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

 Messages: [ Previous | Next ]
 Bill Taylor Posts: 1,909 Registered: 12/8/04
Re: Random Triangle Problem
Posted: Aug 4, 1997 10:33 PM

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

|> To say the same thing
|> slightly differently, it was not for me obvious a priori that it was right
|> to assume the vertices to be independently and uniformly distributed on the
|> circumcircle. Why should there not be a tendency for them to be a bit
|> bunched, or a bit dispersed?

Indeed, good point. A priori it is not at all obvious they should be
independent. But closer inspection reveals that it is merely a somewhat
disguised form of the angles-at-the-centre-and-at-the-circumference result.

|> 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...

-------------------------------------------------------------------------------
Bill Taylor W.Taylor@math.canterbury.ac.nz
-------------------------------------------------------------------------------
There was never a problem so difficult, but that if you just
looked at it in the right way - it became even more difficult!
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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