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

 Messages: [ Previous | Next ]
 Hauke Reddmann Posts: 202 Registered: 12/12/04
Re: Random Triangle Problem
Posted: Jul 28, 1997 4:59 AM

Charles H. Giffen (chg4k@virginia.edu) wrote:
:
: An argument involving the incircle can be given, but one must be
: more careful (since one is dealing with a distribution conditional
: on the requirement that the three points yield a triangle with the
: circle as its incircle) -- the calculations are rather more tedious,
: but do produce the same result: P(obtuse) = 3/4.
:
Noted the same thing.
BTW, as a chemist a "mixing triangle" (to draw three quantities
for which x+y+z=1) is well known to me. If you use this on
random triangle angles, then outcircle and incircle immediately
give P=3/4. (Shall I elaborate?)
But let's try to complicate things as much as possible :-)
Assume random quantities of y=s/R and x=r/R, where s,r,R are half
0<x<1/2. y is bound by the equation (y^2+x^2-10x-2)^2<(1-2x)^3*4.
(A triangle cannot be "more than isosceles")
The dividing line of the bounded y-x-area is y=2+x. (Below are
the obtuse, above the acute) Can anybody compute the two
elliptic integrals arising?
--
Hauke Reddmann <:-EX8
fc3a501@math.uni-hamburg.de PRIVATE EMAIL
fc3a501@rzaixsrv1.rrz.uni-hamburg.de BACKUP
reddmann@chemie.uni-hamburg.de SCIENCE ONLY

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