Abraham Albert Ungar

Analytic Hyperbolic Geometry in N Dimensions (eBook, PDF)

An Introduction

• Format: PDF

Produktbeschreibung

This book introduces for the first time the hyperbolic simplex as an important concept in n-dimensional hyperbolic geometry. The extension of common Euclidean geometry to N dimensions, with N being any positive integer, results in greater generality and succinctness in related expressions. Using new mathematical tools, the book demonstrates that this is also the case with analytic hyperbolic geometry. For example, the author analytically determines the hyperbolic circumcenter and circumradius of any hyperbolic simplex.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 622
• Erscheinungstermin: 17. Dezember 2014
• Englisch
• ISBN-13: 9781482236682
• Artikelnr.: 42365800

Autorenporträt

Abraham Albert Ungar

Inhaltsangabe

List of Figures. Preface. Author's Biography. Introduction. Einstein
Gyrogroups and Gyrovector Spaces. Einstein Gyrogroups. Problems. Einstein
Gyrovector Spaces. Problems. Relativistic Mass Meets Hyperbolic Geometry.
Problems. Mathematical Tools for Hyperbolic Geometry. Barycentric and
Gyrobarycentric Coordinates. Problems. Gyroparallelograms and
Gyroparallelotopes. Problems. Gyrotrigonometry. Problems. Hyperbolic
Triangles and Circles. Gyrotriangles and Gyrocircles. Problems. Gyrocircle
Theorems. Problems. Hyperbolic Simplices, Hyperplanes and Hyperspheres in N
Dimensions. Gyrosimplices. Problems. Gyrosimplex Gyrovolume. Problems.
Hyperbolic Ellipses and Hyperbolas. Gyroellipses and Gyrohyperbolas.
Problems. VI Thomas Precession. Thomas Precession. Problems. Bibliography.
Index.