A refinement of Foreman's four-vertex theorem and its dual version (Q1928322)
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scientific article; zbMATH DE number 6121392
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A refinement of Foreman's four-vertex theorem and its dual version |
scientific article; zbMATH DE number 6121392 |
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A refinement of Foreman's four-vertex theorem and its dual version (English)
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3 January 2013
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The authors refine \textit{B. Foreman}'s four-vertex theorem on semi-osculating conics of a strictly convex curve \(\Gamma\) [Am. Math. Mon. 114, No. 4, 351--356 (2007; Zbl 1158.53300)]. Foreman's theorem is an application of Ghys' theorem on diffeomorphisms of \(S^{1}\). The authors deduce a projectively dual version of their refinement which is a claim about semi-osculating conics passing through two fixed points on \(\Gamma\).
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convex curves
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four-vertex theorem
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semi-osculating conics
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