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Theorem on six vertices of a plane curve via the Sturm theory

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 clas...

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Bibliographic Details
Published in:arXiv.org 1995-10
Main Authors: Guieu, L, Mourre, E, V Yu Ovsienko
Format: Article
Language:English
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Summary: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.
ISSN:2331-8422