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

L. Guieu·E. Mourre·V. Yu. Ovsienko
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Abstract

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.

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BibTeXRIS

L. Guieu, E. Mourre, V. Yu. Ovsienko. 1995-10-26. Theorem on six vertices of a plane curve via the Sturm theory. https://arxiv.org/abs/dg-ga/9510008

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