36 citations · 38 across the 4 of their papers we have counts for
4 papers
Tractrices, Bicycle Tire Tracks, Hatchet Planimeters, and a 100-year-old Conjecture
R. L. Foote, M. Levi, S. Tabachnikov
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 r…
Infinitesimal isometries along curves and generalized Jacobi equations
Robert L. Foote, Chong-Kyu Han, Jong-Won Oh
A Jacobi field on a Riemannian manifold M is defined along a geodesic. We generalize this notion to an arbitrary smooth curve, and call it an infinitesimal isometry along the curve…
Integral-Geometric Formulas for Perimeter in S^2, H^2, and Hilbert Planes
Ralph Alexander, I. D. Berg, Robert L. Foote
We develop two types of integral formulas for the perimeter of a convex body K in planar geometries. We derive Cauchy-type formulas for perimeter in planar Hilbert geometries. Spec…
Geometry of the Prytz Planimeter
Robert L. Foote
The Prytz planimeter is a simple example of a system governed by a non-holonomic constraint. It is unique among planimeters in that it measures something more subtle than area, com…