The Historical Roots of Elementary Mathematics

Exciting, hands-on approach to understanding fundamental underpinnings of modern arithmetic, algebra, geometry and number systems, by examining their origins in early Egyptian, Babylonian and Greek sources. Students can do division like the ancient Egyptians, solve quadratic equations like the Babylonians, and more.

Preface
The Greek alphabet
1 EGYPTIAN MATHEMATICS
  1-1 Prehistoric mathematics
  1-2 The earliest written mathematics
  1-3 Numerical notation
  1-4 Arithmetic operations
  1-5 Multiplication
  1-6 Fractions and division
  1-7 The red auxiliary numbers
  1-8 The 2 ÷ n table
  1-9 The leather roll
  1-10 Algebraic problems
  1-11 Geometry
2 BABYLONIAN MATHEMATICS
  2-1 Some historical facts
  2-2 Babylonian numerical notation
  2-3 The fundamental operations
  2-4 Extraction of roots
  2-5 Babylonian algebra
  2-6 A Babylonian text
  2-7 Babylonian geometry
  2-8 Approximations to p
  2-9 Another problem and a farewell to the Babylonians
3 THE BEGINNING OF GREEK MATHEMATICS
  3-1 The earliest records
  3-2 Greek numeration systems
  3-3 Thales and his importance to mathematics
  3-4 Pythagoras and the Pythagoreans
  3-5 The Pythagoreans and music
  3-6 Pythagorean arithmetica
  3-7 Pythagorean numerology
  3-8 Pythagorean astronomy
  3-9 Pythagorean geometry
  3-10 Incommensurable segments and irrational numbers
4 THE FAMOUS PROBLEMS OF GREEK ANTIQUITY
  4-1 Introduction
  4-2 Hippocrates of Chios and the quadrature of lunes
  4-3 Other quadratures
  4-4 Hippocrates' geometry
  4-5 Duplication of the cube
  4-6 The trisection problem
  4-7 Hippias and squaring of the circle
  4-8 The solutions of the Greek problems
5 EUCLID'S PHILOSOPHICAL FORERUNNERS
  5-1 Philosophy and philosophers
  5-2 Plato
  5-3 Aristotle and his theory of statements
  5-4 Concepts and definitions
  5-5 Special notations and undefined terms
6 EUCLID
  6-1 Elements
  6-2 The structure of the Elements of Euclid
  6-3 The definitions
  6-4 Postulates and common notions
  6-5 The meaning of a construction
  6-6 The purport of Postulate III
  6-7 Congruence
  6-8 Congruence (continued)
  6-9 The theory of parallels
  6-10 The comparison of areas
  6-11 The theorem of Pythagoras
  6-12 The difference between the Euclidean and the modern method of comparing areas
  6-13 Geometric algebra and regular polygons
  6-14 Number theory in the Elements
7 GREEK MATHEMATICS AFTER EUCLID. EUCLIDEAN VS. MODERN METHODS
  7-1 The span of Greek mathematics
  7-2 Archimedes and Eratosthenes
  7-3 Apollonius of Perga
  7-4 Heron of Alexandria and Diophantus
  7-5 Ptolemy and Pappus
  7-6 Review of the Greek method
  7-7 Objections to the Euclidean system
  7-8 The meaning of deduction
  7-9 Euclid's system is not purely deductive
  7-10 How is geometry built up purely deductively?
  7-11 A four-point system
8 NUMERATION AND ARITHMETIC AFTER THE GREEKS
  8-1 Roman numerals
  8-2 The abacus and tangible arithmetic
  8-3 The Hindu-Arabic numerals
  8-4 An early American place-value numeration system
  8-5 Later developments in positional notation
  8-6 Conversions between numeration systems
  8-7 Addition and subtraction algorithms in nondecimal bases
  8-8 Multiplication alogorithms in nondecimal bases
  8-9 "Fractions, rational numbers, and place-value numeration"
  8-10 Irrational numbers
  8-11 Modern theoretical foundations of arithmetic
  8-12 Modern numeration
HINTS AND ANSWERS TO SELECTED ANSWERS
INDEX