All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Three Points in a Square (Posted on 2008-03-17)
Three points are chosen at random inside a square. Each point is chosen by choosing a random x-coordinate and a random y-coordinate.

A triangle is drawn with the three random points as the vertices. What is the probability that the center of the square is inside the triangle?

 No Solution Yet Submitted by Brian Smith Rating: 3.2000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 Not faster, simpler, or better | Comment 9 of 18 |
The average area of a random triangle in the unit square is 11/144, significantly less than 1/4.   This value comes from Mathworld (see my earlier reference).  It is not surprising that the probability of a random triangle containing the center of the square is a lot bigger then the average area of a random triangle.  For instance, the maximum area of a triangle inside a square is 1/2 (just as Ed suggested).    Consider the set of all embedded triangles whose area is 1/2.  Their average area of 1/2 is a lot less than the probability that they contain the center, which turns out to be 100%.

Edited on March 18, 2008, 12:55 am
 Posted by Steve Herman on 2008-03-18 00:54:09

Please log in:
 Login: Password: Remember me: Sign up! | Forgot password

 Search: Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information