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A study on densities of sets of points and lines
Author(s) -
Şentürk Gülsüm Yeliz,
Yüce Salim
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5404
Subject(s) - mathematics , euclidean geometry , planar , euclidean distance , plane (geometry) , connection (principal bundle) , motion (physics) , set (abstract data type) , mathematical analysis , pure mathematics , combinatorics , geometry , classical mechanics , physics , computer science , computer graphics (images) , programming language
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.