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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.

References [Enhancements On Off] (What's this?)

  • [1] T. Banchoff, Polyhedral catastrophe theory. I: Maps of the line to the line, Dynamical Systems, Academic Press, New York and London, 1973. MR 0341517 (49:6268)
  • [2] B. Halpern, Global theorems for closed plane curves, Bull. Amer. Math. Soc. 76 (1970), 96-100. MR 41 #7541. MR 0262936 (41:7541)
  • [3] Fr. Fabricius-Bjerre, On the double tangents of plane closed curves, Math. Scand. 11 (1962), 113-116. MR 28 #4439. MR 0161231 (28:4439)

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Keywords: Polygon, inflections, double tangency, support line, deformations
Article copyright: © Copyright 1974 American Mathematical Society

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