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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Double normals and tangent normals for polygons


Author: Benjamin Halpern
Journal: Proc. Amer. Math. Soc. 51 (1975), 434-437
MSC: Primary 53C70; Secondary 52A10
DOI: https://doi.org/10.1090/S0002-9939-1975-0372797-6
MathSciNet review: 0372797
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Abstract | References | Similar Articles | Additional Information

Abstract: Given a polygonal closed plane curve $ \gamma $. Each segment of $ \gamma $ has a tangent direction and a normal direction; each vertex of $ \gamma $ has a cone of tangent directions and a cone of normal directions. Formulas are established connecting the numbers of various kinds of straight lines which either intersect $ \gamma $ twice in a normal direction, or once in a normal direction and once in a tangent direction.


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

  • [1] T. Banchoff, Global geometry of polygons. I: The theorem of Fabricius-Bjerre, Proc. Amer. Math. Soc. 45 (1974), 237-241. MR 0370599 (51:6826)
  • [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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0372797-6
Keywords: Polygonal plane curve, double normal
Article copyright: © Copyright 1975 American Mathematical Society

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