Systems of Lines in the Plane

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 5 in Bodies of Constant Width, 2019, pp 95-126 from Springer

Abstract: 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.

Date: 2019
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DOI: 10.1007/978-3-030-03868-7_5

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