Disks in Curves of Bounded Convex Curvature
- 28 July 2020
- journal article
- research article
- Published by Taylor & Francis in The American Mathematical Monthly
- Vol. 127 (7) , 579-593
Abstract
We say that a simple, closed curve γ in the plane has bounded convex curvature if for every point x on γ, there is an open unit disk Ux and such that and . We prove that the interior of every curve of bounded convex curvature contains an open unit disk.
Keywords
All Related Versions
This publication has 11 references indexed in Scilit:
- Length minimising bounded curvature paths in homotopy classesTopology and its Applications, 2015
- An inequality for the maximum curvature through a geometric flowArchiv der Mathematik, 2015
- Precise prediction of forces in milling circular cornersInternational Journal of Machine Tools and Manufacture, 2015
- Corner optimization for pocket machiningInternational Journal of Machine Tools and Manufacture, 2004
- Mitered offset for profile machiningComputer-Aided Design, 2003
- A corner-looping based tool path for pocket millingComputer-Aided Design, 2003
- Curvature-Constrained Shortest Paths in a Convex PolygonSIAM Journal on Computing, 2002
- Reachability by paths of bounded curvature in convex polygons2000
- A Reverse Isoperimetric Inequality, Stability and Extremal Theorems for Plane Curves with Bounded CurvatureRocky Mountain Journal of Mathematics, 1995
- On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and TangentsAmerican Journal of Mathematics, 1957