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The Crest of the Peacock

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

George Gheverghese Joseph
Copyright Date: 2011
Edition: STU - Student edition
Pages: 610
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  • Book Info
    The Crest of the Peacock
    Book Description:

    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.

    eISBN: 978-1-4008-3636-9
    Subjects: Mathematics, History of Science & Technology

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-x)
  3. Preface to the Third Edition
    (pp. xi-xxii)
    George Gheverghese Joseph
  4. Preface to the First Edition
    (pp. xxiii-xxx)
    George Gheverghese Joseph
  5. Chapter One The History of Mathematics: Alternative Perspectives
    (pp. 1-29)

    An interest in history marks us for life. How we see ourselves and others is shaped by the history we absorb, not only in the classroom but also from the Internet, films, newspapers, television programs, novels, and even strip cartoons. From the time we first become aware of the past, it can fire our imagination and excite our curiosity: we ask questions and then seek answers from history. As our knowledge develops, differences in historical perspectives emerge. And, to the extent that different views of the past affect our perception of ourselves and of the outside world, history becomes an...

  6. Chapter Two Mathematics from Bones, Strings, and Standing Stones
    (pp. 30-78)

    It is taking an unnecessarily restrictive view of the history of mathematics to confine our study to written evidence. Mathematics initially arose from a need to count and record numbers. As far as we know there has never been a society without some form of counting or tallying (i.e., matching a collection of objects with some easily handled set of markers, whether it be stones, knots, or inscriptions such as notches on wood or bone). If we define mathematics as any activity that arises out of, or directly generates, concepts relating to numbers or spatial configurations together with some form...

  7. Chapter Three The Beginnings of Written Mathematics: Egypt
    (pp. 79-124)

    In the previous chapter we began our examination of early evidence of mathematical activity with an artifact found in the middle of Africa. For the next stage of our journey we remain on the same continent but move north to Egypt. Egypt is generally recognized as the homeland of one of the four early civilizations that grew up along the great river valleys of Africa and Asia over five thousand years ago, the other three being in Mesopotamia, India, and China. Egyptian civilization did not emerge out of the blue as a full-blown civilization without any African roots. This is...

  8. Chapter Four The Beginnings of Written Mathematics: Mesopotamia
    (pp. 125-176)

    Studying ancient Mesopotamian history is rather like going on a long and unfamiliar journey: we are not sure whether we are on the right road until we reach our destination. The abridged chronology given in table 4.1 will be of some help in plotting our course across this difficult terrain; the places mentioned in the table are shown in the accompanying map (figure 4.1). The earliest protocuneiform written records are from around the last few centuries of the fourth millennium BC, and the last cuneiform records are from around the end of the first millennium BC. With the Persian conquest...

  9. Chapter Five Egyptian and Mesopotamian Mathematics: An Assessment
    (pp. 177-187)

    A particular view of Egyptian and Mesopotamian mathematics held not too long ago is crystallized in the writings of Morris Kline, a well-known American historian of mathematics. Dismissing all the evidence to the contrary marshaled by both ancient Greeks and modern scholars, he considers that the Egyptian and Mesopotamian contributions to mathematics were “almost insignificant.” This is followed by his astonishing statement that, compared with what the Greeks achieved, “the mathematics of the Egyptians and Mesopotamians is the scrawling of children just learning to write, as opposed to great literature.” In any case, Kline continues, these civilizations “barely recognized mathematics...

  10. Chapter Six Ancient Chinese Mathematics
    (pp. 188-245)

    To understand the history of Chinese mathematics requires some familiarity with Chinese history. The history of China is a vast subject, as befits a country that can trace the continuity of its civilization through 4,500 years. The period we are concerned with runs from prehistoric times to the end of the Ming dynasty (AD 1386–1644) and the beginnings of European contact. It will help if we divide this long time span into five shorter periods. The reader may find it useful to refer to the map of China, figure 6.1, for places mentioned in the following account.

    The first...

  11. Chapter Seven Special Topics in Chinese Mathematics
    (pp. 246-310)

    The last half of the thirteenth century and the early fourteenth marked the culmination of over a thousand years of development of Chinese mathematics, built on the solid foundation of theJiu Zhang. In the historical introduction to the previous chapter we saw that the Song period produced outstanding scientific and technological achievements. Four of the greatest Chinese mathematicians—Qin Jiushao, Li Ye, Yang Hui, and Zhu Shijie—lived during this period, and there were more than thirty mathematical schools scattered across the country. As in the Tang dynasty, when a number of ancient texts were collected and then designated...

  12. Chapter Eight Ancient Indian Mathematics
    (pp. 311-371)

    Ancient Indian history raises many problems. The period before the Christian era takes on a haziness that seems to have prompted opposing reactions. There are those who make excessive claims for the antiquity of Indian mathematics, and others who go to the opposite extreme and deny the existence of any “real” Indian mathematics before about AD 500. The principal motive of the former is to emphasize the uniqueness of Indian mathematical achievements. In this view, if there was any influence, it was always a one-way traffic from India to the rest of the world. The motives of the latter are...

  13. Chapter Nine Indian Mathematics: The Classical Period and After
    (pp. 372-417)

    From the previous chapter it is clear that our evidence of mathematical activities after the Vedic period, as represented by Jaina canonical literature and the Bakhshali Manuscript, is imperfect and incomplete. Our knowledge of the development of mathematics and astronomy between theSulbasutrasand the period of Aryabhata I (c. AD 500) is therefore fairly sketchy. Yet this hiatus in our knowledge is particularly puzzling given the wealth of evidence we have for the same period in other fields, notably in medicine and chemistry, and in philosophy, where outstanding work was produced by the Nyaya and Mimamsa schools.

    Various explanations...

  14. Chapter Ten A Passage to Infinity: The Kerala Episode
    (pp. 418-449)

    Along the southwest coast near the tip of the Indian peninsula lies a strip of land known as Kerala. It has figured prominently in history, not only as a stopover for travelers and explorers such as ibn Battuta (b. 1304) and Vasco da Gama (b. 1460) arriving from across the Arabian Sea, but as a center of maritime trade, with its variety of spices greatly in demand even as early as the time of the Mesopotamians. While most of India was in political upheaval during the first part of the second millennium AD, Kerala was a place of relative tranquillity,...

  15. Chapter Eleven Prelude to Modern Mathematics: The Islamic Contribution
    (pp. 450-520)

    The year AD 622 is a momentous one in world history. It was then that the Prophet Muhammad fled from Mecca and took refuge in Yathrib (now Medina) about 350 kilometers away. He had incurred the wrath of pilgrims who had come to worship at a shrine called the K’aba—a shrine then dedicated to many gods. Muhammad’s preaching of a monotheistic faith, which he claimed had been directly revealed to him by the Archangel Gabriel, had aroused considerable hostility, contributing to his decision to flee his birthplace. Eight years later he returned at the head of an army, and...

  16. References
    (pp. 521-542)
  17. Name Index
    (pp. 543-548)
  18. Subject Index
    (pp. 549-561)