The Crest of the Peacock: Non-European Roots of Mathmatics

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

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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 Editionp. xi
Preface to the First Editionp. xxiii
The History of Mathematics: Alternative Perspectivesp. 1
A Justification for This Bookp. 1
The Development of Mathematical Knowledgep. 3
Mathematical Signposts and Transmissions across the Agesp. 12
Mathematics from Bones, Strings, and Standing Stonesp. 30
Beginnings: The Ishango Bonep. 30
Native Americans and Their Mathematicsp. 45
The Emergence of Written Number Systems: A Digressionp. 58
Mayan Numerationp. 66
The Beginnings of Written Mathematics: Egyptp. 79
The Urban Revolution and Its African Originsp. 79
Sources of Egyptian Mathematicsp. 81
Number Recording among the Egyptiansp. 84
Egyptian Arithmeticp. 88
Egyptian Algebra: The Beginnings of Rhetorical Algebrap. 102
Egyptian Geometryp. 109
Egyptian Mathematics: A General Assessmentp. 119
The Beginnings of Written Mathematics: Mesopotamiap. 125
Fleshing Out the Historyp. 125
Sources of Mesopotamian Mathematicsp. 132
The Mesopotamian Number Systemp. 136
Babylonian Algebrap. 150
Babylonian Geometryp. 159
Egyptian and Mesopotamian Mathematics: An Assessmentp. 177
Changing Perceptionsp. 178
Neglect of Egyptian and Mesopotamian Mathematicsp. 181
The Babylonian-Egyptian-Greek Nexus: A Seamless Story or Three Separate Episodes?p. 184
Ancient Chinese Mathematicsp. 188
Background and Sourcesp. 188
The Development of Chinese Numeralsp. 198
Chinese Magic Squares (and Other Designs)p. 206
Mathematics from the Jiu Zhang (Suan Shu)p. 215
Special Topics in Chinese Mathematicsp. 246
The "Piling-Up of Rectangles": The Pythagorean Theorem in Chinap. 248
Estimation of p. 261
Solution of Higher-Order Equations and Pascal's Trianglep. 270
Indeterminate Analysis in Chinap. 282
The Influence of Chinese Mathematicsp. 296
Chinese Mathematics: A Final Assessmentp. 301
Ancient Indian Mathematicsp. 311
A Restatement of Intent and a Brief Historical Sketchp. 311
Math from Bricks: Evidence from the Harappan Culturep. 317
Mathematics from the Vedasp. 323
Early Indian Numerals and Their Developmentp. 338
Jaina Mathematicsp. 349
Mathematics on the Eve of the Classical Periodp. 356
Indian Mathematics: The Classical Period and Afterp. 372
Major Indian Mathematician-Astronomersp. 373
Indian Algebrap. 380
Indian Trigonometryp. 392
Other Notable Contributionsp. 403
A Passage to Infinity: The Kerala Episodep. 418
The Actorsp. 418
Transmission of Kerala Mathematicsp. 435
Prelude to Modern Mathematics: The Islamic Contributionp. 450
Historical Backgroundp. 450
Major Medieval Islamic Mathematiciansp. 455
Medieval Islam's Role in the Rise and Spread of Indian Numeralsp. 461
Arithmetic in the Islamic Worldp. 466
Algebra in the Islamic Worldp. 475
Islamic Algebra and Its Influence on Europep. 486
Geometry in the Islamic Worldp. 487
Trigonometry in the Islamic Worldp. 496
Mathematics from Related Sourcesp. 503
The Islamic Contribution: A Final Assessmentp. 508
Referencesp. 521
Name Indexp. 543
Subject Indexp. 549
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