Double normals and tangent normals for polygons

Halpern, Benjamin

doi:10.1090/S0002-9939-1975-0372797-6

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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
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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.

[1] Thomas F. Banchoff, Global geometry of polygons. I: The theorem of Fabricius-Bjerre, Proc. Amer. Math. Soc. 45 (1974), 237–241. MR 0370599 (51 #6826), http://dx.doi.org/10.1090/S0002-9939-1974-0370599-7
[2] Benjamin Halpern, Global theorems for closed plane curves, Bull. Amer. Math. Soc. 76 (1970), 96–100. MR 0262936 (41 #7541), http://dx.doi.org/10.1090/S0002-9904-1970-12380-1
[3] Fr. Fabricius-Bjerre, On the double tangents of plane closed curves, Math. Scand 11 (1962), 113–116. MR 0161231 (28 #4439)

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