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 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)

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 re(4): Not faster, simpler, or better | Comment 14 of 18 |
(In reply to re(3): Not faster, simpler, or better by ed bottemiller)

There are the same number of points inside a triangle as on the triangle's perimeter, but there still is a zero probability of a random point in the square being on the perimeter of the triangle.

Think of the one-to-one correspondence of the set of integers with the set of integers that are divisible by 1,000,000. There are the same number: aleph-null. But if you take an integer at random, it's not likely to be divisible by 1,000,000. In the aleph-1 case of lines vs areas, it's even more drastic.

 Posted by Charlie on 2008-03-18 17:01:00

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