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Published in:
2019 | OriginalPaper | Chapter
15. Bodies of Constant Width in Discrete Geometry
Authors : Horst Martini, Luis Montejano, Déborah Oliveros
Published in: Bodies of Constant Width
Publisher: Springer International Publishing
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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: It is easy to see that both sets are convex bodies. From this, the following variant of Helly’s theorem is immediately obtained.
$$\begin{aligned} \{x\in \mathbb {E}^n&\mid x + \phi \subset \psi \},\\ \{x\in \mathbb {E}^n&\mid x + \phi \supset \psi \}. \end{aligned}$$