Systems of Lines in the Plane

  • Horst MartiniEmail author
  • Luis Montejano
  • Déborah Oliveros


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.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Horst Martini
    • 1
    Email author
  • Luis Montejano
    • 2
  • Déborah Oliveros
    • 2
  1. 1.Faculty of MathematicsChemnitz University of TechnologyChemnitzGermany
  2. 2.Instituto de MatemáticasUniversidad Nacional Autónoma de México, Campus JuriquillaQuerétaroMéxico

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