This is not intended as a textbook aimed at introducing readers to the theory of relativity so they may calculate formally, but rather its aim is to show the connection with synthetic geometry –– a first in books on special relativity.
The book is written at an introductory (undergraduate) level, with the formal mathematics behind the constructions provided in the appendices. The novel presentation allows teaching staff to learn from it, too.
2 The World of Space and Time
2.2 Surveying space–time
2.3 Physical prerequisites of geometry
3 Reflection and Collision
3.1 Geometry and reflection
3.2 The reflection of mechanical motion
4 The Relativity Principle of Mechanics and Wave Propagation
5 Relativity Theory and its Paradoxes
5.1 Pseudo–Euclidean geometry
5.2 Einstein′s mechanics
5.4 Kinematic peculiarities .
5.5 Aberration and Fresnel′s paradox .
5.6 The net
5.7 Faster than light
6 The Circle Disguised as Hyperbola
7.1 Spheres and hyperbolic shells .
7.2 The universe
8 The Projective Origin of the Geometries of the Plane
9 The Nine Geometries of the Plane
10 General Remarks
10.1 The theory of relativity .
10.2 Geometry and physics
B.2 Inertial reference systems
B.3 Riemannian spaces, Einstein worlds
C Projective Geometry
C.1 Algebra .
C.2 Projective maps
C.3 Conic sections
D The Transition from the Projective to the Metrical Plane
D.3 Velocity space
D.4 Circles and peripheries
D.5 Two examples
E The Metrical Plane
E.2 The Metric