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

**by**Joseph, George Gheverghese

3rd

### 9780691135267

0691135266

Paperback

10/4/2010

Princeton Univ Pr

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## 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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