Tractrices, Bicycle Tire Tracks, Hatchet Planimeters, and a 100-year-old Conjecture

2012/07/03 by Foote, R. L., Levi, M., Tabachnikov, S. · 4 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1207.0834

Abstract

Geometry of the tracks left by a bicycle is closely related with the so-called Prytz planimeter and with linear fractional transformations of the complex plane. We describe these relations, along with the history of the problem, and give a proof of a conjecture made by Menzin in 1906.

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• On the Complexity of Bicycle Unitracks
• Dynamical systems on torus related to general Heun equations: phase-lock areas and constriction breaking

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