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

 Messages: [ Previous | Next ]
 John Rickard Posts: 55 Registered: 12/6/04
Re: Random Triangle Problem
Posted: Aug 1, 1997 1:59 PM

Chris Thompson (cet1@cus.cam.ac.uk) wrote:
: Can one extend this to show that the distribution of triangle shapes
: (not just the probability of obtuseness) is the same for three points
: picked independantly from the circular normal distribution as for three
: lines with independant uniformly distributed orientations [Bill Taylor's
: interpretation of the original problem]?

The distribution of shapes is different. For small epsilon, the
probability that the directions of the lines are all within epsilon of
each other is roughly proportional to epsilon with the normal
distribution, but to epsilon^2 with Bill Taylor's distribution; this
isn't hard to see.

To put it another way, given that the angle at A is very small, with
the normal distribution it's probable that one of the other angles
will also be small, but B and C won't be especially close; with the
line directions independent it's probable that B and C will be close
(compared with their distance from A), but neither of the other angles
will be especially small.

--
John Rickard

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