Shifting the Earth : The Mathematical Quest to Understand the Motion of the Universe

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: Archimedes, Apollonius, and the Punic Wars Ptolemy and the rise of Christianity Copernicus and the Renaissance Kepler and the Counter-Reformation Newton and the Enlightenment Einstein and the detonation of the atom bomb 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. CONTENTS......Page 6 PREFACE......Page 10 ACKNOWLEDGMENTS......Page 16 1 PERFECTION......Page 18 ATOUROFATHENS......Page 22 PLATO’S CHALLENGE......Page 25 The Stars......Page 27 The Sun......Page 28 The Planets......Page 30 THE MATH......Page 31 INSANITY......Page 41 ARISTARCHUS AND......Page 46 A HEAVY HAND......Page 55 PATRIARCHS......Page 58 THE IRONY......Page 60 FUN......Page 61 APOLLONIUS’ OSCULATING CIRCLE AND THE ELLIPSE......Page 63 The Radius of Curvature......Page 71 The Osculating Circle......Page 75 The Evolute and the Osculating Circle......Page 76 FUN’S HARVEST......Page 79 THE IMPERIAL THEOCRACY......Page 80 PTOLEMY’S UNIVERSE......Page 84 PTOLEMY AND THE......Page 87 Ptolemy’s Sun......Page 88 Ptolemy’s Mars......Page 90 INSPIRATION......Page 108 POSSIBILITIES......Page 110 , THE PURSUIT OF ELEGANCE......Page 120 Refutation......Page 122 THE MODEL......Page 123 The Martian Year......Page 125 Calibrating with Ptolemy......Page 126 Calibrating with Copernicus’ Own Observations......Page 129 Relative Radii of the Deferents of Earth and Mars......Page 130 AN ELEGANT RESULT......Page 133 COUNTERING THE REFORMATION......Page 134 THE TRIO: TYCHO, KEPLER, AND RUDOLF......Page 136 MEANWHILE IN ITALY......Page 148 , IN KEPLER’S OWN LIKENESS......Page 151 APATHSTREWNWITHCASUALTIES......Page 153 THE PHYSICIST’S LAW......Page 159 TYCHO’S GIFT......Page 162 MARS’ BED......Page 164 CONFIGURING THE ELLIPSE: THE SECOND LAW......Page 166 The Second Law and Archimedes......Page 172 Kepler’s Result......Page 178 THE MENTOR......Page 184 LOUIS XIV, THE SUN KING......Page 185 NEWTON, THE MATH KING......Page 189 THE INFLUENTIAL......Page 198 The Dry......Page 199 WITHOUT FLUXIONS Newton’s Laws without Fluxions......Page 201 The Ellipse without Fluxions: Some Preliminary Considerations......Page 208 Constructing the Ellipse, No Fluxions......Page 210 Fluxions......Page 215 The Ellipse and Newton’s Second Law......Page 219 NEWTON’S LAWS, KEPLER’S LAWS, AND CALCULUS......Page 224 Conservation of Angular Momentum; Kepler’s Second Law......Page 225 The Ellipse; Kepler’s First Law......Page 228 The Ellipse; Kepler’s First Law by a Differential Equation......Page 233 The Planet’s Periodicity, Kepler’s Third Law......Page 237 Newton and Apollonius......Page 238 NEWTON’S AGENDA......Page 241 BEGINNINGS......Page 242 DEBUNKING THE ETHER......Page 249 THE ESTABLISHED AND THE UNKNOWN......Page 257 TROUBLE......Page 263 EXITING THE QUANTUM UNIVERSE......Page 266 BENDING THE LIGHT......Page 268 AN ERGODIC LIFE......Page 269 VICTORY......Page 271 THE EXPERIMENT......Page 276 THE FAMOUS AND THE INFAMOUS......Page 277 EXODUS......Page 281 THE END......Page 284 RELATIVITY......Page 285 SPECIAL RELATIVITY The Principle of Relativity and Symmetry......Page 288 The Lorentz Transformations......Page 290 The Twin Paradox......Page 297 Relativistic Velocity......Page 298 Relativistic Mass......Page 301 Energy......Page 306 A Strange Universe......Page 309 EPILOGUE......Page 310 BIBLIOGRAPHY......Page 312 INDEX......Page 318 "Combining history, astronomy, and philosophy, this insightful book demonstrates how mathematics evolved and was used to explain planetary movements based on centuries of manual observations and careful data collection. Historical and social contexts behind the mathematical advances are provided, and the history includes the larger political and philosophical environment that affected the lives of the contributing scientists. A prime objective is to illustrate how Kepler's heliocentric pathway evolved from Ptolemy's geocentric model, with Copernicus as the critical intermediary. This reference will be valuable to science and mathematics enthusiasts, and will serve as a textbook or supplemental recommended reading for undergraduates"-- Provided by publisher