Surface of the intersection of $n$ balls

Surface and volumes can be calculated analytically for any n value. For intersections of n=5 spheres and more, they can be calculated from the 4 by 4 intersections: see theorems 4.5 and 4.6 in my book chapter:

Spheres Unions and Intersections and some of their Applications in Molecular Modeling, In: Distance Geometry: Theory, Methods, and Applications, chap. 4, pp. 61--83. Mucherino, A.; Lavor, C.; Liberti, L.; Maculan, N. (Eds.), Springer, 2013. ISBN 978-1-4614-5127-3, DOI 10.1007/978-1-4614-5128-0_4

A free preprint is available at: https://hal.archives-ouvertes.fr/hal-01955983

Does an iterated exponential $z^{z^{z^{...}}}$ always have a finite period

Let $A$ and $x$ be $n \times n$ and $n \times 1$ matrices, all entries real and strictly positive. Assume that $A^2 x = x$. Show that $A x = x$.

What does the second antiderivative of a function represent?

Points of differentiability of $f(x) = \sum\limits_{n : q_n < x} c_n$

Calculating growth rate of a population of Minecraft chickens

Proving an integral is finite

Intuitive meaning of high order Fréchet derivative $D^k f_p(v_1, \cdots, v_l)$

Are nearby simple closed geodesics ambient isotopic?

Determinant of $5 \times 5$ Boolean matrix

Is my proof of differentiability correct?

If $f'+f''\geq f^2$ show that $\frac{f'}{f''}\leq 1$ for all $x\in(0,+\infty)$.