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

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Robert Hill

Posts: 529
Registered: 12/8/04
Re: Random Triangle Problem
Posted: Jul 24, 1997 11:05 AM
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In article <33D6B081.35ED@navpoint.com>, "T. Sheridan" <stop---junk---mail---sparky@navpoint.com> writes:
> I think the problems is you need to know if the region is bounded.
> If it's on an infinite plane then the probability of the triangle being
> obtuse aproaches 1.
>
> The reason is simple. Just imagine two points are picked. (A,B) They
> always form a line. [AB} Now there are two perpendiculars extending
> from each point.
> . * .
> | |
> | |
> * | * | *
> | |
> A------------------B
> | |
> | * |
> | |
> . * |
>
>
> They define two half planes wherein the third point will create an
> obtuse. That's virtually all the area. Within the two perpendiculars
> There is a small band of area close th ethe line where the triangle can
> also be obtuse but the rest is acute.
>
> If the region is bounded then the calculs gets miserable.
>
> Unless I'm just wrong :)


The "small band" is circular.

As I've pointed out in reply to Tony Richards in this thread, all variants
of this approach make an obtuse angle at the third vertex less likely than
at the other two, and are therefore presumably wrong.

I think that your version (which is a bit less sophisticated than his)
is a disguised form of the following old paradox: two people each
choose a positive integer "at random" (with an assumed uniform distribution).
Whatever the first person's number, almost all possibilities for the second
person's number are larger, therefore with probability one the second person's
number is larger. But you could say the same for the first person's number.

--
Robert Hill

University Computing Service, Leeds University, England

"Though all my wares be trash, the heart is true."
- John Dowland, Fine Knacks for Ladies (1600)






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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