Eight points are selected at random from the interior of a unit circle.
What is the probability that these eight points constitute the eight vertices of a convex octagon?
If the random points were anywhere in a square rather than a circle the probability would be lower (about 1 in 137 rather than the 1 in 114).
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That's 3658 hits in 500,000 trials for about 1 in 137 or 0.73%.
Results from commenting out the requirement that points be within the unit circle:
' Do
xp = 2 * Rnd(1) - 1
yp = 2 * Rnd(1) - 1
' Loop Until xp * xp + yp * yp < 1
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Posted by Charlie
on 2016-08-25 09:34:10 |
Just for curiosity, random points in a square
