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From: jfp@emory.UUCP
Newsgroups: net.math
Subject: Re: Re(2): circle probability (spoiler)
Message-ID: <1143@emory.UUCP>
Date: Wed, 21-Sep-83 14:37:59 EDT
Article-I.D.: emory.1143
Posted: Wed Sep 21 14:37:59 1983
Date-Received: Thu, 22-Sep-83 02:39:45 EDT
References: <38@ism780.UUCP>
Organization: Math & Computer Science, Emory University, Atlanta
Lines: 18

Soon after posting the problem I found, by coincidence, a problem
in The Mathematical Intelligencer, Volume 5, No. 3, asking for the
probability of n points chosen at random being within a small circle
of radius r. The editor noted that the N points lying within a
hemisphere on the surface of an n-sphere had been solved by
J.G. Wendel, the answer being
                    n-1
            1      ----
          -----    \       (  N - 1  )
           N-1     /       (    k    )
          2        ----
                   k = 0
Unfortunately there was no reference to the proof.
If anyone knows of the reference, or has their own proof,
I'd be very interested to hear. I like Jim Bailey's proof
in the case n = 2, and I also don't follow Silvio Levy's complaint.
---------
John Pedersen.  {sb1,akgua}!emory!jfp