
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 20131002 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/sfwritten Please read it before posting.

