Introduction to Iso-Euclidean Geometry: Iso-Plane Geometry

The main purpose in this book is to represent some recent researches of Santilli iso-mathematics in the area of the plane geometry. This book is devoted to the iso-plane geometry. It summarizes the most recent contributions in this area. The book is intended for senior undergraduate students and beginning graduate students of engineering and science courses. The book contains five chapters. The chapters in the book are pedagogically organized. Each chapter concludes with a section with practical problems. In Chapter 1 we introduce iso-real numbers with one and several iso-units. They are defined the basic operations with them and they are deducted some of their basic properties. In the chapter they are defined iso-matrices, iso-determinants and iso-trigonometric functions. Chapter 2 deals with straight iso-lines. It is defined iso-angle between two iso-vectors. They are introduced iso-lines and they are deducted the main equations of iso-lines. They are given criteria for iso-perpendicularity and iso-parallel of iso-lines. In Chapter 3 we introduce iso-motions: iso-reflections, iso-rotations, iso-translations and iso-glide iso-reflections. Chapter 4 is devoted on iso-circles. They are given the iso- parametric iso-representations of the iso-circles. In Chapter 5 they are introduced iso-parabolas, iso-ellipses and iso-hyperbolas. The aim of this book is to present a clear and well-organized treatment of the concept behind the development of iso-mathematics as well as solution techniques. The text material of this book is presented in a readable and mathematically solid format.