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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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Published in: | arXiv.org 1995-10 |
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Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Online Access: | Get full text |
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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. |
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ISSN: | 2331-8422 |