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Crest of the Peacock: Non-European Roots of Mathematics 3ed

by George Gheverghese Joseph Princeton University Press
Pub Date:
Pbk 592 pages
AU$99.00 NZ$104.35
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From the Ishango Bone of central Africa and the Inca quipu of South America to the dawn of modern mathematics, The Crest of the Peacock makes it clear that human beings everywhere have been capable of advanced and innovative mathematical thinking. George Gheverghese Joseph takes us on a breathtaking multicultural tour of the roots and shoots of non-European mathematics. He shows us the deep influence that the Egyptians and Babylonians had on the Greeks, the Arabs' major creative contributions, and the astounding range of successes of the great civilizations of India and China.

The third edition emphasizes the dialogue between civilizations, and further explores how mathematical ideas were transmitted from East to West. The book's scope is now even wider, incorporating recent findings on the history of mathematics in China, India, and early Islamic civilizations as well as Egypt and Mesopotamia. With more detailed coverage of proto-mathematics and the origins of trigonometry and infinity in the East, The Crest of the Peacock further illuminates the global history of mathematics.

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

Praise for Princeton's previous editions: ''Enthralling. . . . After reading it, we cannot see the past in the same comforting haze of age-old stories, faithfully and uncritically retold from teacher to pupil down the years. . . . Invaluable for mathematics teachers at all levels.''--New Scientist

Praise for Princeton's previous editions: ''What is valuable here is the unified approach that Joseph brings . . . and the non-technical clarity that the attempt to reorder historical priorities and educate his readers out of their European prejudices requires.''--Times Literary Supplement
George Gheverghese Joseph was born in Kerala, India; grew up in Mombasa, Kenya; and completed his degrees in England. He has worked in various occupations that have taken him to places all over the world, including East and Central Africa, India, Papua New Guinea, and South East Asia.