Mathematics and the Laws of Nature: Developing the language of science

Cover......Page 1
Front Matter......Page 4
Table of Contents......Page 8
Acknowledgments......Page 10
Introduction: Natural Laws......Page 12
1. Nature as Geometry......Page 16
The Ancient Sky......Page 17
Recording the Stars to Predict the Future......Page 21
The Astronomical Calculations......Page 24
The Tablets......Page 27
Ratios and the Measure of the Universe......Page 30
A Geometry of the Universe......Page 37
A Rotating Earth......Page 42
Archimedes: Fusing Physics with Mathematics......Page 43
The Law of the Lever......Page 47
The Siege of Syracuse......Page 49
3. A Period of Transition......Page 55
Nicholas Oresme......Page 56
Nicolaus Copernicus......Page 61
Johannes Kepler......Page 66
Platonic Solids......Page 72
Leonardo da Vinci and the Equation of Continuity......Page 74
Proving Leonardo's Equation of Continuity......Page 79
4. New Sciences......Page 81
Simon Stevin......Page 83
Stevin and Music......Page 87
Galileo Galilei......Page 90
Fermat, Descartes, and Wallis......Page 95
5. Mathematics and the Law of Conservation of Momentum......Page 103
The Laws of Motion......Page 108
The Discovery of Neptune......Page 113
6. Mathematics and the Law of Conservation of Mass......Page 118
Leonhard Euler and the Science of Fluid Dynamics......Page 122
The Mathematics of Combustion......Page 124
7. Mathematics and the Laws of Thermodynamics......Page 127
Sadi Carnot......Page 133
Calculating the Efficiency of a Carnot Engine......Page 139
James Prescott Joule......Page 141
The First Law of Thermodynamics......Page 143
The Second Law of Thermodynamics......Page 148
Entropy......Page 154
8. Modern Ideas about Conservation Laws......Page 157
Olga Oleinik......Page 162
9. Natural Laws and Randomness......Page 168
Population Genetics......Page 176
The Limits of Predictability......Page 184
Genetic Counseling......Page 189
Chronology......Page 192
Glossary......Page 210
Further Reading......Page 216
Index......Page 226