© 2008

The Mathematics of Minkowski Space-Time

With an Introduction to Commutative Hypercomplex Numbers


Part of the Frontiers in Mathematics book series (FM)

About this book


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.


Lorentz surfaces Matrix Minkowski space Minkowski space-time gauss differential geometry hyperbolic numbers hypercomplex numbers special relativity twin paradox

Authors and affiliations

  1. 1.RomaItaly
  2. 2.Dipartimento di MatematicaUniversità di Roma “La Sapienza”RomaItaly
  3. 3.C.R. CasacciaENEARomaItaly

Bibliographic information


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)