Fundamental Theories of Physics

Hyperbolic Triangle Centers

The Special Relativistic Approach

Authors: Ungar, A.A.

  • Offers a continuation of A. Ungar’s successful work on hyperbolic geometry, now with an introduction of hyperbolic barycentric coordinates
  • Proves how, contrary to general belief, Einstein’s relativistic mass meshes up well with Minkowski’s four-vector formalisms of special relativity
  • Sets the ground for investigating hyperbolic triangle centers analytically with respect to its hyperbolic triangle vertices
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eBook $109.00
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  • ISBN 978-90-481-8637-2
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Hardcover $139.00
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  • ISBN 978-90-481-8636-5
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  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
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  • ISBN 978-94-007-3265-0
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About this book

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 general belief, Einstein’s relativistic mass hence meshes up extraordinarily well with Minkowski’s four-vector formalism of special relativity. In Euclidean geometry, barycentric coordinates can be used to determine various triangle centers. While there are many known Euclidean triangle centers, only few hyperbolic triangle centers are known, and none of the known hyperbolic triangle centers has been determined analytically with respect to its hyperbolic triangle vertices. In his recent research, the author set the ground for investigating hyperbolic triangle centers via hyperbolic barycentric coordinates, and one of the purposes of this book is to initiate a study of hyperbolic triangle centers in full analogy with the rich study of Euclidean triangle centers. Owing to its novelty, the book is aimed at a large audience: it can be enjoyed equally by upper-level undergraduates, graduate students, researchers and academics in geometry, abstract algebra, theoretical physics and astronomy. For a fruitful reading of this book, familiarity with Euclidean geometry is assumed. Mathematical-physicists and theoretical physicists are likely to enjoy the study of Einstein’s special relativity in terms of its underlying hyperbolic geometry. Geometers may enjoy the hunt for new hyperbolic triangle centers and, finally, astronomers may use hyperbolic barycentric coordinates in the velocity space of cosmology.

Table of contents (10 chapters)

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-90-481-8637-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-90-481-8636-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-94-007-3265-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Hyperbolic Triangle Centers
Book Subtitle
The Special Relativistic Approach
Authors
Series Title
Fundamental Theories of Physics
Series Volume
166
Copyright
2010
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-90-481-8637-2
DOI
10.1007/978-90-481-8637-2
Hardcover ISBN
978-90-481-8636-5
Softcover ISBN
978-94-007-3265-0
Series ISSN
0168-1222
Edition Number
1
Number of Pages
XVI, 319
Topics