The Britannica Guide to Numbers and Measurement
by Hosch, William L.Format: Hardcover
Pub. Date: 2010-08-15
Publisher(s): Britannica Educational Pub
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Summary
Communication and, indeed, our comprehension of the world in general are largely ordered by the number and measurement systems that have arisen over time. Numbers lend structure to human interaction by standardizing the language we use to interpret quantities and by helping us understand natural relationships between varying concepts. This book delves into the history of mathematical reasoning and the progression of numerical thought around the world. With detailed biographies of seminal thinkers and theorists, readers develop a sophisticated understanding of some of the most fundamental arithmetical concepts as well as the individuals who established them.
Table of Contents
| Introduction | p. 12 |
| Numbers | p. 21 |
| Numerals and Numeral Systems | p. 22 |
| Number Bases | p. 22 |
| Numeral Systems | p. 24 |
| Simple Grouping Systems | p. 24 |
| Multiplicative Grouping Systems | p. 30 |
| Ciphered Numeral Systems | p. 30 |
| Positional Numeral Systems | p. 31 |
| Development of Modern Numerals and Numeral Systems | p. 34 |
| The Hindu-Arabic System | p. 34 |
| The Binary System | p. 36 |
| Decimal Numerals Represented by Digits | p. 36 |
| Arithmetic | p. 36 |
| Fundamental Definitions and Laws | p. 37 |
| Natural Numbers | p. 37 |
| Addition and Multiplication | p. 38 |
| Fundamental Laws of Arithmatic | p. 39 |
| Integers | p. 40 |
| Exponents | p. 41 |
| Theory of Divisors | p. 41 |
| Fundamental Theory | p. 43 |
| Some Divisibility Rules | p. 44 |
| Rational Numbers | p. 45 |
| Irrational Numbers | p. 47 |
| Modular Arithmetic | p. 49 |
| Logarithms | p. 51 |
| Properties of Logarithms | p. 52 |
| History of Logarithms | p. 53 |
| Number Theory | p. 56 |
| From Prehistory Through Classical Greece | p. 57 |
| Pythagoras | p. 57 |
| Euclid | p. 58 |
| Diophantus | p. 60 |
| Number Theory in the East | p. 60 |
| Modern Number Theory | p. 61 |
| Pierre de Fermat | p. 62 |
| Number Theory in the 18th Century | p. 64 |
| Number Theory in the 19th Century | p. 66 |
| Number Theory in the 20th Century | p. 68 |
| Unsolved Problems | p. 70 |
| Set Theory | p. 71 |
| Introduction to Naive Set Theory | p. 72 |
| Fundamental Set Concepts | p. 72 |
| Essential Features of Cantorian Set Theory | p. 75 |
| Axiomatic Set Theory | p. 80 |
| The Zermelo-Fraenkel Axioms | p. 81 |
| The Neumann-Bernays-Gödel Axioms | p. 90 |
| Limitations of Axiomatic Set Theory | p. 92 |
| Present Status of Axiomatic Set Theory | p. 94 |
| Great Arithmeticians and Number Theorists | p. 97 |
| The Ancient World | p. 97 |
| Aryabhata I | p. 97 |
| Diophantus of Alexandria | p. 99 |
| Muhammad ibn Musaal-Khwarizmi | p. 103 |
| Nicomachus of Gerasa | p. 105 |
| Leonardo Pisano | p. 105 |
| Qin Jiushao | p. 109 |
| Renaissance Europe | p. 111 |
| Henry Briggs | p. 111 |
| Joost Bürgi | p. 113 |
| Pierre de Fermat | p. 114 |
| Carl Friedrich Gauss | p. 116 |
| Christian Goldbach | p. 118 |
| Marin Mersenne | p. 119 |
| John Napier | p. 121 |
| The Modern Era | p. 124 |
| Paul Isaak Bernays | p. 124 |
| Georg Cantor | p. 25 |
| Paul Joseph Cohen | p. 127 |
| Richard Dedekind | p. 129 |
| Peter Gustav Lejeune Dirichlet | p. 132 |
| Gottlob Frege | p. 133 |
| Kurt Gödel | p. 135 |
| Bertrand Russell | p. 138 |
| Alan Mathison Turing | p. 142 |
| Ivan Matveyevich Vinogradov | p. 144 |
| John von Neumann | p. 145 |
| Numerical Terms and Concepts | p. 150 |
| Algorithm | p. 150 |
| Arithmetic Function | p. 152 |
| Associative Laws | p. 152 |
| Axiom of Choice | p. 153 |
| Binary Code | p. 155 |
| Binary Number System | p. 155 |
| Cantor's Theorem | p. 156 |
| Chinese Remainder Theorem | p. 157 |
| Church's Thesis | p. 158 |
| Commutative Laws | p. 158 |
| Complex Number | p. 158 |
| Continuum Hypothesis | p. 159 |
| Decimal Number System | p. 160 |
| Decision Problem | p. 160 |
| Dedekind Cut | p. 161 |
| Diophantine Equation | p. 162 |
| Dirichlet's Theorem | p. 162 |
| Distributive Law | p. 163 |
| Equivalence Relation | p. 163 |
| Euclidean Algorithm | p. 164 |
| Euclid's Twin Prime Conjecture | p. 165 |
| Factor | p. 166 |
| Factorial | p. 167 |
| Fermat Prime | p. 167 |
| Fermat's Last Theorem | p. 168 |
| Fermat's Little Theorem | p. 168 |
| Fibonacci Numbers | p. 169 |
| Fraction | p. 171 |
| Fundamental Theorem of Arithmetic | p. 171 |
| Geometric Series | p. 171 |
| Goldbach Conjecture | p. 172 |
| Harmonic Sequence | p. 173 |
| Imaginary Number | p. 175 |
| Incompleteness Theorems | p. 175 |
| Inequality | p. 176 |
| Infinite Series | p. 176 |
| Infinity | p. 178 |
| Integer | p. 178 |
| Lagrange's Four-Square Theorem | p. 179 |
| Mersenne Number | p. 180 |
| Number | p. 181 |
| Perfect Number | p. 182 |
| Prime | p. 183 |
| Prime Number Theorem | p. 184 |
| Pseudoprime | p. 185 |
| Rational Number | p. 186 |
| Real Number | p. 187 |
| Riemann Zeta Function | p. 188 |
| Root | p. 189 |
| Russell's Paradox | p. 191 |
| Set | p. 193 |
| Square Root | p. 193 |
| Transfinite Number | p. 194 |
| Transitive Law | p. 194 |
| Turing Machine | p. 195 |
| Vinogradov's Theorem | p. 197 |
| Waring's Problem | p. 197 |
| Wilson's Theorem | p. 198 |
| Zorn's Lemma | p. 198 |
| Measurements | p. 201 |
| Measurement Systems | p. 201 |
| Early Units and Standards | p. 202 |
| Ancient Mediterranean Systems | p. 202 |
| Medieval Systems | p. 209 |
| The English and U.S. Customary Systems of Weights and Measures | p. 209 |
| The English System | p. 209 |
| British Imperial and U.S. Customary Systems of Weights and Measurements | p. 210 |
| The United States Customary System | p. 216 |
| The Metric System of Measurement | p. 219 |
| The Development and Establishment of the Metric System | p. 219 |
| The International System of Units | p. 222 |
| Measurement Instruments and Systems | p. 225 |
| Measurement Theory | p. 227 |
| Measurement Pioneers | p. 230 |
| Norman Robert Campbell | p. 230 |
| Anders Celsius | p. 231 |
| Giovanni Giorgi | p. 232 |
| Edmund Gunter | p. 233 |
| Joseph-Louis Lagrange | p. 234 |
| Pierre-Simon Laplace | p. 235 |
| Pierre Mechain | p. 235 |
| Jesse Ramsden | p. 236 |
| Measurement Terms and Concepts | p. 237 |
| Acre | p. 237 |
| Amphora | p. 237 |
| Angstrom (Å) | p. 238 |
| Apothecaries' Weight | p. 238 |
| Are | p. 239 |
| Avoirdupois Weight | p. 239 |
| Barrel | p. 240 |
| Bat | p. 240 |
| British Imperial System | p. 241 |
| Bushel | p. 243 |
| Centimetre (cm) | p. 244 |
| Cord | p. 244 |
| Cubit | p. 245 |
| Cup | p. 245 |
| Dram | p. 245 |
| Fathom | p. 246 |
| Finger | p. 246 |
| Foot | p. 247 |
| Furlong | p. 247 |
| Gal | p. 248 |
| Gill | p. 248 |
| Grain | p. 248 |
| Gram (gm or g) | p. 249 |
| Gunter's Chain | p. 249 |
| Hand | p. 250 |
| Hectare | p. 250 |
| Inch | p. 250 |
| International Bureau of Weights and Measures | p. 251 |
| International System of Units | p. 252 |
| International Unit (IU) | p. 253 |
| Kilometre (km) | p. 254 |
| Knot | p. 254 |
| League | p. 255 |
| Libra | p. 255 |
| Litre (l) | p. 256 |
| Log | p. 257 |
| Metre | p. 257 |
| Metretes | p. 258 |
| Metric System | p. 259 |
| Micrometre | p. 260 |
| Mile | p. 261 |
| Millimetre (mm) | p. 262 |
| Mina | p. 262 |
| Mou | p. 262 |
| Ounce | p. 263 |
| Peck | p. 263 |
| Pint | p. 264 |
| Pound | p. 264 |
| Qa | p. 265 |
| Quart | p. 266 |
| Rod | p. 266 |
| Scruple | p. 266 |
| Shi | p. 267 |
| Steradian | p. 267 |
| Stere | p. 267 |
| Stone | p. 268 |
| Talent | p. 268 |
| Ton | p. 269 |
| Troy Weight | p. 270 |
| Zhang | p. 270 |
| Glossary | p. 271 |
| Bibliography | p. 274 |
| Index | p. 278 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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