Double normals and tangent normals for polygons
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- by Benjamin Halpern PDF
- Proc. Amer. Math. Soc. 51 (1975), 434-437 Request permission
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
- Thomas F. Banchoff, Global geometry of polygons. I: The theorem of Fabricius-Bjerre, Proc. Amer. Math. Soc. 45 (1974), 237–241. MR 370599, DOI 10.1090/S0002-9939-1974-0370599-7
- 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 1975 American Mathematical Society
- 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