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Bodies of Constant Width in Discrete Geometry

In: Bodies of Constant Width

Author

Listed:
  • 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)

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.

Suggested Citation

  • Horst Martini & Luis Montejano & Déborah Oliveros, 2019. "Bodies of Constant Width in Discrete Geometry," Springer Books, in: Bodies of Constant Width, chapter 0, pages 343-367, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-03868-7_15
    DOI: 10.1007/978-3-030-03868-7_15
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