perplexus.info :: Just Math : Spacy colors

Spacy colors (Posted on 2006-08-25)

Every point in 3D-space 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 non-negative real numbers.

Submitted by JLo

Rating: 4.0000 (2 votes)

Solution: (Hide)

There is nothing I could add to Bractals excellent solution:
1. Main proof
2. Proof of a geometric detail which ensures that the set sphere(N,b) ^ sphere(M,g) ^ sphere(L,r) of case C is non-empty.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Can this be generalized...	JLo	2006-08-28 16:42:45
re(2): Solution (Some details required)	Bractals	2006-08-28 16:17:34
re: Solution (Some details required)	JLo	2006-08-28 11:02:51
re(2): Solution (Some details required)	Bractals	2006-08-27 20:13:52
re: Solution (Some details required)	Richard	2006-08-27 16:06:19
Solution (Some details required)	Bractals	2006-08-25 17:23:07
Handwaving proof	vswitchs	2006-08-25 16:57:44
re: treja vu - solution	Charlie	2006-08-25 15:58:03
re: treja vu - no solution	vswitchs	2006-08-25 15:50:15
treja vu - solution	Leming	2006-08-25 14:54:16

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