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Sections of Bodies of Constant Width

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

In Chapter 3 it was proven that the property of constant width is inherited under orthogonal projection but not under sections. TheSection proof of this fact was not a constructive one, that is, no nonconstant width section of a body of constant width was actually exhibited. In fact, it was proven that if all sections of a convex body have constant width, then the body is a ball. Since there are bodies of constant width other than the ball, it was concluded that they must all have at least one section that is not of constant width. To show this could, however, be tricky, even in cases as simple as the body produced by rotating the Reuleaux triangle around one of its axes of symmetry.

Suggested Citation

  • Horst Martini & Luis Montejano & Déborah Oliveros, 2019. "Sections of Bodies of Constant Width," Springer Books, in: Bodies of Constant Width, chapter 0, pages 197-207, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-03868-7_9
    DOI: 10.1007/978-3-030-03868-7_9
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