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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: 108
Registered: 9/5/13
Re: cotpi 69 - Black and white plane
Posted: Oct 2, 2013 3:12 PM
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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?

How about the Gaussian integers?

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
Please read it before posting.


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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