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

 Messages: [ Previous | Next ]
 Keith Ramsay Posts: 1,745 Registered: 12/6/04
Re: Random Triangle Problem
Posted: Aug 2, 1997 11:46 AM

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

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 Mike Housky
7/21/97 Bill Taylor
7/22/97 tony richards
7/24/97 Brian M. Scott
7/23/97 tony richards
7/23/97 T. Sheridan
7/24/97 Bill Taylor
7/24/97 Bill Taylor
7/25/97 Ilias Kastanas
7/23/97 Robert Hill
7/23/97 tony richards
7/27/97 Bill Taylor
7/24/97 Robert Hill
7/28/97 tony richards
7/30/97 Bill Taylor
7/30/97 tony richards
8/1/97 Bill Taylor
7/24/97 Robert Hill
7/24/97 Robert Hill
7/24/97 Robert Hill
7/25/97 Robert Hill
7/30/97 Bill Taylor
8/1/97 Charles H. Giffen
8/1/97 John Rickard
8/1/97 Chris Thompson
8/1/97 John Rickard
8/4/97 Bill Taylor
8/5/97 John Rickard
7/25/97 Charles H. Giffen
7/25/97 Charles H. Giffen
7/28/97 Hauke Reddmann
7/28/97 Robert Hill
7/28/97 Robert Hill
7/28/97 Robert Hill
7/29/97 tony richards
7/30/97 Keith Ramsay
7/30/97 tony richards
8/2/97 Keith Ramsay
7/29/97 tony richards
8/4/97 Bill Taylor
8/5/97 Charles H. Giffen
8/6/97 Terry Moore
8/7/97 Terry Moore
8/16/97 Kevin Brown
8/17/97 Kevin Brown
7/30/97 Robert Hill
7/31/97 tony richards
8/6/97 Terry Moore
7/31/97 John Rickard
7/30/97 Robert Hill
7/31/97 Robert Hill
7/31/97 Robert Hill
8/1/97 R J Morris
8/4/97 Robert Hill
8/4/97 Robert Hill
8/5/97 Charles H. Giffen
8/6/97 Robert Hill