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

 Messages: [ Previous | Next ]
 Terry Moore Posts: 538 Registered: 12/8/04
Re: Random Triangle Problem
Posted: Aug 6, 1997 7:07 PM

In article <5s63dg\$pgj\$3@cantuc.canterbury.ac.nz>,
mathwft@math.canterbury.ac.nz (Bill Taylor) wrote:

> eclrh@sun.leeds.ac.uk (Robert Hill) writes:

> |> Another question: is there some interesting shape of bounded set
> |> such that the probability is 3/4 for vertices independently and
> |> uniformly distributed within that set?
>
> What an excellent question! I hope someone finds one. Meanwhile we
> need those n-gon results...

I thought it was an excellent question too, and sent an
answer by email. But it turns out to be a triviality.
Consider randomly selecting the vertices from a rectangle of
of height 1. The probability of obtuseness is obvioulsy a
continuous function of the length of the rectangle. As the
square and a long thin rectangle give probabilites either
side of 3/4, the intermediate value theorem says there is
a rectangle with the given property.

--

Terry Moore, Statistics Department, Massey University, New Zealand.

Theorems! I need theorems. Give me the theorems and I shall find the
proofs easily enough. Bernard Riemann

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