PreprintCC BY 4.0arXiv
The sphere is the only closed surface satisfying the fixed-width Archimedean property
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 ℝ3, this property characterizes the unit sphere for a single fixed width.
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BibTeX
@misc{lai2026sphere,
title = {{The sphere is the only closed surface satisfying the fixed-width Archimedean property}},
author = {Mijia Lai},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01550},
eprint = {2610.01550},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01550},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The sphere is the only closed surface satisfying the fixed-width Archimedean property
AU - Mijia Lai
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.01550
UR - https://arxiv.org/abs/2610.01550
AB - 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 ℝ^3, this property characterizes the unit sphere for a single fixed width.
ER -