Convex curves of bounded type

Convex curves of bounded type

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 Theor...

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Bibliographic Details
Main Author: A. W. Goodman
Format: Article
Language:English
Published: Hindawi Limited 1985-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
convex curve
bounded type
perimeter centroid
Blaschke's rolling theorem
parallel curve
mass distribution on a curve.
Online Access:http://dx.doi.org/10.1155/S0161171285000680
Description
Summary: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.
ISSN:0161-1712
1687-0425

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