History of Mathematics John Tabak Mathematics and the Laws of Nature Developing the Language of Science Facts on File

The History of Mathematics is a fascinating survey of the development of math through discovery, innovation, collaboration, and experimentation. The set presents a compelling overview of myriad aspects of mathematics using understandable language and appealing line illustrations and photographs. Mathematics and the Laws of Nature is an insightful examination of the pioneering ideas, works, and applications that have made mathematics the language of science. Author John Tabak looks at the many ways in which so-called pure math has been used in the applied sciences. For example, he explores how mathematical theories contributed to the development of Kepler's laws of planetary motion as well as to combustion modeling and hydrodynamics. The book gives students insight into the ways that math is used to explain the world around them, offering many examples that show how nature can be descibed mathematically and how the physical sciences and math connect. Mathematics and the Laws of Nature includes an index, a chronology of notable events, a glossary of terms, a helpful list of Internet resources, and an array of historical and current print sources for further research. Keyed to current principles and standards in teaching math, The History of Mathematics set is essential for young readers who require information on relevant topics in mathematics. 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 Cover 1 Front Matter 4 Table of Contents 8 Acknowledgments 10 Introduction: Natural Laws 12 1. Nature as Geometry 16 The Ancient Sky 17 Recording the Stars to Predict the Future 21 The Astronomical Calculations 24 The Tablets 27 2. Mathematics and Science in Ancient Greece 30 Ratios and the Measure of the Universe 30 A Geometry of the Universe 37 A Rotating Earth 42 Archimedes: Fusing Physics with Mathematics 43 The Law of the Lever 47 Archimedes' Measurement of a Circle 49 The Siege of Syracuse 49 3. A Period of Transition 55 Nicholas Oresme 56 Nicolaus Copernicus 61 Johannes Kepler 66 Platonic Solids 72 Leonardo da Vinci and the Equation of Continuity 74 Proving Leonardo's Equation of Continuity 79 4. New Sciences 81 Simon Stevin 83 Stevin and Music 87 Galileo Galilei 90 Fermat, Descartes, and Wallis 95 5. Mathematics and the Law of Conservation of Momentum 103 The Laws of Motion 108 The Discovery of Neptune 113 6. Mathematics and the Law of Conservation of Mass 118 Leonhard Euler and the Science of Fluid Dynamics 122 The Mathematics of Combustion 124 7. Mathematics and the Laws of Thermodynamics 127 Sadi Carnot 133 Calculating the Efficiency of a Carnot Engine 139 James Prescott Joule 141 The First Law of Thermodynamics 143 The Second Law of Thermodynamics 148 Entropy 154 8. Modern Ideas about Conservation Laws 157 Olga Oleinik 162 9. Natural Laws and Randomness 168 Population Genetics 176 The Limits of Predictability 184 Genetic Counseling 189 Chronology 192 Glossary 210 Further Reading 216 Index 226 Examining the pioneering ideas, works, and applications that have made math the language of science, Mathematics and the Laws of Nature looks at the many ways in which so-called''pure''math has been used in the applied sciences. For example, the volume explores how mathematical theories contributed to the development of Kepler's laws of planetary motion, as well as to that of combustion modeling and hydrodynamics. Offering many examples showing how nature can be described mathematically and how the physical sciences and math are connected, this attention-holding and easy-to-understand volume. Describes the evolution of the idea that nature can be described in the language of mathematics. --from publisher description Examines the development of mathematical ideas, works, and applications in relation to applied sciences.