ON THE RATIO OF DIRECTED LENGTHS ON THE PLANE WITH GENERALIZED ABSOLUTE VALUE METRIC AND RELATED PROPERTIES


Soydan G., Dogru Y., Arslandogan N. U.

FILOMAT, vol.26, no.1, pp.119-128, 2012 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 1
  • Publication Date: 2012
  • Doi Number: 10.2298/fil1201119s
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.119-128
  • Keywords: Ceva theorem, distance, metric, Menelaus theorem, protractor geometry

Abstract

In this paper, we show that a point of division divides a related line segment in the same ratio on the plane with generalized absolute value metric and Euclidean plane. Then the coordinates of the division point can be determined by the same formula as in the Euclidean plane. In the latter parts of the work, we give Ceva's and Menelaus'es theorems and the theorem of directed lines on the plane with generalized absolute value metric.