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Bodies of Constant Width in Discrete Geometry

  • Horst MartiniEmail author
  • Luis Montejano
  • Déborah Oliveros
Chapter

Abstract

We start with the versions of the Helly’s Theorem developed by V. Klee [628]. Let \(\phi \) and \(\psi \) be two convex bodies in \(\mathbb {E}^n\), and consider the following two subsets:
$$\begin{aligned} \{x\in \mathbb {E}^n&\mid x + \phi \subset \psi \},\\ \{x\in \mathbb {E}^n&\mid x + \phi \supset \psi \}. \end{aligned}$$
It is easy to see that both sets are convex bodies. From this, the following variant of Helly’s theorem is immediately obtained.

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Horst Martini
    • 1
    Email author
  • Luis Montejano
    • 2
  • Déborah Oliveros
    • 2
  1. 1.Faculty of MathematicsChemnitz University of TechnologyChemnitzGermany
  2. 2.Instituto de MatemáticasUniversidad Nacional Autónoma de México, Campus JuriquillaQuerétaroMéxico

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