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

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Re: Random Triangle Problem
Posted: Jul 30, 1997 12:14 PM

Just wondering:

Suppose you are given a "random" triangle.
It does have a longest side. Call it n, and its enpoints a and b.
Call the third point of the triangle c.
c
/ \
/ \
/________ a n b

What is wrong with the assumption that the distances from a to c and the
distances from b to c are independent, and that the distance from a to c
(and likewise the distance from b to c) is uniformly distributed over (0,n]?
(ie the ratios of the two other sides to the longest side should be
uniformly distributed over (0,1])
These seem like viable, intuitive assumptions about a random triangle.
If not, then in what way should the lengths of the sides be dependent?

The reason I ask is because these simple assumptions alone (not
assumptions involving random points in R^2 and the like) allow the
construction of a measure space of triangles that does not give 3/4 as
the probability of obtuseness. If 3/4 is the accepted answer, then this
implies that a "random" triangle follows nonuniform distributions in the
ratios of its sides. This doesn't make sense to me.

Kris Schmidt

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