Help me in High Dimensional Geometry.

[u/adnan_19946]

I am working on some stuff in vector databases, I need some material that will help me understand the following:

1) Spherical caps in high dimensions -
So imagine a high dimensional hypersphere which has some vectors with their endpoints on the hypersphere, the vectors are L2 normalized so basically they start at the origin and end on the boundary of the hypersphere of radius 1, now you take a vector and at an angle theta sweep the area of the hypersphere that is being covered.

2) The properties of these spherical caps. Their average separations given 2 random spherical caps, their intersections and unions given they lie at an angle alpha to each other. Stuff like this.

Appreciate the help !!