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An alternative proof of Petty's theorem on equilateral sets

Tomasz Kobos (2013)

Annales Polonici Mathematici

The main goal of this paper is to provide an alternative proof of the following theorem of Petty: in a normed space of dimension at least three, every 3-element equilateral set can be extended to a 4-element equilateral set. Our approach is based on the result of Kramer and Németh about inscribing a simplex into a convex body. To prove the theorem of Petty, we shall also establish that for any three points in a normed plane, forming an equilateral triangle of side p, there exists a fourth point,...

Ausbohrung von Rhomben


Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

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