Meissner's mysterious bodies

DOI10.1007/s00283-011-9239-yzbMath1231.52002OpenAlexW2012161162WikidataQ29396650 ScholiaQ29396650MaRDI QIDQ645305

Christof Weber, Bernhard Kawohl

Publication date: 14 November 2011

Published in: The Mathematical Intelligencer (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00283-011-9239-y

zbMATH Keywords

minimal volumeBlaschke--Lebesgue problembody of constant widthMeissner body

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (3) dimensions (including convex surfaces) (52A15)

Related Items (12)

Parametric shape optimization using the support function ⋮ A doubly monotone flow for constant width bodies in ℝ³ ⋮ On a normed version of a Rogers-Shephard type problem ⋮ Asymmetry for convex body of revolution ⋮ Two dimensions are easier ⋮ On a formula for sets of constant width in 2D ⋮ On a strengthening of the Blaschke-Leichtweiss theorem ⋮ Shape optimization under width constraint ⋮ Structure of the space of diametrically complete sets in a Minkowski space ⋮ On the 1-measure of asymmetry for convex bodies of constant width ⋮ On convex bodies that are characterizable by volume function. ``Old and recent problems for a new generation: a survey ⋮ More on the potential for the farthest-point distance function

Uses Software

• OEIS

Cites Work

• Über die maximale Dicke der ebenen Schnitte eines konvexen Körpers
• On \(C^{2}\)-smooth surfaces of constant width
• Inner and outer \(j\)-radii of convex bodies in finite-dimensional normed spaces
• Unsolved problems in geometry
• Analytic parametrization of three-dimensional bodies of constant width
• Sets of constant width
• On the three-dimensional Blaschke-Lebesgue problem
• Bodies of constant width in arbitrary dimension
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