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)
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Research
Illustrationen
Maße
Höhe: 244 mm
Breite: 170 mm
Dicke: 16 mm
Gewicht
ISBN-13
978-3-7643-8613-9 (9783764386139)
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).
