Dierck-Ekkehard Liebscher, Dr.Professor of Theoretical PhysicsInstitute of Astrophysics University of Potsdam, Germany Dierck-Eckehard Liebscher studied physics at the Humboldt University, Berlin, and received two PhDs in 1966 and 1973, both on topics of general relativity. From 1967 to 1991, he worked at the Central Institute for Astrophysics of the former GDR. In 1992, he accepted a post as senior scientist at the Astrophysical Institute, Potsdam, where he still works. Professor Liebscher is the author of several books and numerous papers.

• 1 Introduction 2 The World of Space and Time 2.1 Time-tables 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 5.3 Energy 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 Curvature 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 A Reections B Transformations B.1 Coordinates 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.1 Polarity D.2 Reection D.3 Velocity space D.4 Circles and peripheries D.5 Two examples E The Metrical Plane E.1 Classi_cation E.2 The Metric Exercises References Glossary

"... the text offers good explanations and builds up concepts well. When students ask for references for relativity, this book will be included on the list."CHOICE

Dierck-Ekkehard Liebscher, Dr.Professor of Theoretical PhysicsInstitute of Astrophysics University of Potsdam, Germany Dierck-Eckehard Liebscher studied physics at the Humboldt University, Berlin, and received two PhDs in 1966 and 1973, both on topics of general relativity. From 1967 to 1991, he worked at the Central Institute for Astrophysics of the former GDR. In 1992, he accepted a post as senior scientist at the Astrophysical Institute, Potsdam, where he still works. Professor Liebscher is the author of several books and numerous papers.

• 1 Introduction 2 The World of Space and Time 2.1 Time-tables 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 5.3 Energy 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 Curvature 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 A Reections B Transformations B.1 Coordinates 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.1 Polarity D.2 Reection D.3 Velocity space D.4 Circles and peripheries D.5 Two examples E The Metrical Plane E.1 Classi_cation E.2 The Metric Exercises References Glossary

"... the text offers good explanations and builds up concepts well. When students ask for references for relativity, this book will be included on the list."CHOICE

Dierck-Ekkehard Liebscher, Dr.Professor of Theoretical PhysicsInstitute of Astrophysics University of Potsdam, Germany Dierck-Eckehard Liebscher studied physics at the Humboldt University, Berlin, and received two PhDs in 1966 and 1973, both on topics of general relativity. From 1967 to 1991, he worked at the Central Institute for Astrophysics of the former GDR. In 1992, he accepted a post as senior scientist at the Astrophysical Institute, Potsdam, where he still works. Professor Liebscher is the author of several books and numerous papers.

• 1 Introduction 2 The World of Space and Time 2.1 Time-tables 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 5.3 Energy 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 Curvature 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 A Reections B Transformations B.1 Coordinates 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.1 Polarity D.2 Reection D.3 Velocity space D.4 Circles and peripheries D.5 Two examples E The Metrical Plane E.1 Classi_cation E.2 The Metric Exercises References Glossary

"... the text offers good explanations and builds up concepts well. When students ask for references for relativity, this book will be included on the list."CHOICE