Epublication content package

Preface to the Third Edition xi
Preface to the First Edition xxiii

Chapter One: The History of Mathematics: Alternative Perspectives 1
A Justification for This Book 1
The Development of Mathematical Knowledge 3
Mathematical Signposts and Transmissions across the Ages 12

Chapter Two: Mathematics from Bones, Strings, and Standing Stones 30
Beginnings: The Ishango Bone 30
Native Americans and Their Mathematics 45
The Emergence of Written Number Systems: A Digression 58
Mayan Numeration 66

Chapter Three: The Beginnings of Written Mathematics: Egypt 79
The Urban Revolution and Its African Origins 79
Sources of Egyptian Mathematics 81
Number Recording among the Egyptians 84
Egyptian Arithmetic 88
Egyptian Algebra: The Beginnings of Rhetorical Algebra 102
Egyptian Geometry 109
Egyptian Mathematics: A General Assessment 119

Chapter Four: The Beginnings of Written Mathematics: Mesopotamia 125
Fleshing Out the History 125
Sources of Mesopotamian Mathematics 132
The Mesopotamian Number System 136
Babylonian Algebra 150
Babylonian Geometry 159

Chapter Five: Egyptian and Mesopotamian Mathematics: An Assessment 177
Changing Perceptions 178
Neglect of Egyptian and Mesopotamian Mathematics 181
The Babylonian-Egyptian-Greek
Nexus: A Seamless Story or Three Separate Episodes? 184

Chapter Six: Ancient Chinese Mathematics 188
Background and Sources 188
The Development of Chinese Numerals 198
Chinese Magic Squares (and Other Designs) 206
Mathematics from the Jiu Zhang (Suan Shu) 215

Chapter Seven: Special Topics in Chinese Mathematics 246
The "Piling-Up of Rectangles": The Pythagorean Theorem in China 248
Estimation of p 261
Solution of Higher-Order
Equations and Pascal's Triangle 270
Indeterminate Analysis in China 282
The Influence of Chinese Mathematics 296
Chinese Mathematics: A Final Assessment 301

Chapter Eight: Ancient Indian Mathematics 311
A Restatement of Intent and a Brief Historical Sketch 311
Math from Bricks: Evidence from the Harappan Culture 317
Mathematics from the Vedas 323
Early Indian Numerals and Their Development 338
Jaina Mathematics 349
Mathematics on the Eve of the Classical Period 356

Chapter Nine: Indian Mathematics: The Classical Period and After 372
Major Indian Mathematician-Astronomers 373
Indian Algebra 380
Indian Trigonometry 392
Other Notable Contributions 403

Chapter Ten: A Passage to Infinity: The Kerala Episode 418
The Actors 418
Transmission of Kerala Mathematics 435

Chapter Eleven: Prelude to Modern Mathematics: The Islamic Contribution 450
Historical Background 450
Major Medieval Islamic Mathematicians 455
Medieval Islam's Role in the Rise and Spread of Indian Numerals 461
Arithmetic in the Islamic World 466
Algebra in the Islamic World 475
Islamic Algebra and Its Influence on Europe 486
Geometry in the Islamic World 487
Trigonometry in the Islamic World 496
Mathematics from Related Sources 503
The Islamic Contribution: A Final Assessment 508

References 521
Name Index 543
Subject Index 549