47 citations · 313 across the 74 of their papers we have counts for
88 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…
Monotone twist maps and Dowker-type theorems
Peter Albers, Serge Tabachnikov
Given a planar oval, consider the maximal area of inscribed -gons resp. the minimal area of circumscribed -gons. One obtains two sequences indexed by , and one of Dowker's…
Iterating skew evolutes and skew involutes: a linear analog of the bicycle kinematics
Serge Tabachnikov
The evolute of a plane curve is the envelope of its normals. Replacing the normals by the lines that make a fixed angle with the curve yields a new curve, called the evolutoid. We…
Differential geometry of space curves: Forgotten chapters
Dmitry Fuchs, Ivan Izmestiev, Matteo Raffaelli +2
We study evolutes and involutes of space curves. Although much of the material presented is not new and can be found in classic treatises, we believe that a modern and unified trea…
Bicycling geodesics are Kirchhoff rods
Gil Bor, Connor Jackman, Serge Tabachnikov
A bicycle path is a pair of trajectories in , the `front' and `back' tracks, traced out by the endpoints of a moving line segment of fixed length (the `bicycle frame…
On conformal points of area preserving maps and related topics
Peter Albers, Serge Tabachnikov
In this article we consider area preserving diffeomorphisms of planar domains, and we are interested in their conformal points, i.e., points at which the derivative is a similarity…