That's quite nice --- though SBG did inadvertantly hint at the answer by asking for an explanation! Here's my stab at the impossibility: given some arrangement of rays R1,...,Rn meeting at mutually obtuse angles in the origin, let F1,...,Fn denote their perpendicular planes through the orgin. Evidently R2,...,Rn lie on the far side of F1 from R1; similarly R3,...,Rn lie in the acute slice between F1 and F2; and R4,...,Rn lie in the acute trihedron formed by F1,F2,F3. Therefore n <= 4. Fred Lunnon On 8/30/10, rcs@xmission.com <rcs@xmission.com> wrote:
Forwarded from SBG ...
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Date: Mon, 30 Aug 2010 12:08:08 -0700 Subject: Re: [math-fun] left vs. right From: "Stephen B. Gray" <stevebg@roadrunner.com>
Here's an exercise in 3D visualization. Given a point P, is it possible to construct FIVE rays coming out from P such that every ray makes an obtuse angle (>90 degrees) with every other one? (That's 10 angles that must be obtuse.) Explain your answer.
Steve Gray