Open AccessClassification of conics and Cassini curves in Minkowski space-time plane
Author(s) -
Emad Shonoda
Publication year - 2016
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2015.07.002
Subject(s) - minkowski space , conic section , mathematics , plane (geometry) , singularity , pure mathematics , space (punctuation) , plane curve , geometry , mathematical physics , computer science , operating system
In this paper we use the Apollonius definition of conics to generate algebraic curves in the Minkowski space-time plane M2, which turn out to be different from classical conic sections. We extend and classify this sort of “M-conics”. We discuss the cases of the singularity points of these M-conics, coming from the transition from timelike world to spacelike world through the lightlike one. Finally, we translate the classical concept of Cassini curves with two foci and that of (multifocal) Cassini curves to Minkowski planes M2