Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 0372797
Full-text PDF Free Access

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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C70, 52A10

Retrieve articles in all journals with MSC: 53C70, 52A10

Additional Information

Keywords: Polygonal plane curve, double normal
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society