Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Robert Hill Posts: 529 Registered: 12/8/04
Re: Random Triangle Problem
Posted: Jul 24, 1997 11:05 AM

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 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