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

 Messages: [ Previous | Next ]
 Charles H. Giffen Posts: 796 Registered: 12/8/04
Re: Random Triangle Problem
Posted: Aug 5, 1997 12:32 PM

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

[snip]
> |> 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...
>

[snip]

Since the probability is (more or less evidently) less than 3/4 for
vertices i.i.d. uniformly in a square and since the probablility
approaches 1 as the (1 x 1) square is stretched to become a (1 x L)
rectangle (where L --> \infty). If one believes in continuity of
the resulting probability as a function of L, then the answer is
"Yes, there is a bounded rectangle for which the probability = 3/4."
Indeed, such L isn't very big at all.

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