Recent Developments in Taxicab Geometry

Shing So

Authors

Shing So Department of Mathematics and Computer Science, Central Missouri 64093, USA.

Keywords:

Bilinear, diamond trigonometric functions, conic sections, eccentricity, iso-taxicab metric, norm, positive definite, pyramidal sections, taxicab circles, taxicab directed distance, taxicab ellipses, taxicab geometry, taxicab hyperbolas, taxicab inner product, taxicab trigonometry

Abstract

Since the time of René Descartes, analytic geometry, which is based on the Euclidean metric, has been a popular area of research. In recent years, mathematicians begin to investigate geometry using other metrics such as the taxicab metric. In this paper, results from the research in traxicab metric and related areas are presented. Various ideas and directions for research in taxicab geometry are introduced and discussed to stimulate further research interest in this area.