International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 625-633
doi:10.1155/S0161171285000680
Convex curves of bounded type
Mathematics Department, University of South Florida, Tampa 33620, Florida, USA
Received 30 November 1984
Copyright © 1985 A. W. Goodman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Let C be a simple closed convex curve in the plane for which the radius of curvature ρ is a continuous function of the arc length. Such a curve is called a convex curve of bounded type, if ρ lies between two fixed positive bounds. Here we give a new and simpler proof of Blaschke's Rolling Theorem. We prove one new theorem and suggest a number of open problems.