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Systems of Lines in the Plane

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

A system of lines consists of an assignment of a line in the plane for any direction. In this section, we will be interested in studying systems of lines, in particular those which are combined with a given convex set by a certain property. For example, the system of lines that leave a fixed proportion of area, or a fixed proportion of perimeter, in one side of the convex set for every direction. Consider, for instance, the collection of tangent lines of a given strictly convex set in the plane which varies continuously with respect an angle, or a system of diametral lines, a system of median lines, etc. The purpose of this chapter is to study some useful and important systems of lines.

Suggested Citation

  • Horst Martini & Luis Montejano & Déborah Oliveros, 2019. "Systems of Lines in the Plane," Springer Books, in: Bodies of Constant Width, chapter 0, pages 95-126, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-03868-7_5
    DOI: 10.1007/978-3-030-03868-7_5
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