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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Barbier's theorem in the Lobachevski plane


Author: Jay P. Fillmore
Journal: Proc. Amer. Math. Soc. 24 (1970), 705-709
MSC: Primary 52.25; Secondary 53.00
MathSciNet review: 0253150
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Abstract: In the Lobachevski plane, horocycles with the same center are geodesic parallels and are natural replacements for the lines used in defining the support function of a convex curve and the notion of constant width in the Euclidean plane. In this paper, analogs based on horocycles are obtained for Christoffel's formula, which expresses the radius of curvature of a convex curve in terms of its support function, and Barbier's theorem, which relates the length and width of a convex curve of constant width.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0253150-8
PII: S 0002-9939(1970)0253150-8
Keywords: Convex curves, constant width, support function
Article copyright: © Copyright 1970 American Mathematical Society