Geometry of Special Relativity

ISBN-10: 1466510471

ISBN-13: 9781466510470

Edition: 2012

Authors: Tevian Dray
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Description: Well-known for connecting mathematical rigor to physics applications, the author of this book presents special relativity in a geometric framework using basic trigonometry. A distinctive feature of the text is its emphasis on the equivalence between special and hyperbolic trigonometry. Suitable for mathematicians and physicists, the book shows how the fascinating and easily accessible mathematics topic of hyperbolic triangle trigonometry is useful in solving problems in relativity.

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Book details

Copyright year: 2012
Publisher: A K Peters, Limited
Publication date: 7/2/2012
Binding: Hardcover
Pages: 150
Size: 6.25" wide x 9.25" long x 0.50" tall
Weight: 1.012

List of Figures and Tables
Preface
Acknowledgments
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
The Geometry of Trigonometry
Distance
Circle Trigonometry
Triangle Trigonometry
Rotations
Projections
Addition Formulas
Hyperbola Geometry
Hyperbolic Trigonometry
Distance
Hyperbola Trigonometry
Triangle Trigonometry
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
Usefull Formulas
Problems II
Mass Isn't Conserved
Identical Particles
Pion Decay I
Mass and Energy
Pion Decay II
Relativistic Electromagnetism
Magnetism from Electricity
Lorentz Transformations
Vectors
Tensors
The Electromagnetic Field
Maxwell's Equations
The Unifications of Special Relativity
Problems III
Vanishing Fields
Parallel and Perpendicular Fields
Beyond Special Relativity
Problems with Special Relativity
Tidal Effects
Differential Geometry
General Relativity
Uniform Accleration and Black Holes
Hyperbolic Geometry
Non-Euclidean Geometry
The Hyperboloid
The Poincar� Disk
The Klein Disk
The Pseudosphere
Calculus
Circle Trigonometry
Hyperbolic Trigonometry
Exponentials (and Logarithms)
Bibliography
Index
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