A 4-point theorem: still another variation on an old theme

Serge Tabachnikov

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arXiv · 2409.12609

A 4-point theorem: still another variation on an old theme

Serge Tabachnikov

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Abstract

An old theorem, due to Graustein, asserts that the average curvature of a plane oval is attained at least at four points. We present a proof by way of wave propagation and extend this result to the spherical and hyperbolic geometries - in the latter case, to horocyclically convex curves only.

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Serge Tabachnikov. 2024-09-19. A 4-point theorem: still another variation on an old theme. https://arxiv.org/abs/2409.12609

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