Counterintuitive Properties of High Dimensional Space (2018)

The distance between two uniform random points on an n-sphere clusters around the equator. The article shows a histogram of the distribution in fig. 11. While it looks Gaussian, it is more closely related to the Beta distribution. I derived it in my notes, as (surprisingly) I could not find it easily in literature:

https://xn--2-umb.com/21/n-sphere

> The distance between two uniform random points on an n-sphere clusters around the equator.

This sentence makes no sense to me.