5
$\begingroup$

Say we have a sphere in d-dimensional space, and k hyperplanes (d-1 dimensional) all passing through the origin. Is there a way to calculate (or approximate) the area of the surface of the sphere enclosed by the half-spaces \begin{align*}w_1 \cdot x &\leq 0 \\ w_2 \cdot x &\leq 0\\ \vdots& \\w_k \cdot x &\leq 0\end{align*}

$\endgroup$

1 Answer 1

2
$\begingroup$

Seven years late here. But this citation might be useful if someone (probably someone else) is looking into this problem.

Cho, Y., & Kim, S. (2020). Volume of Hypercubes Clipped by Hyperplanes and Combinatorial Identities. In The Electronic Journal of Linear Algebra (Vol. 36, Issue 36, pp. 228–255). University of Wyoming Libraries. https://doi.org/10.13001/ela.2020.5085 https://journals.uwyo.edu/index.php/ela/article/download/5085/5047

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .