Straightening polygonal arcs and convexifying polygonal cycles
type: Item
instance of: scholarly article
title: Straightening polygonal arcs and convexifying polygonal cycles
zbMATH Open document ID: 1046.52016
author: Robert Connelly
author: Erik D. Demaine
author: Günter Rote
published in: Discrete \& Computational Geometry
publication date: 2004-03-07T00:00:00Z
review text: A planar polygonal arc or open polygonal chain is a sequence of finitely many line segments in the plane connected in a path without self-intersections. It has been an outstanding question as to whether it is possible to move a polygonal arc continuously in such a way that each edge remains a fixed length, there are no self-intersections during the motion, and at the end of the motion the arc lies on a straight line. This has come to be known as the carpenter's rule problem. A related question is whether it is possible to move a polygonal simple closed curve continuously in the plane, often called a closed polygonal chain or polygon, again without creating self-intersections or changing the lengths of the edges, so that it ends up a convex closed curve. The authors solve both problems by showing that in both cases there is such a motion.
Mathematics Subject Classification ID: 52C25
Mathematics Subject Classification ID: 51E12
Mathematics Subject Classification ID: 52B55
Mathematics Subject Classification ID: 55U15
zbMATH DE Number: 2051390
zbMATH Keywords: planar linkage
zbMATH Keywords: bar framework
zbMATH Keywords: planar polygonal arc
zbMATH Keywords: carpenter's rule problem
zbMATH Keywords: arc straightened by a motion
zbMATH Keywords: convexifying a polygon
zbMATH Keywords: outer-convex configuration
zbMATH Keywords: nested arc
zbMATH Keywords: expansiveness
zbMATH Keywords: infinitesimal motions
zbMATH Keywords: equilibrium stresses
zbMATH Keywords: planarization
zbMATH Keywords: Maxwell-Cremona correspondence
zbMATH Keywords: polyhedral graph
zbMATH Keywords: global motion
zbMATH Keywords: smoothness
zbMATH Keywords: symmetry
zbMATH Keywords: increasing area
zbMATH Keywords: topology of configuration spaces
reviewed by: Serguey M. Pokas
Wikidata QID: Q55967391
MaRDI profile type: Publication
full work available at URL: s00454-003-0006-7
OpenAlex ID: W2068564171
DBLP publication ID: journals/dcg/ConnellyDR03
DOI: 10.1007/S00454-003-0006-7
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description: scientific article; zbMATH DE number 2051390