Average distance from a random point to N points in a circle

hpinvent · Jan 10, 2009

How can I calculate the distance from a random point IN a circle to N points uniformly distributed within the circle? Would the average distance decrease with N?

mathman · Jan 10, 2009

hpinvent said:

How can I calculate the distance from a random point IN a circle to N points uniformly distributed within the circle? Would the average distance decrease with N?

If the coordinates of the random point and the N points are given, the calculation is simple, but tedious for large N.

The average distance (for a fixed initial point) would not change with increasing N, although the standard deviation would get smaller.

Average distance from a random point to N points in a circle

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Average distance from a random point to N points in a circle

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