TABLE OF CONTENTS In the small arena of terrestrial and planetary measurements, Euclidean geometry is the shoe that fits the foot. Over the vast reaches of intergalactic spacetime, Lorentzian geometry, the geometry of general relativity, appears to be what is wanted. Neglecting gravitation, the geometry needed is the hyperbolic geometry of Bolyai and Lobachevsky, the geometry of special relativity, [Criado and Alamo (2001); Criado and Alamo (2002)].
The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate physics student. Some undergraduate physics students regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. But this book opens the door on its mission to make the hyperbolic geometry of Bolyai and Lobachevsky, which underlies the special theory of relativity, accessible to a wider audience in terms of gyrogeometry, the super analytic geometry that unifies analytic Euclidean and hyperbolic geometry.
Special relativity was introduced by Einstein a century ago in order to explain the massive experimental evidence against ether as the medium for propagating electromagnetic waves. However, as studied in all modern physics books, special relativity is not Einsteinian special relativity, the special theory of relativity as was originally formulated by Einstein in 1905 [Einstein (1905)]. Rather, it is Minkowskian special relativity, the special theory of relativity as was subsequently reformulated by Minkowski in 1908 [Lorentz, Einstein, Minkowski and Weyl (1952)]. Einsteinian and Minkowskian special relativity form two different approaches to...
