On the conics in the taxicab geometry

In this thesis consisted of three parts, basic definitions of the well-known conics in the Euclid plane are given and introducing the taxicab plane geometry, the taxicab analogues of definitions of conics, which are given only by point and line, are determined. In the first chapter, Euclidean plane geometry is presented axiomatically, and it is emphasized that notions and properties about distance can be interesting subjects for metric geometries. In the second chapter, first, the fundamental definitions of the conics in the Euclid plane, more clearly definitions as a cross section of a plane and a surface, given by using a point and a line, using two points and using two lines, are collected, and then the taxicab plane, which takes place in non-Euclidean geometry class metric geometry, is presented and the analogues of the point and line definitions of the conics are investigated. In the third chapter, the given analogues are classified and compared. As a result, contrary to those in the Euclid plane, the taxicab analogues of these only point-line definitions of the well-known conics in the Euclid plane, has different shapes except in some special cases.