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

ISBN: 978-1-118-02427-0
328 pages
October 2011
Shifting the Earth: The Mathematical Quest to Understand the Motion of the Universe (1118024273) cover image
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.

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A Tour of Athens / 5

Plato’s Challenge / 8

Eudoxus’ Universe / 10

The Math (a mathematical presentation requiring linear algebra) / 14


Insanity / 24

A Disturbing Insight / 29

Aristarchus and On the Sizes and Distances of the Sun and Moon (a mathematical presentation requiring trigonometry) / 29


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


The Imperial Theocracy / 63

Ptolemy’s Universe / 67

Ptolemy and The Almagest (a mathematical presentation requiring trigonometry) / 70

Inspiration / 91


Possibilities / 93

Copernicus’ On Revolutions, the Pursuit of Elegance / 103

The Model (a mathematical presentation requiring trigonometry) / 106

An Elegant Result / 116


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


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


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




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ARTHUR MAZER, PhD, is Manager of Quantitative Analytics at Southern California Edison, where he oversees the risk assessment of the company's power and gas portfolio. Throughout his career, he has held various academic positions as well as analyst positions at Electrabel, Progress Energy, and Energy Power Marketing Corporation. Dr. Mazer is the author of Electric Power Planning for Regulated and Deregulated Markets and The Ellipse: A Historical and Mathematical Journey, both published by Wiley.

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“Summing Up: Recommended.  Upper-division undergraduates through researchers/faculty; general readers.”  (Choice, 1 June 2012)


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Shifting the Earth: The Mathematical Quest to Understand the Motion of the Universe (US $64.95)

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