Convex solids whose point-source shadow-boundaries lie in hyperplanes
type: Item
instance of: scholarly article
title: Convex solids whose point-source shadow-boundaries lie in hyperplanes
zbMATH Open document ID: 1271.52002
published in: Journal of Geometry
publication date: 2013-01-03T00:00:00Z
review text: The light from any point source divides an ellipsoid into the bright and the dark halves, whose common boundary is contained in a hyperplane. This property characterizes ellipsoids among all convex bodies (i. e. bounded closed convex sets), see [\textit{T.~Kubota}, Lond. M. S. Proc. (2) 14, 230--239 (1915; JFM 45.1347.05)] for the 3-dimensional case and [\textit{G.~R.~Burton}, Isr. J. Math. 28, 339--349 (1977; Zbl 0368.52004)] for the general one. The author classifies unbounded closed convex sets, satisfying this property, and proves that such a set is either a convex component of a quadric, or the product of a 2-dimensional strictly convex set and an affine space, or the product of a 3-dimensional strictly convex cone and an affine space.
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 14N25
zbMATH DE Number: 6121635
zbMATH Keywords: convex
zbMATH Keywords: body
zbMATH Keywords: solid
zbMATH Keywords: ellipsoid
zbMATH Keywords: quadric
zbMATH Keywords: hypersurface
zbMATH Keywords: shadow-boundary
author: Valeriu Soltan
reviewed by: Alexander Esterov
MaRDI profile type: Publication
full work available at URL: s00022-012-0114-6
OpenAlex ID: W2010435763
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DOI: 10.1007/S00022-012-0114-6
description: scientific article; zbMATH DE number 6121635