Bodies of Constant Width in Discrete Geometry

Horst Martini (), Luis Montejano and Déborah Oliveros
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Horst Martini: Chemnitz University of Technology, Faculty of Mathematics
Luis Montejano: Universidad Nacional Autónoma de México, Campus Juriquilla, Instituto de Matemáticas
Déborah Oliveros: Universidad Nacional Autónoma de México, Campus Juriquilla, Instituto de Matemáticas

Chapter Chapter 15 in Bodies of Constant Width, 2019, pp 343-367 from Springer

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

Date: 2019
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DOI: 10.1007/978-3-030-03868-7_15

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