Hyperbolic numbers are proposed for a rigorous geometric formalization of the space-time symmetry of two-dimensional Special Relativity. The system of hyperbolic numbers as a simple extension of the field of complex numbers is extensively studied in the book. In particular, an exhaustive solution of the "twin paradox" is given, followed by a detailed exposition of space-time geometry and trigonometry. Finally, an appendix on general properties of commutative hypercomplex systems with four unities is presented.
Rezensionen / Stimmen
From the reviews:
"It is worth pointing out that the book is mainly a text about commutative hypercomplex numbers and some of their applications to a 2-dimensional Minkowski spacetime. . This book should be interesting to anybody who is interested in applications of hypercomplex numbers . . In conclusion, I recommend this book to anyone who wants to learn about hypercomplex numbers." (Emanuel Gallo, Mathematical Reviews, Issue 2010 d)
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ISBN-13
978-3-7643-8614-6 (9783764386146)
DOI
10.1007/978-3-7643-8614-6
Schweitzer Klassifikation
N-Dimensional Commutative Hypercomplex Numbers.- The Geometries Generated by Hypercomplex Numbers.- Trigonometry in the Minkowski Plane.- Uniform and Accelerated Motions in the Minkowski Space-Time (Twin Paradox).- General Two-Dimensional Hypercomplex Numbers.- Functions of a Hyperbolic Variable.- Hyperbolic Variables on Lorentz Surfaces.- Constant Curvature Lorentz Surfaces.- Generalization of Two-Dimensional Special Relativity (Hyperbolic Transformations and the Equivalence Principle).
