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International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 625-633

Convex curves of bounded type

Mathematics Department, University of South Florida, Tampa 33620, Florida, USA

Received 30 November 1984

Copyright © 1985 Hindawi Publishing Corporation. 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.


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.