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Random Numbers, Obtuse Triangles, and π

Author:
David Richeson
Topic:
Numbers, Triangles
The probability that two values a and b chosen at random between 0 and 1 will yield an obtuse triangle with side lengths 1, a, and b is . Geometrically, being an obtuse triangle corresponds to the point (a,b) being inside the unit circle but above the line . (Source: Ingenuity in Mathematics by Ross Honsberger.)

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