You choose a random point, uniformly, within an equilateral triangle.
What's the average distance to the three sides?
I am nearly sure I have seen this problem elsewhere on this site.
The sum of the distances to the three sides of an equilateral is constant for all interior points. So the average is a third of this sum.
By choosing the centre of the triangle, the distance to each side is height/3.
Either way, for the triangle with unit side, the sum = sqrt(3)/2, so the average is sqrt(3)/6.
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Posted by goFish
on 2005-11-24 10:06:11 |
Old problem
