Tire track geometry: variations on a theme

DOI10.1007/BF02777353zbMath1124.52005arXivmath/0405445MaRDI QIDQ2382341

Sergei Tabachnikov

Publication date: 9 October 2007

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0405445

zbMATH Keywords

rigiditybicycle curvesclosed smooth convex plane curvesflexible bicycle polygons

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Convex sets in (2) dimensions (including convex curves) (52A10) Rotation numbers and vectors (37E45)

Related Items (14)

Configuration spaces of plane polygons and a sub-Riemannian approach to the equitangent problem ⋮ Addendum to: ``Capillary floating and the billiard ball problem ⋮ On the bicycle transformation and the filament equation: results and conjectures ⋮ Schrödinger's equation and ``bike tracks -- a connection ⋮ Offsets and front tire tracks to projective hedgehogs ⋮ Some comments on floating and centroid bodies in the plane ⋮ Self-Bäcklund curves in centroaffine geometry and Lamé’s equation ⋮ Generalized plane offsets and rational parameterizations ⋮ Isoperimetric inequalities for wave fronts and a generalization of Menzin's conjecture for bicycle monodromy on surfaces of constant curvature ⋮ Book review of: R. D. Mauldin, The Scottish Book. Mathematics from the Scottish Café. With selected problems from the New Scottish Book. 2nd ed. ⋮ Billiard dynamics: An updated survey with the emphasis on open problems ⋮ Capillary floating and the billiard ball problem ⋮ Floating Body Problems in Two Dimensions ⋮ A number theoretic question arising in the geometry of plane curves and in billiard dynamics

Cites Work

• Circles minimize most knot energies
• A classification theorem for Zindler carousels
• Carousels, Zindler curves and the floating body problem
• The Track of a Bicycle Back Tire
• The geometry of spherical curves and the algebra of quaternions
• Sur un problème de M. Ulam concernant l'équilibre des corps flottants
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