Year: 2026
Type: preprint
Abstract: Among Archimedes' many celebrated discoveries is a striking fact: the region of the unit sphere between two parallel planes, both meeting the sphere and separated by a distance $h$, has area $2πh$. We prove that, among connected smooth closed embedded surfaces in $\mathbb R^3$, this property characterizes the unit sphere for a single fixed width.
Source: arXiv (Cornell University)
Author: Lai, Mijia
Institution: Shanghai Jiao Tong University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7216195459