On comparison of hyperbolic and complex numbers

In this thesis, the foundamental mathematical structures of complex and hyperbolic numbers were examined, focusing on their geometric interpretations. In the first chapter, the theoretical foundation of the study was established by presenting fundamental concepts. The second chapter detailed the definition, properties, and geometric interpretations of complex numbers. In the third chapter,the place of hyperbolic numbers in the Lorentz plane was analyzed,offering perspectives distinct from classical geometry. Hyperbolic numbers and the Lorentz plane, especially at the intersection of physics and mathematics, hold significant importance in modeling space and time concepts. These structures, which share similarities with complex numbers, also exhibit unique geometric characteristics, differing from them in various aspects. Based on this foundation, the fourth chapter explores the structural and functional differences between hyperbolic and complex number systems, presenting some analyses regarding their counterparts in the physical world. The aim is to contribute to the understanding of these two numerical systems by examining their geometric interpretations and abstract mathematical concepts in the context of their physical counterparts. The conclusion chapter summarizes the findings of this study. Keywords: Complex Numbers, Hyperbolic Numbers, Lorentz Metric, Lorentz Plane