A study on densities of sets of points and lines


ŞENTÜRK G. Y., YÜCE S.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.42, no.16, pp.5427-5437, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 16
  • Publication Date: 2019
  • Doi Number: 10.1002/mma.5404
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.5427-5437
  • Yıldız Technical University Affiliated: Yes

Abstract

In this paper, firstly, our purpose is to give the relationship among the densities of the sets of collinear points, the relationship among the densities of the sets of noncollinear points, and the relationship among the densities of the sets of the intersecting lines in Euclidean plane, respectively. In addition to that, we define the density formulas for the sets of points and lines under the two-parameter planar Euclidean motion. By means of these results, we obtain essential properties that explain the connection among the densities of the sets of points and among the densities of the sets of intersecting lines under the two-parameter planar Euclidean motion.