The Crest of the Peacock

by Joseph, George Gheverghese

• ISBN13: 9780691135267
• ISBN10: 0691135266
• Edition: 3rd
• Format: Paperback
• Copyright: 2010-10-04
• Publisher: Princeton Univ Pr

Summary

From the Ishango Bone of central Africa and the Incaquipuof South America to the dawn of modern mathematics,The Crest of the Peacockmakes 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 Peacockfurther illuminates the global history of mathematics.

Author Biography

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	p. xi
Preface to the First Edition	p. xxiii
The History of Mathematics: Alternative Perspectives	p. 1
A Justification for This Book	p. 1
The Development of Mathematical Knowledge	p. 3
Mathematical Signposts and Transmissions across the Ages	p. 12
Mathematics from Bones, Strings, and Standing Stones	p. 30
Beginnings: The Ishango Bone	p. 30
Native Americans and Their Mathematics	p. 45
The Emergence of Written Number Systems: A Digression	p. 58
Mayan Numeration	p. 66
The Beginnings of Written Mathematics: Egypt	p. 79
The Urban Revolution and Its African Origins	p. 79
Sources of Egyptian Mathematics	p. 81
Number Recording among the Egyptians	p. 84
Egyptian Arithmetic	p. 88
Egyptian Algebra: The Beginnings of Rhetorical Algebra	p. 102
Egyptian Geometry	p. 109
Egyptian Mathematics: A General Assessment	p. 119
The Beginnings of Written Mathematics: Mesopotamia	p. 125
Fleshing Out the History	p. 125
Sources of Mesopotamian Mathematics	p. 132
The Mesopotamian Number System	p. 136
Babylonian Algebra	p. 150
Babylonian Geometry	p. 159
Egyptian and Mesopotamian Mathematics: An Assessment	p. 177
Changing Perceptions	p. 178
Neglect of Egyptian and Mesopotamian Mathematics	p. 181
The Babylonian-Egyptian-Greek Nexus: A Seamless Story or Three Separate Episodes?	p. 184
Ancient Chinese Mathematics	p. 188
Background and Sources	p. 188
The Development of Chinese Numerals	p. 198
Chinese Magic Squares (and Other Designs)	p. 206
Mathematics from the Jiu Zhang (Suan Shu)	p. 215
Special Topics in Chinese Mathematics	p. 246
The "Piling-Up of Rectangles": The Pythagorean Theorem in China	p. 248
Estimation of ¿	p. 261
Solution of Higher-Order Equations and Pascal's Triangle	p. 270
Indeterminate Analysis in China	p. 282
The Influence of Chinese Mathematics	p. 296
Chinese Mathematics: A Final Assessment	p. 301
Ancient Indian Mathematics	p. 311
A Restatement of Intent and a Brief Historical Sketch	p. 311
Math from Bricks: Evidence from the Harappan Culture	p. 317
Mathematics from the Vedas	p. 323
Early Indian Numerals and Their Development	p. 338
Jaina Mathematics	p. 349
Mathematics on the Eve of the Classical Period	p. 356
Indian Mathematics: The Classical Period and After	p. 372
Major Indian Mathematician-Astronomers	p. 373
Indian Algebra	p. 380
Indian Trigonometry	p. 392
Other Notable Contributions	p. 403
A Passage to Infinity: The Kerala Episode	p. 418
The Actors	p. 418
Transmission of Kerala Mathematics	p. 435
Prelude to Modern Mathematics: The Islamic Contribution	p. 450
Historical Background	p. 450
Major Medieval Islamic Mathematicians	p. 455
Medieval Islam's Role in the Rise and Spread of Indian Numerals	p. 461
Arithmetic in the Islamic World	p. 466
Algebra in the Islamic World	p. 475
Islamic Algebra and Its Influence on Europe	p. 486
Geometry in the Islamic World	p. 487
Trigonometry in the Islamic World	p. 496
Mathematics from Related Sources	p. 503
The Islamic Contribution: A Final Assessment	p. 508
References	p. 521
Name Index	p. 543
Subject Index	p. 549
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