ISBN-10:
0691135266
ISBN-13:
9780691135267
Pub. Date:
10/04/2010
Publisher:
Princeton University Press
The Crest of the Peacock: Non-European Roots of Mathematics (Third Edition) / Edition 3

The Crest of the Peacock: Non-European Roots of Mathematics (Third Edition) / Edition 3

by George Gheverghese Joseph

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Overview

The Crest of the Peacock: Non-European Roots of Mathematics (Third Edition) / Edition 3

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.

Product Details

ISBN-13: 9780691135267
Publisher: Princeton University Press
Publication date: 10/04/2010
Edition description: Third
Pages: 610
Sales rank: 569,434
Product dimensions: 6.00(w) x 9.20(h) x 1.30(d)

About the Author

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.

Table of Contents

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


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