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Article #2364Re: Random Points on a Sphere
From: Matthew J. Freeman
Date: Sun, 22 Nov 1992 02:01
Date: Sun, 22 Nov 1992 02:01
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isaak@aurora.com (Mark Isaak) writes: >This problem has me stumped: >Four points are randomly selected from the surface of a sphere. >What is the probability that all four lie in the same hemisphere? >How about for 5 points? 6? more? >-- >Mark Isaak "Every generation thinks it has the answers, and every >isaak@aurora.com generation is humbled by nature." - Philip Lubin Think of placing 4 points on an otherwise featureless sphere. The first three points will define a hemisphere no matter where they are placed, and the probability that the fourth is in the same hemisphere is 1/2. For 5 points, the probability goes down to (1/2)*(1/2). Unless all of the points lie on a great circle ... -Matt Freeman hubcap.clemson.edu
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Newsgroups: rec.puzzles Path: arc1-ca.pugleaf.net!sparky!uunet!gatech!hubcap!mjfreem From: mjfreem@hubcap.clemson.edu (Matthew J. Freeman) Subject: Re: Random Points on a Sphere Message-ID: <1992Nov22.020105.27398@hubcap.clemson.edu> Organization: Clemson University References: <1992Nov20.181709.13148@aurora.com> Date: Sun, 22 Nov 1992 02:01:05 GMT Lines: 21