One-Parameter Equations of Spherical Conics and Its Applications

Abstract

If we transform definitions of the conics in Euclidean plane on sphere, we obtain spherical conics. To calculate the E. Study Map of the spherical conics, we have to find one parameter equations of them. We had done this before in (Altunkaya, Yaylı, Hacısalihoglu, & Arslan, 2011). In this paper, we not only developed the results that we have found before, but also calculated the E. Study Map of the spherical conics when they are great circles by using the theorems in (Hacısalihoglu, 1977).

Constructive curves in non-Euclidean planes

“…We mention here some other papers with similar results written by Dirnböck [17] at the end of the last century the recent paper of Altunkaya at all. from 2014 [4] and the nice book of Glaeser, Stachel and Odehnal [28,66]. This latter contains valuable informations of non-Euclideans conics, too.…”