On Mon, Aug 30, 2010 at 6:32 PM, <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.
Not possible. Rotate the coordinates so that one ray passes through (0,0,1). Then the other 4 must all have negative z-components. Project these 4 onto the X-Y plane. The angle between two of these projections must be right or acute. The angle between the original rays whose projections form a nonobtuse angle will also form a nonobtuse angle. Andy