Tractrices, Bicycle Tire Tracks, Hatchet Planimeters, and a 100-year-old Conjecture
Differential Geometry
2012-07-17 v1
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.
Keywords
Cite
@article{arxiv.1207.0834,
title = {Tractrices, Bicycle Tire Tracks, Hatchet Planimeters, and a 100-year-old Conjecture},
author = {R. L. Foote and M. Levi and S. Tabachnikov},
journal= {arXiv preprint arXiv:1207.0834},
year = {2012}
}
Comments
20 pages, 18 figures