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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 5, 1997 7:29 AM

Bill Taylor (mathwft@math.canterbury.ac.nz) wrote:
: I agree with the epsilon-squared, but the following paragraph purporting
: to explain the epsilon for the normal case seemed just a wee bit glib - I

Well, it wasn't actually meant to explain it; I was just making bald
assertions.

Will a lower bound do? (I'm sure that probability/epsilon does tend
to a limit as epsilon tends to 0, but it's easier just to prove that
it's bounded below.)

In the following, eps = epsilon, and c1, c2, etc. are positive
constants. Assume eps < pi/2.

With probability > c1, A and B are within distance 1 of the origin but
AB > 1. Consider the rhombus with A and B at opposite corners, and
interior angle eps at A and B. The area of the rhombus is
AB tan(eps/2) > c2 eps. The rhombus lies entirely within distance c3
of the origin, so the probability density for C is > c4 within the
rhombus. Thus the probability that C lies within the rhombus is
> c5 eps; if it does, then the directions of all three lines are
within eps of each other.

--
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