The Crest of the Peacock

by Joseph, George Gheverghese

• ISBN13: 9780691006598
• ISBN10: 0691006598
• Format: Paperback
• Copyright: 2000-07-01
• Publisher: Princeton Univ Pr

Summary

From the Ishango Bone of central Africa and the Inca quipu of 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 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. This challenging and erudite book questions familiar assumptions and enlarges our sense of what we mean by mathematics.

Table of Contents

Acknowledgements	xi
Preface to the First Edition	xii
Preface to the Second Edition	xvii
The History of Mathematics: Alternative Perspectives	1	(22)
A Justification for This Book	1	(2)
The Development of Mathematical Knowledge	3	(9)
Mathematical Signposts and Transmissions Across the Ages	12	(11)
Mathematics from Bones, Strings and Standing Stones	23	(34)
Beginnings: The Ishango Bone	23	(5)
Knotted Strings from South America: The Inca Quipu	28	(13)
The Emergence of Written Number Systems: A Digression	41	(8)
Mayan Numeration	49	(8)
The Beginnings of Written Mathematics: Egypt	57	(34)
The Urban Revolution and its African Origins	57	(2)
Sources of Egyptian Mathematics	59	(2)
Number Recording Among the Egyptians	61	(2)
Egyptian Arithmetic	63	(13)
Egyptian Algebra: The Beginnings of Rhetorical Algebra	76	(5)
Egyptian Geometry	81	(10)
The Beginnings of Written Mathematics: Babylonia	91	(34)
Sources of Babylonian Mathematics	95	(1)
The Babylonian Number System	96	(12)
Babylonian Algebra	108	(5)
Babylonian Geometry	113	(12)
Egyptian and Babylonian Mathematics: An Assessment	125	(5)
Ancient Chinese Mathematics	130	(48)
Background and Sources	130	(10)
The Development of Chinese Numerals	140	(8)
Chinese Magic Squares (and Other Designs)	148	(8)
Mathematics from the Chiu Chang	156	(22)
Special Topics in Chinese Mathematics	178	(37)
The `Piling-up of Rectangles': The Pythagorean Theorem in China	180	(8)
Estimation of π	188	(9)
Solution of Higher-order Equations and Pascal's Triangle	197	(8)
Indeterminate Analysis in China	205	(6)
Chinese Mathematics: A Final Assessment	211	(4)
Ancient Indian Mathematics	215	(49)
A Restatement of Intent and a Brief Historical Sketch	215	(6)
Maths from Bricks: Evidence from the Harappan Culture	221	(3)
Mathematics from the Vedas	224	(15)
Early Indian Numerals and Their Development	239	(10)
Jaina Mathematics	249	(7)
Mathematics on the Eve of the Classical Period	256	(8)
Indian Mathematics: The Classical Period and After	264	(37)
Major Indian Mathematician-Astronomers	265	(7)
Indian Algebra	272	(8)
Indian Trigonometry	280	(6)
Kerala Mathematics	286	(8)
Other Notable Contributions	294	(7)
Prelude to Modern Mathematics: The Arab Contribution	301	(48)
Historical Background	301	(3)
Major Arab Mathematicians	304	(7)
The Arab Role in the Rise and Spread of Indian Numerals	311	(5)
Arab Arithmetic	316	(8)
Arab Algebra	324	(9)
Arab Geometry	333	(5)
Arab Trigonometry	338	(6)
The Arab Contribution: A Final Assessment	344	(5)
Reflections	349	(76)
The History of Mathematics: Alternative Perspectives	349	(8)
Mathematics from Bones, Strings and Standing Stones	357	(12)
The Beginnings of Written Mathematics: Egypt	369	(8)
The Beginnings of Written Mathematics: Babylonia	377	(8)
Ancient Chinese Mathematics	385	(4)
Special Topics in Chinese Mathematics	389	(6)
Ancient Indian Mathematics	395	(11)
Indian Mathematics: The Classical Period and After	406	(11)
Prelude to Modern Mathematics: The Arab Contribution	417	(8)
Bibliography	425	(16)
Name Index	441	(6)
Subject Index	447