Every point in 3Dspace is colored either red, green or blue. Let R (resp. G and B) be the set of distances between red (resp. green and blue) points. Prove that at least one of R, G, or B, consists of all the nonnegative real numbers.
(In reply to
re: Solution (Some details required) by JLo)
The only way that
sphere(N,b) ^ sphere(M,g) ^ sphere(L,r)
would be empty is if b is greater than the
diameter of the space circle
sphere(M,g) ^ sphere(L,r)
This would occur if
b > 2h,
g^2 = x^2 + h^2, and
r^2 = (rx)^2 + h^2
or
b > g*sqrt(4  [g/r]^2) > g
A contradiction since b <= g.

Posted by Bractals
on 20060828 16:17:34 