The Britannica Guide to Numbers and Measurement by Publishing, Britannica Educational -- Read -- Imperial Library of Trantor

Index

Cover Page Title Page Copyright Page Contents Introduction Chapter 1: Numbers

Numerals and Numeral Systems

Number Bases Numeral Systems

Simple Grouping Systems Multiplicative Grouping Systems Ciphered Numeral Systems Positional Numeral Systems

Development of Modern Numerals and Numeral Systems

The Hindu-Arabic System The Binary System Decimal Numerals Represented by Digits

Arithmetic

Fundamental Definitions and Laws

Natural Numbers Addition and Multiplication Fundamental Laws of Arithmetic Integers Exponents

Theory of Divisors

Fundamental Theory Some Divisibility Rules Rational Numbers Irrational Numbers

Modular Arithmetic Logarithms

Properties of Logarithms History of Logarithms

Number Theory

From Prehistory Through Classical Greece

Pythagoras Euclid Diophantus

Number Theory in the East Modern Number Theory

Pierre de Fermat Number Theory in the 18th Century Number Theory in the 19th Century Number Theory in the 20th Century

Unsolved Problems

Set Theory

Introduction to Naive Set Theory

Fundamental Set Concepts Essential Features of Cantorian Set Theory

Axiomatic Set Theory

The Zermelo-Fraenkel Axioms The Neumann-Bernays-Gödel Axioms Limitations of Axiomatic Set Theory Present Status of Axiomatic Set Theory

Chapter 2: Great Arithmeticians and Number Theorists

The Ancient World

Aryabhata I Diophantus of Alexandria Muhammad ibn Mūsā al-Khwārizmī Nicomachus of Gerasa Leonardo Pisano Qin Jiushao

Renaissance Europe

Henry Briggs Joost Bürgi Pierre de Fermat Carl Friedrich Gauss Christian Goldbach Marin Mersenne John Napier

The Modern Era

Paul Isaak Bernays Georg Cantor Paul Joseph Cohen Richard Dedekind Peter Gustav Lejeune Dirichlet Gottlob Frege Kurt Gödel Bertrand Russell Alan Mathison Turing Ivan Matveyevich Vinogradov John von Neumann

Chapter 3: Numerical Terms and Concepts

Algorithm Arithmetic Function Associative Laws Axiom of Choice Binary Code Binary Number System Cantor’s Theorem Chinese Remainder Theorem Church’s Thesis Commutative Laws Complex Number Continuum Hypothesis Decimal Number System Decision Problem Dedekind Cut Diophantine Equation Dirichlet’s Theorem Distributive Law Equivalence Relation Euclidean Algorithm Euclid’s Twin Prime Conjecture Factor Factorial Fermat Prime Fermat’s Last Theorem Fermat’s Little Theorem Fibonacci Numbers Fraction Fundamental Theorem of Arithmetic Geometric Series Goldbach Conjecture Harmonic Sequence Imaginary Number Incompleteness Theorems Inequality Infinite Series Infinity Integer Lagrange’s Four-Square Theorem Mersenne Number Number Perfect Number Prime Prime Number Theorem Pseudoprime Rational Number Real Number Riemann Zeta Function Root Russell’s Paradox Set Square Root Transfinite Number Transitive Law Turing Machine Vinogradov’s Theorem Waring’s Problem Wilson’s Theorem Zorn’s Lemma

Chapter 4: Measurements

Measurement Systems

Early Units and Standards

Ancient Mediterranean Systems Medieval Systems

The English and U.S. Customary Systems of Weights and Measures

The English System British Imperial and U.S. Customary Systems of Weights and Measurements The United States Customary System

The Metric System of Measurement

The Development and Establishment of the Metric System The International System of Units

Measurement Instruments and Systems Measurement Theory

Chapter 5: Measurement Pioneers

Norman Robert Campbell Anders Celsius Giovanni Giorgi Edmund Gunter Joseph-Louis Lagrange Pierre-Simon Laplace Pierre Mechain Jesse Ramsden

Chapter 6: Measurement Terms and Concepts

Acre Amphora Angstrom (Å) Apothecaries’ Weight Are Avoirdupois Weight Barrel Bat British Imperial System Bushel Centimetre (cm) Cord Cubit Cup Dram Fathom Finger Foot Furlong Gal Gill Grain Gram (gm or g) Gunter’s Chain Hand Hectare Inch International Bureau of Weights and Measures International System of Units International Unit (IU) Kilometre (km) Knot League Libra Litre (l) Log Metre Metrētēs Metric System Micrometre Mile Millimetre (mm) Mina Mou Ounce Peck Pint Pound Qa Quart Rod Scruple Shi Steradian Stere Stone Talent Ton Troy Weight Zhang

Glossary Bibliography Index

← Prev
Back
Next →

← Prev
Back
Next →