Mathematics and the Laws of Nature: Developing the Language of Science

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Overview

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.
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Editorial Reviews

School Library Journal
Gr 10-Up-In uniform but independent volumes, Tabak offers sustained, meaty historical and methodological studies of the major branches of mathematics. Beginning, in some cases, with prehistoric evidence, he traces: developments in our very idea of what algebra is; the nature of ancient, projective (including non-Euclidian), and coordinate geometry; the uses of mathematics in finding precise ways to describe natural laws; the "invention" of rational, irrational and imaginary numbers, and the idea of infinity; and advances in probability theory and statistics. In each volume he analyzes the insights and accomplishments of many thinkers, ancient and modern, providing a generous array of illuminating demonstrations and examples while keeping extraneous biographical details-and, for that matter, illustrations-to a minimum, then closes with a time line, a specialized glossary, and annotated, multimedia reading lists. General readers may prefer to start with such single-volume histories as William Berlinghoff and Fernando Gouvea's Math through the Ages (Oxton House, 2002) or Ivor Grattan-Guinness's Rainbow of Mathematics (Norton, 2000), but for serious students of the subject, and collections supporting strong science programs, these make appropriate additions to both reference and circulating shelves.-John Peters, New York Public Library Copyright 2004 Reed Business Information.
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Product Details

  • ISBN-13: 9780816049578
  • Publisher: Facts on File, Incorporated
  • Publication date: 6/28/2004
  • Series: Facts on File Math Library
  • Pages: 240
  • Age range: 11 - 17 Years
  • Product dimensions: 6.20 (w) x 9.32 (h) x 0.78 (d)

Table of Contents

Acknowledgments ix
Introduction: Natural Laws xi
1 Nature as Geometry 1
The Ancient Sky 2
Recording the Stars to Predict the Future 6
The Astronomical Calculations 9
The Tablets 12
2 Mathematics and Science in Ancient Greece 15
Ratios and the Measure of the Universe 15
A Geometry of the Universe 22
A Rotating Earth 27
Archimedes: Fusing Physics with Mathematics 28
The Law of the Lever 32
Archimedes' Measurement of a Circle 34
The Siege of Syracuse 34
3 A Period of Transition 40
Nicholas Oresme 41
Nicolaus Copernicus 46
Johannes Kepler 51
Platonic Solids 57
Leonardo da Vinci and the Equation of Continuity 59
Proving Leonardo's Equation of Continuity 64
4 New Sciences 66
Simon Stevin 68
Stevin and Music 72
Galileo Galilei 75
Fermat, Descartes, and Wallis 80
5 Mathematics and the Law of Conservation of Momentum 88
The Laws of Motion 93
The Discovery of Neptune 98
6 Mathematics and the Law of Conservation of Mass 103
Leonhard Euler and the Science of Fluid Dynamics 107
The Mathematics of Combustion 109
7 Mathematics and the Laws of Thermodynamics 112
Sadi Carnot 118
Calculating the Efficiency of a Carnot Engine 124
James Prescott Joule 126
The First Law of Thermodynamics 128
The Second Law of Thermodynamics 133
Entropy 139
8 Modern Ideas about Conservation Laws 142
Olga Oleinik 147
9 Natural Laws and Randomness 153
Population Genetics 161
The Limits of Predictability 169
Genetic Counseling 174
Chronology 177
Glossary 195
Further Reading 201
Index 211
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