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The Geometry of Special Relativity
Tevian Dray
Table of Contents
Introduction
Newton’s Relativity
Einstein’s Relativity
The Physics of Special Relativity
Observers and Measurement
The Postulates of Special Relativity
Time Dilation and Length Contraction
Lorentz Transformations
Addition of Velocities
The Interval
Circle Geometry
Distance
Trigonometry
Triangle Trig
Rotations
Projections
Addition Formulas
Hyperbola Geometry
Trigonometry
Distance
Triangle Trig
Rotations
Projections
Addition Formulas
The Geometry of Special Relativity
The Surveyors
Spacetime Diagrams
Lorentz Transformations
Space and Time
Dot Product
Applications
Drawing Spacetime Diagrams
Addition of Velocities
Length Contraction
Time Dilation
Doppler Shift
Problems I
Practice
The Getaway
Angles are not Invariant
Interstellar Travel
Cosmic Rays
Doppler Effect
Paradoxes
Special Relativity Paradoxes
The Pole and Barn Paradox
The Twin Paradox
Manhole Covers
Relativistic Mechanics
Proper Time
Velocity
Conservation Laws
Energy
Useful Formulas
Problems II
Mass isn’t Conserved
Colliding Oarticles I
Colliding Oarticles II
Colliding Oarticles III
Colliding Oarticles IV
Relativistic Electromagnetism
Magnetism from Electricity
Lorentz Transformations
Vectors
Tensors
The Electromagnetic Field
Maxwell’s Equations
The Unification of Special Relativity
Problems III
Electricity vs. Magnetism I
Electricity vs. Magnetism II
Beyond Special Relativity
Problems with Special Relativity
Tidal Effects
Differential Geometry
General Relativity
Uniform Acceleration and Black Holes
Hyperbolic Geometry
Non-Euclidean Geometry
The Hyperboloid
The Poincaré Disk
The Klein Disk
The Pseudosphere
Calculus
Circle Trigonometry
Hyperbolic Trigonometry
Exponentials (and Logarithms)
Bibliography