Counterintuitive Properties of High Dimensional Space (2018)

For high-dimensional spheres, most of the volume is in the "shell", ie near the boundary [0]. This sort of makes sense to me, but I don't know how to square that with the observation in the article that most of the surface area is near the equator. (In particular, by symmetry, it's near any equator; so, one would think, in their intersection. That is near the centre, though, not the shell.)

Anyway. Never buy a high-dimensional orange, it's mostly rind.

[0] https://www.math.wustl.edu/~feres/highdim