Can you cover your shadows?
type: Item
instance of: scholarly article
title: Can you cover your shadows?
zbMATH Open document ID: 0593.52002
DOI: 10.1007/BF02187682
published in: Discrete \& Computational Geometry
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/130980
review text: The authors prove that a subset X of the Euclidean d-space \({\mathbb{R}}^ d\) can cover its shadows in \({\mathbb{R}}^ d\), if every orthogonal projection of X onto a (d-1)-dimensional linear subspace of \({\mathbb{R}}^ d\) is contained in some congruent copy of X. Every 2-dimensional convex set \(C\subset {\mathbb{R}}^ d\) has this property; but for \(d\geq 4\) no (d-1)- polytope. The authors consider also closely related problems and end with an interesting collection of open problems.
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52Bxx
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 3953702
zbMATH Keywords: convex polytope
zbMATH Keywords: coverings
zbMATH Keywords: convex body
author: Hans E. Debrunner
author: P. Mani-Levitska
reviewed by: Jörg M. Wills
MaRDI profile type: Publication
cites work: Q5842420
cites work: Q5556250
cites work: Q5515089
cites work: On the copositive representation of binary and continuous nonconvex quadratic programs
cites work: Q5503714
cites work: Q5621733
cites work: Q5523721
OpenAlex ID: W2063734744
description: scientific article; zbMATH DE number 3953702