Shonoda, E. (2016). Classification of conics and Cassini curves in Minkowski space-time plane. test, 24(2), 270-278. doi: 10.1016/j.joems.2015.07.002
Emad N. Shonoda. "Classification of conics and Cassini curves in Minkowski space-time plane". test, 24, 2, 2016, 270-278. doi: 10.1016/j.joems.2015.07.002
Shonoda, E. (2016). 'Classification of conics and Cassini curves in Minkowski space-time plane', test, 24(2), pp. 270-278. doi: 10.1016/j.joems.2015.07.002
Shonoda, E. Classification of conics and Cassini curves in Minkowski space-time plane. test, 2016; 24(2): 270-278. doi: 10.1016/j.joems.2015.07.002

Classification of conics and Cassini curves in Minkowski space-time plane

Journal of the Egyptian Mathematical Society
Volume 24, Issue 2, 2016, Pages 270-278    PDF (3 M)
DOI: 10.1016/j.joems.2015.07.002
Author
Emad N. Shonoda
Department of Mathematics and Computer Science, Faculty of Science, Port-Said University, Port-Said, Egypt
Abstract
In this paper we use the Apollonius definition of conics to generate algebraic curves in
the Minkowski space-time plane M 2 , 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 M 2 .
Keywords
Minkowski space-time; plane curve; multi foci curves; Cassini curves
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