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

 Messages: [ Previous | Next ]
 tony richards Posts: 164 Registered: 12/8/04
Re: Random Triangle Problem
Posted: Jul 28, 1997 4:18 AM

eclrh@sun.leeds.ac.uk (Robert Hill) wrote:
(snip)
Tony Richards wrote:
>>
>> So my final answer is 0.75 + pi/48, and not 0.75.<< (typo corrected)

>
>Considering separately the three terms for an obtuse angle at the first, second
>and third points, I get that (conditionally on x) the probabilities are
>
>obtuse at first point: 1/2
>obtuse at second point: 1/2 - |x|/(2L)
>obtuse at third point: pi |x|^2 / (16L^2)
>all angles acute: |x|/(2L) - pi |x|^2
>
>which after integration over x become respectively
>
>obtuse at first point: 1/2
>obtuse at second point: 1/4
>obtuse at third point: pi/48
>all angles acute: 1/4 - pi/48
>
>Surely a correct answer would give equal probabilities for obtuseness at
>the three vertices.

First, thanks for taking the trouble to read my post and point out the typos.
I stick by my answer, 0.75+pi/48.

The reason that the probabilities for obtuse at each vertex are different
must be because of the bias introduced as a result of placing the origin at
the first point, making its location non-random in the plane (which,
by making L-> infinity, becomes infinite eventually).
The other two points are then randomly located with respect to this
first fixed point.
So it is not surprising that the probabilities for each vertex
are different.

--
Tony Richards 'I think, therefore I am confused'
Rutherford Appleton Lab '
UK '

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