PreprintCC BY 4.0arXiv
Maximal volumes of pyramids in the unit cube
Abstract
Let Qn=[0,1]n, n≥2. Denote by Mn be the maximal volume of a pyramid in Qn whose base is a hyperplane section of Qn, and by Mn0 the corresponding maximum when the section contains the center of Qn. We prove that nMn<(n+1)Mn+10.
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BibTeX
@misc{nikolov2026maximal,
title = {{Maximal volumes of pyramids in the unit cube}},
author = {Nikolai Nikolov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14047},
eprint = {2610.14047},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14047},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Maximal volumes of pyramids in the unit cube
AU - Nikolai Nikolov
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.14047
UR - https://arxiv.org/abs/2610.14047
AB - Let Q_n=[0,1]^n, n≥2. Denote by M_n be the maximal volume of a pyramid in Q_n whose base is a hyperplane section of Q_n, and by M_n^0 the corresponding maximum when the section contains the center of Q_n. We prove that nM_n<(n+1)M_n+1^0.
ER -