47 citations · 313 across the 74 of their papers we have counts for
5 papers · 1 filter
On the discrete bicycle transformation
Serge Tabachnikov, Emmanuel Tsukerman
We study the dynamics of the discrete bicycle (Darboux, Backlund) transformation of polygons in n-dimensional Euclidean space. This transformation is a discretization of the contin…
Osculating curves: around the Tait-Kneser Theorem
E. Ghys, S. Tabachnikov, V. Timorin
The Tait-Kneser theorem states that the osculating circles of a plane curve with monotonic curvature are pairwise disjoint and nested. We discuss this theorem and a number of its v…
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…
The equal tangents property
J. Jeronimo-Castro, G. Ruiz-Hernandez, S. Tabachnikov
Let M be a smooth strictly convex closed surface in space and denote by H the set of points x in the exterior of M such that all the tangent segments from x to M have equal lengths…
On fibrations with flat fibers
Valentin Ovsienko, Serge Tabachnikov
We describe pairs (p,n) such that n-dimensional affine space is fibered by pairwise skew p-dimensional affine subspaces. The problem is closely related with the theorem of Adams on…