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“Summing Up: Recommended. Upper-division undergraduates through researchers/faculty; general readers.” (Choice, 1 June 2012)
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Discover how mathematics and science have propelled history
From Ancient Greece to the Enlightenment and then on to modern times, Shifting the Earth: The Mathematical Quest to Understand the Motion of the Universe takes readers on a journey motivated by the desire to understand the universe and the motion of the heavens. The author presents a thought-provoking depiction of the sociopolitical environment in which some of the most prominent scientists in history lived and then provides a mathematical account of their contributions.
From Eudoxus to Einstein, this fascinating book describes how, beginning in ancient times, pioneers in the sciences and mathematics have dramatically changed our vision of who we are as well as our place in the universe. Readers will discover how Ptolemy's geocentric model evolved into Kepler's heliocentric model, with Copernicus as the critical intermediary. The author explains how one scientific breakthrough set the stage for the next one, and he also places the scientists and their discoveries within the context of history, including:
Each chapter presents the work of a single scientist or mathematician, building on the previous chapters to demonstrate the evolutionary process of discovery. Chapters begin with a narrative section and conclude with a mathematical presentation of one of the scientist's original works. Most of these mathematical presentations, including the section on Einstein's special relativity, are accessible using only basic mathematics; however, readers can skip the mathematical sections and still follow the evolution of science and mathematics.
Shifting the Earth is an excellent book for anyone interested in the history of mathematics and how the quest to understand the motion of the heavens has influenced the broader history of humankind.
“Summing Up: Recommended. Upper-division undergraduates through researchers/faculty; general readers.” (Choice, 1 June 2012)
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
Overview
Discover how mathematics and science have propelled history
From Ancient Greece to the Enlightenment and then on to modern times, Shifting the Earth: The Mathematical Quest to Understand the Motion of the Universe takes readers on a journey motivated by the desire to understand the universe and the motion of the heavens. The author presents a thought-provoking depiction of the sociopolitical environment in which some of the most prominent ...