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Hyperbolic triangle centers: The special relativistic approach

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After A. Ungar had introduced vector algebra and Cartesian coordinates into hyperbolic geometry in his earlier books, along with novel applications in Einstein's special theory of relativity, the purpose of his new book is to introduce hyperbolic barycentric coordinates, another important concept to embed Euclidean geometry into hyperbolic geometry. It will be demonstrated that, in full analogy to classical  Read more...

Abstract: After A. Ungar had introduced vector algebra and Cartesian coordinates into hyperbolic geometry in his earlier books, along with novel applications in Einstein's special theory of relativity, the purpose of his new book is to introduce hyperbolic barycentric coordinates, another important concept to embed Euclidean geometry into hyperbolic geometry. It will be demonstrated that, in full analogy to classical mechanics where barycentric coordinates are related to the Newtonian mass, barycentric coordinates are related to the Einsteinian relativistic mass in hyperbolic geometry. Contrary to gener

Author(s): Ungar, Abraham A
Series: Fundamental Theories of Physics 166
Publisher: Springer
Year: 2010

Language: English
Pages: 321
City: Dordrecht
Tags: Geometry, Hyperbolic.;Special relativity (Physics);Mathematics.

Content: Preface
Contents
Acronyms
The Special Relativistic Approach to Hyperbolic Geometry
Einstein Gyrogroups
Einstein Gyrovector Spaces
When Einstein Meets Minkowski
Mathematical Tools for Hyperbolic Geometry
Euclidean and Hyperbolic Barycentric Coordinates
Gyrovectors
Gyrotrigonometry
Hyperbolic Triangle Centers
Gyrotriangle Gyrocenters
Gyrotriangle Exgyrocircles
Gyrotriangle Gyrocevians
Epilogue
Glossary
References
Author Index
Subject Index.