Meissner's mysterious bodies
type: Item
instance of: scholarly article
title: Meissner's mysterious bodies
zbMATH Open document ID: 1231.52002
author: Christof Weber
author: Bernd Kawohl
published in: The Mathematical Intelligencer
publication date: 2011-11-14T00:00:00Z
review text: Precisely a century ago, Ernst Meissner introduced the special convex bodies of constant width, based on a regular tetrahedron, that are now named after him. It is a well-known and still unsolved conjecture that the Meissner bodies have the smallest volume among all three-dimensional convex bodies of the same constant width. This well-written and nicely illustrated popular survey article describes the Meissner bodies, presents their history, and explains some recently established necessary conditions for the solution bodies of the mentioned extremal problem. The article concludes with a short biography of Ernst Meissner. It has a useful list of references.
reviewed by: Rolf Schneider
Mathematics Subject Classification ID: 52A15
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 5971474
zbMATH Keywords: Meissner body
zbMATH Keywords: body of constant width
zbMATH Keywords: Blaschke--Lebesgue problem
zbMATH Keywords: minimal volume
describes a project that uses: OEIS
MaRDI profile type: Publication
Wikidata QID: Q29396650
full work available at URL: s00283-011-9239-y
OpenAlex ID: W2012161162
cites work: On the three-dimensional Blaschke-Lebesgue problem
cites work: Analytic parametrization of three-dimensional bodies of constant width
cites work: Q4000260
cites work: Q3840976
cites work: Q5440991
cites work: Q4871559
cites work: Sets of constant width
cites work: Q3667511
cites work: Unsolved problems in geometry
cites work: Über die maximale Dicke der ebenen Schnitte eines konvexen Körpers
cites work: On \(C^{2}\)-smooth surfaces of constant width
cites work: Inner and outer \(j\)-radii of convex bodies in finite-dimensional normed spaces
cites work: Q4274008
cites work: Bodies of constant width in arbitrary dimension
cites work: Q3644254
cites work: Q4003732
DOI: 10.1007/S00283-011-9239-Y
description: scientific article; zbMATH DE number 5971474