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

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Charles H. Giffen

Posts: 796
Registered: 12/8/04
Re: Random Triangle Problem
Posted: Jul 25, 1997 1:32 PM
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Robert Hill wrote:
>
[ snip ]
> More seriously, there is an assumption here
> that the answer for a square is the same as "the answer" (whatever that means)
> for the whole plane. I have an informal argument (which I suspect
> I could make rigorous) that the probability of obtuseness for triangles whose
> vertices are uniformly distributed on any convex set of finite area is < 3/4,
> but I still suspect that the best answer for "a uniform distribution on
> the whole plane" is = 3/4. But that's like a statement about unicorns.
>


Your argument for any convex set cannot be correct. Consider
a very, very long and very, very thin rectangle. I claim that if
the vertices of a triangle are uniformly distributed in such a set,
then the probability of obtuseness approaches 1 -- and I invite you
to consider why this must (or might) be so.






Date Subject Author
7/16/97
Read Random Triangle Problem
Mike Housky
7/21/97
Read Re: Random Triangle Problem
Bill Taylor
7/22/97
Read Re: Random Triangle Problem
tony richards
7/24/97
Read Re: Random Triangle Problem
Brian M. Scott
7/23/97
Read Re: Random Triangle Problem
tony richards
7/23/97
Read Re: Random Triangle Problem
T. Sheridan
7/24/97
Read Re: Random Triangle Problem
Bill Taylor
7/24/97
Read Re: Random Triangle Problem
Bill Taylor
7/25/97
Read Re: Random Triangle Problem
Ilias Kastanas
7/23/97
Read Re: Random Triangle Problem
Robert Hill
7/23/97
Read Re: Random Triangle Problem
tony richards
7/27/97
Read Re: Random Triangle Problem
Bill Taylor
7/24/97
Read Re: Random Triangle Problem
Robert Hill
7/28/97
Read Re: Random Triangle Problem
tony richards
7/30/97
Read Re: Random Triangle Problem
Bill Taylor
7/30/97
Read Re: Random Triangle Problem
tony richards
8/1/97
Read Re: Random Triangle Problem
Bill Taylor
7/24/97
Read Re: Random Triangle Problem
Robert Hill
7/24/97
Read Re: Random Triangle Problem
Robert Hill
7/24/97
Read Re: Random Triangle Problem
Robert Hill
7/25/97
Read Re: Random Triangle Problem
Robert Hill
7/30/97
Read Re: Random Triangle Problem
Bill Taylor
8/1/97
Read Re: Random Triangle Problem
Charles H. Giffen
8/1/97
Read Re: Random Triangle Problem
John Rickard
8/1/97
Read Re: Random Triangle Problem
Chris Thompson
8/1/97
Read Re: Random Triangle Problem
John Rickard
8/4/97
Read Re: Random Triangle Problem
Bill Taylor
8/5/97
Read Re: Random Triangle Problem
John Rickard
7/25/97
Read Re: Random Triangle Problem
Charles H. Giffen
7/25/97
Read Re: Random Triangle Problem
Charles H. Giffen
7/28/97
Read Re: Random Triangle Problem
Hauke Reddmann
7/28/97
Read Re: Random Triangle Problem
Robert Hill
7/28/97
Read Re: Random Triangle Problem
Robert Hill
7/28/97
Read Re: Random Triangle Problem
Robert Hill
7/29/97
Read Re: Random Triangle Problem
tony richards
7/30/97
Read Re: Random Triangle Problem
Keith Ramsay
7/30/97
Read Re: Random Triangle Problem
tony richards
8/2/97
Read Re: Random Triangle Problem
Keith Ramsay
7/29/97
Read Re: Random Triangle Problem
tony richards
8/4/97
Read Re: Random Triangle Problem
Bill Taylor
8/5/97
Read Re: Random Triangle Problem
Charles H. Giffen
8/6/97
Read Re: Random Triangle Problem
Terry Moore
8/7/97
Read Re: Random Triangle Problem (LONG summary)
Terry Moore
8/16/97
Read Re: Random Triangle Problem (LONG summary)
Kevin Brown
8/17/97
Read Re: Random Triangle Problem (LONG summary)
Kevin Brown
7/30/97
Read Re: Random Triangle Problem
Muad'dib
7/30/97
Read Re: Random Triangle Problem
Robert Hill
7/31/97
Read Re: Random Triangle Problem
tony richards
8/6/97
Read Re: Random Triangle Problem
Terry Moore
7/31/97
Read Re: Random Triangle Problem
John Rickard
7/30/97
Read Re: Random Triangle Problem
Robert Hill
7/31/97
Read Re: Random Triangle Problem
Robert Hill
7/31/97
Read Re: Random Triangle Problem
Robert Hill
8/1/97
Read Re: Random Triangle Problem
R J Morris
8/4/97
Read Re: Random Triangle Problem
Robert Hill
8/4/97
Read Re: Random Triangle Problem
Robert Hill
8/5/97
Read Re: Random Triangle Problem
Charles H. Giffen
8/6/97
Read Re: Random Triangle Problem
Robert Hill

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