Iterating evolutes and involutes

DOI10.1007/s00454-017-9890-yzbMath1381.51007arXiv1510.07742OpenAlexW2963770963MaRDI QIDQ2408188

Ivan Izmestiev, Emmanuel Tsukerman, Maxim Arnold, Sergei Tabachnikov, Dmitry Fuchs

Publication date: 10 October 2017

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.07742

zbMATH Keywords

hedgehogdiscrete Fourier transformpolygonsupport functiondiscrete differential geometryinvoluteSteiner pointhypocycloid4-vertex theoremiterated evolute

Mathematics Subject Classification ID

Discrete geometry (52C99) Curves in Euclidean and related spaces (53A04) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Euclidean geometries (general) and generalizations (51M05) (n)-vertex theorems via direct methods (51L15)

Related Items (6)

Fifty new invariants of \(N\)-periodics in the elliptic billiard ⋮ On involutes of order k of a null Cartan curve in Minkowski spaces ⋮ Closed cycloids in a normed plane ⋮ Unnamed Item ⋮ Discrete cycloids from convex symmetric polygons ⋮ The normal map as a vector field

Cites Work

• New geometric inequalities for hedgehogs
• Curvature extrema and four-vertex theorems for polygons and polyhedra
• The perpendicular bisector construction
• On Steiner points of convex bodies
• A Four Vertex Theorem for Polygons
• The Perpendicular Bisectors Construction, the Isoptic Point and the Simson Line of a Quadrilateral
• The Ergodic Character of Sequences of Pedal Triangles
• The limit of a pedal sequence of triangles
• The Sequence of Pedal Triangles
• Mixing Property of the Pedal Mapping
• The Symbolic Dynamics of the Sequence of Pedal Triangles
• Convex Polytopes
• Iterating evolutes of spatial polygons and of spatial curves
• Convex Bodies The Brunn-MinkowskiTheory
• Geometric Study of Minkowski Differences of Plane Convex Bodies
• A Uniqueness Theorem for the Steiner Point of a Convex Region
• The Finite Fourier Series and Elementary Geometry
• On the Oscillation of the Derivatives of A Periodic Function
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Iterating evolutes and involutes