5 citations · 8 across the 3 of their papers we have counts for
9 papers
Geometry of Integrable Linkages
Ron Perline, Sergei Tabachnikov
In analogy with the well-known 2-linkage tractor-trailer problem, we define a 2-linkage problem in the plane with novel non-holonomic ``no-slip'' conditions. Using constructs from…
Tire tracks and integrable curve evolution
Gil Bor, Mark Levi, Ron Perline +1
We study a simple model of bicycle motion: a segment of fixed length in multi-dimensional Euclidean space, moving so that the velocity of the rear end is always aligned with the se…
Two Universality Properties Associated with the Monkey Model of Zipf's Law
Richard Perline, Ronald Perline
The distribution of word probabilities in the monkey model of Zipf's law is associated with two universality properties: (1) the power law exponent converges strongly to as th…
Geometry of Thin Films
Ronald Perline
We study ray optics in the context of double mirror systems, in the limit as the two mirrors approach one another (thin films). This leads to a novel set of differential equations…
Localized Induction Hierarchy and Weingarten Systems
Ron Perline
We describe a method of constructing Weingarten systems of triply orthogonal coordinates, related to the localized induction equation hierarchy of integrable geometric evolution eq…
Localized induction equation and pseudospherical surfaces
Ron Perline
We describe a close connection between the localized induction equation hierarchy of integrable evolution equations on space curves, and surfaces of constant negative Gauss curvatu…