Dekzan Conjecture: Singularity of Manhattan Distance^s Geometric Representation
Kenzie Faza Ramadhan, Dean Refangga Setiadi

SMAS Laboratorium Percontohan - Universitas Pendidikan Indonesia

Abstract

The purpose of this research is to find the existence of singularity in Manhattan distance geometric representation like the geometric representation in geometry Euclid which every geometrical object such as point, line, plane, etc. has singularity. The research was conducted to find out if such singularity also existed in taxicab geometry especially the geometric representation of Manhattan distance as the fundamental function of distance in Taxicab geometry. The research was done by exploring the geometric representation of Manhattan Distance, applying some changes, observing the outcome, making a conjecture, and proposing the proof. The result shows that a kind of singularity was found and based from this a conjecture is created, whom can be said as a singularity in Manhattan Distance. However, the systematic proof is still needed as it stills in the form of a conjecture. For future research, findings suggest to research on another geometrical object and explore more about Taxicab geometry.

Keywords: Singularity- Manhattan distance- Taxicab geometry

Topic: Mathematics