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Article #2358Re: Random Points on a Sphere
From: Matt Crawford
Date: Sun, 22 Nov 1992 05:02
Date: Sun, 22 Nov 1992 05:02
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That's two questions in a row dealing with randomly selected points in or on a sphere and neither one stated the distribution. Assuming uniform distribution, I have a half-answer to this one: >Four points are randomly selected from the surface of a sphere. >What is the probability that all four lie in the same hemisphere? If A is the solid angle subtended by 3 points on the sphere, the probability that a 4th point chosen uniformly on the sphere is, uh, cohemispheric with the 3 is 1-A/4pi if A!=2pi; 1 if A=2pi. (People who think it's needless to pick on the "name your distribution" nit may wish to compute the probability that a randomly selected chord of a circle is longer than the radius.) __________________________________________________________ Matt Crawford matt@severian.chi.il.us Java Man
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Newsgroups: rec.puzzles Path: arc1-ca.pugleaf.net!sparky!uunet!cs.utexas.edu!uwm.edu!linac!newsaintmail From: matt@severian.chi.il.us (Matt Crawford) Subject: Re: Random Points on a Sphere Message-ID: <SL9BJ1230@linac.fnal.gov> Sender: daemon@linac.fnal.gov (The Background Man) Nntp-Posting-Host: severian.chi.il.us Organization: The Chrome Plated Megaphone of Destiny References: <1992Nov20.181709.13148@aurora.com> Date: Sun, 22 Nov 1992 05:02:40 GMT Lines: 16