On dual number programming and applications

This thesis consists of four chapters. The first chapter is dedicated to the introduction, where the fundamental concepts, definitions, and necessary theorems of two-dimensional Euclidean space that will be required in later chapters are presented. In the second chapter, after providing the fundamental concepts of the Lorentz plane, vectors in the two-dimensional Lorentz plane and their properties are examined using inner products and matrices. The third chapter defines dual numbers and the set of dual numbers. Then, algebraic structures in the Lorentz space with dual numbers are explored. The fourth chapter is based on Harry H. Cheng's [4] article, "Programming with Dual Numbers and its Application in Mechanisms Design". It considers the mathematical applications of the defined dual numbers in CH terms (addition, multiplication, exponentiation, square root extraction, and angle calculation). Building on this, the original contribution of the study involves implementing calculations in a program written in the C# programming language. This includes addressing mathematical uncertainties in the program and presenting unique examples. This chapter also contains the results and recommendations.