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27 Aprile, 2007 11:00
Sezione di Geometria, Algebra e loro applicazioni

A few short combinatorial proofs in Geometry

Joseph Zaks, University of Haifa , Haifa (Israel)
Aula Seminari del III piano del Dipartimento di Matematica Francesco Brioschi , Politecnico di Milano, via Bonardi n. 9 (edificio La Nave )
Abstract

We will treat the unit-distance graph over the real (or rational) points in Ed, discuss their connectivity and chromatic numbers, and use it in connection with the Beckman-Quarels Theorem ( Every mapping from Ed to itself, d >= 2, that preserves distance one is an isometry ). We will show that every closed curve on the unit sphere in E^d that meets all the d major hyperplanes has length of at least pi.

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Seminari Matematici
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