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Proceedings of the American Mathematical Society

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Global geometry of polygons. I: The theorem of Fabricius-Bjerre


Author: Thomas F. Banchoff
Journal: Proc. Amer. Math. Soc. 45 (1974), 237-241
MSC: Primary 57C15; Secondary 14B05
MathSciNet review: 0370599
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Abstract: Deformation methods provide a direct proof of a polygonal analogue of a theorem proved by Fabricius-Bjerre and by Halpern relating the numbers of crossings, pairs of inflections, and lines of double tangency for smooth closed plane curves.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0370599-7
Keywords: Polygon, inflections, double tangency, support line, deformations
Article copyright: © Copyright 1974 American Mathematical Society