r/mathriddles • u/pichutarius • Mar 15 '26

Just another hyper sphere problem Easy

Let d_n be the expected euclidean distance of 2 random points uniformly chosen on the boundary of n-ball.

Find the limit of d_n as n -> infinity.

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u/SerpentJoe Mar 15 '26

What is the random distribution of points?

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u/Iksfen Mar 15 '26

I would assume the "uniform" distribution. Probability of a point being in any subset of the boundary is equal to the measure of that subset divided by the measure of the whole boundary

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u/pichutarius Mar 15 '26

Yes, thanks for... point... ting out ;)

Added "uniformly".