Sorry, I should have said more clearly...

来源: Commentate 于 2008-05-02 12:40:41 [] [旧帖] [给我悄悄话] 阅读数 : (480 bytes)
回答: 3/4 由 Commentate 于 2008-05-02 07:13:13

I understand that it is impossible to defind a uniform probability on the plane. But this problem still has an answer.

First, any triangle is inscribed in a unique circle, and the triangle is obtuse if and only if the three points are located on a semi-circle.

Infinite plane is equivalently converted into finite circle.

It is not hard to show, if you drop three points randomly on a circle, the probability that they are ona same semi-circle is 3/4.

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• 不同意 -说了就走- ♂ 给 说了就走 发送悄悄话 (131 bytes) () 05/05/2008 postreply 16:47:07

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