Central slices of the regular simplex
type: Item
instance of: scholarly article
title: Central slices of the regular simplex
zbMATH Open document ID: 0853.52007
DOI: 10.1007/BF00149416
author: Simon Webb
published in: Geometriae Dedicata
publication date: 1997-01-12T00:00:00Z
review text: The following result is proved using probabilistic methods. Let \(S\) be a regular \(n\)-dimensional simplex with edges of length \(\sqrt{2}\). The volume of every \((n -1)\)-dimensional slice of \(S\) passing through the centroid of \(S\) is at most \((\sqrt{n+1})/(\Gamma(n)\sqrt {2})\). This value is attained if and only if the slice contains \(n - 1\) vertices of \(S\).
reviewed by: Marek Lassak
Mathematics Subject Classification ID: 52A38
Mathematics Subject Classification ID: 52B11
zbMATH DE Number: 883873
zbMATH Keywords: face
zbMATH Keywords: regular \(n\)-dimensional simplex
zbMATH Keywords: volume
zbMATH Keywords: slice
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00149416
OpenAlex ID: W2053952124
description: scientific article; zbMATH DE number 883873