Vol. 9, No. 1, 2016

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Polygonal bicycle paths and the Darboux transformation

Ian Alevy and Emmanuel Tsukerman

Vol. 9 (2016), No. 1, 57–66
Abstract

A bicycle (n,k)-gon is an equilateral n-gon whose k diagonals are of equal length. In this paper we introduce periodic bicycle (n,k)-paths, which are a natural variation in which the polygon is replaced with a periodic polygonal path, and study their rigidity and integrals of motion.

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Keywords
bicycle polygons, tire track problem, floating bodies in equilibrium
Mathematical Subject Classification 2010
Primary: 37J35, 52C25
Milestones
Received: 7 September 2013
Revised: 1 September 2014
Accepted: 8 December 2014
Published: 17 December 2015

Communicated by Kenneth S. Berenhaut
Authors
Ian Alevy
Division of Applied Mathematics
Brown University
Providence, RI 02912
United States
Emmanuel Tsukerman
Department of Mathematics
University of California, Berkeley
Berkeley, CA 94720
United States