The History of Mathematics: An Introduction

The History of Mathematics: An Introduction, 7e by David M. Burton Preface 1Early Number Systems and Symbols 1.1 Primitive Counting A Sense of Number Notches as Tally Marks The Peruvian Quipus: Knots as Numbers 1.2 Number Recording of the Egyptians and Greeks The History of Herodotus Hieroglyphic Representation of Numbers Egyptian Hieratic Numeration The Greek Alphabetic Numeral System 1.3 Number Recording of the Babylonians Babylonian Cuneiform Script Deciphering Cuneiform: Grotefend and Rawlinson The Babylonian Positional Number System Writing in Ancient China 2 Mathematics in Early Civilizations 2.1 The Rhind Papyrus Egyptian Mathematical Papyri A Key to Deciphering: The Rosetta Stone 2.2 Egyptian Arithmetic Early Egyptian Multiplication The Unit Fraction Table Representing Rational Numbers 2.3 Four Problems from the Rhind Papyrus The Method of False Position A Curious Problem Egyptian Mathematics as Applied Arithmetic 2.4 Egyptian Geometry Approximating the Area of a Circle The Volume of a Truncated Pyramid Speculations About the Great Pyramid 2.5 Babylonian Mathematics A Tablet of Reciprocals The Babylonian Treatment of Quadratic Equations Two Characteristic Babylonian Problems 2.6 Plimpton A Tablet Concerning Number Triples Babylonian Use of the Pythagorean Theorem The Cairo Mathematical Papyrus 3 The Beginnings of Greek Mathematics 3.1 The Geometric Discoveries of Thales Greece and the Aegean Area The Dawn of Demonstrative Geometry: Thales of Miletos Measurements Using Geometry 3.2 Pythagorean Mathematics Pythagoras and His Followers Nichomachus' Introductio Arithmeticae The Theory of Figurative Numbers Zeno's Paradox 3.3 The Pythagorean Problem Geometric Proofs of the Pythagorean Theorem Early Solutions of the Pythagorean Equation The Crisis of Incommensurable Quantities Theon's Side and Diagonal Numbers Eudoxus of Cnidos 3.4 Three Construction Problems of Antiquity Hippocrates and the Quadrature of the Circle The Duplication of the Cube The Trisection of an Angle 3.5 The Quadratrix of Hippias Rise of the Sophists Hippias of Elis The Grove of Academia: Plato's Academy 4 The Alexandrian School: Euclid 4.1 Euclid and the Elements A Center of Learning: The Museum Euclid's Life and Writings 4.2 Euclidean Geometry Euclid's Foundation for Geometry Book I of the Elements Euclid's Proof of the Pythagorean Theorem Book II on Geometric Algebra Construction of the Regular Pentagon 4.3 Euclid's Number Theory Euclidean Divisibility Properties The Algorithm of Euclid The Fundamental Theorem of Arithmetic An Infinity of Primes 4.4 Eratosthenes, the Wise Man of Alexandria