: what kind of plane makes equilateral triangles impossible?

Is there something similar to the Gaussian integers, but for rationals?
In other words, {a+bi | a,b in Q}
You can't have equilateral triangles in whatever this would be called,
but would it have the property initially specified?

--
Michael F. Stemper
The FAQ for rec.arts.sf.written is at:
http://leepers.us/evelyn/faqs/sf-written

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