Shifting the Earth: The Mathematical Quest to Understand the Motion of the UniverseISBN: 978-1-118-02427-0
Paperback
328 pages
October 2011
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ACKNOWLEDGMENTS xv
1 PERFECTION 1
2 PERFECTIONISTS 5
A Tour of Athens / 5
Plato’s Challenge / 8
Eudoxus’ Universe / 10
The Math (a mathematical presentation requiring linear algebra) / 14
3 THE ICONOCLAST 24
Insanity / 24
A Disturbing Insight / 29
Aristarchus and On the Sizes and Distances of the Sun and Moon (a mathematical presentation requiring trigonometry) / 29
4 INSTIGATORS 38
A Heavy Hand / 38
Patriarchs / 41
The Irony / 43
Fun / 44
Apollonius’ Osculating Circle and the Ellipse (a mathematical presentation requiring calculus) / 46
Fun’s Harvest / 62
5 RETROGRADE 63
The Imperial Theocracy / 63
Ptolemy’s Universe / 67
Ptolemy and The Almagest (a mathematical presentation requiring trigonometry) / 70
Inspiration / 91
6 REVOLUTIONARY 93
Possibilities / 93
Copernicus’ On Revolutions, the Pursuit of Elegance / 103
The Model (a mathematical presentation requiring trigonometry) / 106
An Elegant Result / 116
7 RENEGADES 117
Countering the Reformation / 117
The Trio: Tycho, Kepler, and Rudolf / 119
Meanwhile in Italy / 131
New Astronomy, in Kepler’s Own Likeness / 134
A Path Strewn with Casualties / 136
The Physicist’s Law / 142
Tycho’s Gift / 145
Mars’ Bed / 147
Configuring the Ellipse: The Second Law (a mathematical presentation requiring trigonometry) / 149
The Mentor / 167
8 THE AUTHORITY 168
Louis XIV, the Sun King / 168
Newton, the Math King / 172
The Influential Principia / 181
Without Fluxions (a mathematical presentation of Newton’s laws of motion and the ellipse requiring high school algebra) / 184
Newton’s Laws, Kepler’s Laws, and Calculus (a calculus-based presentation of Newton’s laws of motion and the ellipse) / 207
Newton’s Agenda / 224
9 RULE BREAKERS 225
Beginnings / 225
Debunking the Ether / 232
The Established and the Unknown / 240
Trouble / 246
Exiting the Quantum Universe / 249
Bending the Light / 251
An Ergodic Life / 252
Victory / 254
The Experiment / 259
The Famous and the Infamous / 260
Exodus / 264
The End / 267
Relativity / 268
Special Relativity (a mathematical presentation requiring high school algebra) / 271
EPILOGUE 293
BIBLIOGRAPHY 295
INDEX 301
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Shifting the Earth: The Mathematical Quest to Understand the Motion of the Universe (US $62.95)
-and- The Ellipse: A Historical and Mathematical Journey (US $63.95)
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