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Topic: Random Triangle Problem
Replies: 57   Last Post: Aug 17, 1997 10:51 PM

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Keith Ramsay

Posts: 1,745
Registered: 12/6/04
Re: Random Triangle Problem
Posted: Aug 2, 1997 11:46 AM
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I found an article in the American Math Monthly, vol 103 #4 p.308,
which discusses the problem and gives a number of references.

The probability that three points picked uniformly and independently
from a disk form an obtuse triangle is 9/8-4/pi^2=.7187.... It's been
conjectured that this is the shape which gives the lowest probability
of obtuseness if you pick three points randomly and uniformly from it.
(As usual, one can take any radius, or let the radius go to infinity,
without changing the answer.) A Gaussian distribution on the plane,
as has been noted, gives the answer 3/4=.75.

The probability of obtuseness of the triangle formed by three points
taken at random from an n-ball tends toward zero as n goes to
infinity. Such a triangle becomes ever more likely to approximate
an equilateral triangle.

The problem of determining the probability of obtuseness of the
triangle formed by three points picked at random from a plane (without
specifying what that's supposed to mean) was included in C.L.Dodgson's
(Lewis Carroll's) "Pillow Problems", problems he suggested thinking
about before going to sleep.

Keith Ramsay There is nothing on this earth, and little beyond it,
kramsay@aol.com that nobody ever denounces. -- Matt McIrvin






Date Subject Author
7/16/97
Read Random Triangle Problem
Mike Housky
7/21/97
Read Re: Random Triangle Problem
Bill Taylor
7/22/97
Read Re: Random Triangle Problem
tony richards
7/24/97
Read Re: Random Triangle Problem
Brian M. Scott
7/23/97
Read Re: Random Triangle Problem
tony richards
7/23/97
Read Re: Random Triangle Problem
T. Sheridan
7/24/97
Read Re: Random Triangle Problem
Bill Taylor
7/24/97
Read Re: Random Triangle Problem
Bill Taylor
7/25/97
Read Re: Random Triangle Problem
Ilias Kastanas
7/23/97
Read Re: Random Triangle Problem
Robert Hill
7/23/97
Read Re: Random Triangle Problem
tony richards
7/27/97
Read Re: Random Triangle Problem
Bill Taylor
7/24/97
Read Re: Random Triangle Problem
Robert Hill
7/28/97
Read Re: Random Triangle Problem
tony richards
7/30/97
Read Re: Random Triangle Problem
Bill Taylor
7/30/97
Read Re: Random Triangle Problem
tony richards
8/1/97
Read Re: Random Triangle Problem
Bill Taylor
7/24/97
Read Re: Random Triangle Problem
Robert Hill
7/24/97
Read Re: Random Triangle Problem
Robert Hill
7/24/97
Read Re: Random Triangle Problem
Robert Hill
7/25/97
Read Re: Random Triangle Problem
Robert Hill
7/30/97
Read Re: Random Triangle Problem
Bill Taylor
8/1/97
Read Re: Random Triangle Problem
Charles H. Giffen
8/1/97
Read Re: Random Triangle Problem
John Rickard
8/1/97
Read Re: Random Triangle Problem
Chris Thompson
8/1/97
Read Re: Random Triangle Problem
John Rickard
8/4/97
Read Re: Random Triangle Problem
Bill Taylor
8/5/97
Read Re: Random Triangle Problem
John Rickard
7/25/97
Read Re: Random Triangle Problem
Charles H. Giffen
7/25/97
Read Re: Random Triangle Problem
Charles H. Giffen
7/28/97
Read Re: Random Triangle Problem
Hauke Reddmann
7/28/97
Read Re: Random Triangle Problem
Robert Hill
7/28/97
Read Re: Random Triangle Problem
Robert Hill
7/28/97
Read Re: Random Triangle Problem
Robert Hill
7/29/97
Read Re: Random Triangle Problem
tony richards
7/30/97
Read Re: Random Triangle Problem
Keith Ramsay
7/30/97
Read Re: Random Triangle Problem
tony richards
8/2/97
Read Re: Random Triangle Problem
Keith Ramsay
7/29/97
Read Re: Random Triangle Problem
tony richards
8/4/97
Read Re: Random Triangle Problem
Bill Taylor
8/5/97
Read Re: Random Triangle Problem
Charles H. Giffen
8/6/97
Read Re: Random Triangle Problem
Terry Moore
8/7/97
Read Re: Random Triangle Problem (LONG summary)
Terry Moore
8/16/97
Read Re: Random Triangle Problem (LONG summary)
Kevin Brown
8/17/97
Read Re: Random Triangle Problem (LONG summary)
Kevin Brown
7/30/97
Read Re: Random Triangle Problem
Muad'dib
7/30/97
Read Re: Random Triangle Problem
Robert Hill
7/31/97
Read Re: Random Triangle Problem
tony richards
8/6/97
Read Re: Random Triangle Problem
Terry Moore
7/31/97
Read Re: Random Triangle Problem
John Rickard
7/30/97
Read Re: Random Triangle Problem
Robert Hill
7/31/97
Read Re: Random Triangle Problem
Robert Hill
7/31/97
Read Re: Random Triangle Problem
Robert Hill
8/1/97
Read Re: Random Triangle Problem
R J Morris
8/4/97
Read Re: Random Triangle Problem
Robert Hill
8/4/97
Read Re: Random Triangle Problem
Robert Hill
8/5/97
Read Re: Random Triangle Problem
Charles H. Giffen
8/6/97
Read Re: Random Triangle Problem
Robert Hill

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