A geometric inequality for plane curves with restricted curvature
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- by G. D. Chakerian, H. H. Johnson and A. Vogt PDF
- Proc. Amer. Math. Soc. 57 (1976), 122-126 Request permission
Abstract:
A geometric proof is given that a closed plane curve of length $L$ and curvature bounded by $K$ can be contained inside a circle of radius $L/4 - (\pi - 2)/2K$.References
- Wilhelm Blaschke, Kreis und Kugel, Chelsea Publishing Co., New York, 1949 (German). MR 0076364
- G. D. Chakerian and M. S. Klamkin, Minimal covers for closed curves, Math. Mag. 46 (1973), 55–61. MR 313944, DOI 10.2307/2689031
- L. E. Dubins, On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents, Amer. J. Math. 79 (1957), 497–516. MR 89457, DOI 10.2307/2372560
- Harold H. Johnson, An application of the maximum principle to the geometry of plane curves, Proc. Amer. Math. Soc. 44 (1974), 432–435. MR 348631, DOI 10.1090/S0002-9939-1974-0348631-6
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 57 (1976), 122-126
- MSC: Primary 52A40
- DOI: https://doi.org/10.1090/S0002-9939-1976-0402611-2
- MathSciNet review: 0402611