Analytic Hyperbolic Geometry: Mathematical Foundations and Applications

Presenting a novel gyrovector space approach to analytic hyperbolic geometry, this text emphasizes the interdisciplinary collaborations required to further develop this extraordinary mathematical innovation and its applications.

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Analytic Hyperbolic Geometry Mathematical Foundations and Applications

Chapter 1: Introduction

Chapter 2: Gyrogroups

Chapter 3: Gyrocommutative Gyrogroups

Chapter 4: Gyrogroup Extension

Chapter 5: Gyrovectors and Cogyrovectors

Chapter 6: Gyrovector Spaces

Chapter 7: Rudiments of Differential Geometry

Chapter 8: Gyrotrigonometry

Chapter 9: Bloch Gyrovector of Quantum Computation

Chapter 10: Special Theory of Relativity: the Analytic Hyperbolic Geometric Viewpoint

10.1: Introduction

10.2: Einstein Velocity Addition

10.3: Status of the General Einstein Addition

10.4: Einstein Addition is an Indispensable Relativistic Tool

10.5: From Thomas Gyration to Thomas Precession

10.6: The Relativistic Gyrovector Space

10.7: Gyrogeodesics, Gyromidpoints and Gyrocentroids

10.8: The Midpoint and the Gyromidpoint - Newtonian and Einsteinian Mechanical Interpretation

10.9: The Einstein Gyroparallelogram

10.10: The Relativistic Gyroparallelogram Law

Notation and Special Symbols

Analytic Hyperbolic Geometry: Mathematical Foundations and Applications

Analytic Hyperbolic Geometry: Mathematical Foundations and Applications

Table of Contents