1997 | OriginalPaper | Buchkapitel
Theorem on six vertices of a plane curve via Sturm theory
verfasst von : L. Guieu, E. Mourre, V. Yu Ovsienko
Erschienen in: The Arnold-Gelfand Mathematical Seminars
Verlag: Birkhäuser Boston
Enthalten in: Professional Book Archive
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We discuss the theorem on the existence of six points on a convex closed plane curve in which the curve has a contact of order six with the osculating conic. (This is the “projective version” of the well known four vertices theorem for a curve in the Euclidean plane.) We obtain this classical fact as a corollary of some general Sturm-type theorems.