Global geometry of polygons. I: The theorem of Fabricius-Bjerre
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- by Thomas F. Banchoff PDF
- Proc. Amer. Math. Soc. 45 (1974), 237-241 Request permission
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.References
- Thomas F. Banchoff, Polyhedral catastrophe theory. I. Maps of the line to the line, Dynamical systems (Proc. Sympos., Univ. Bahia, Salvador, 1971) Academic Press, New York, 1973, pp. 7–21. MR 0341517
- Benjamin Halpern, Global theorems for closed plane curves, Bull. Amer. Math. Soc. 76 (1970), 96–100. MR 262936, DOI 10.1090/S0002-9904-1970-12380-1
- Fr. Fabricius-Bjerre, On the double tangents of plane closed curves, Math. Scand. 11 (1962), 113–116. MR 161231, DOI 10.7146/math.scand.a-10656
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 45 (1974), 237-241
- MSC: Primary 57C15; Secondary 14B05
- DOI: https://doi.org/10.1090/S0002-9939-1974-0370599-7
- MathSciNet review: 0370599