The Mathematics of Egypt, Mesopotamia, China, India and Islam

by Katz, Victor J.

• ISBN13: 9780691114859
• ISBN10: 0691114854
• Format: Hardcover
• Copyright: 2007-07-16
• Publisher: Princeton Univ Pr

Summary

In recent decades it has become obvious that mathematics has always been a worldwide activity. But this is the first book to provide a substantial collection of English translations of key mathematical texts from the five most important ancient and medieval non-Western mathematical cultures, and to put them into full historical and mathematical context.The Mathematics of Egypt, Mesopotamia, China, India, and Islamgives English readers a firsthand understanding and appreciation of these cultures' important contributions to world mathematics. The five section authors--Annette Imhausen (Egypt), Eleanor Robson (Mesopotamia), Joseph Dauben (China), Kim Plofker (India), and J. Lennart Berggren (Islam)--are experts in their fields. Each author has selected key texts and in many cases provided new translations. The authors have also written substantial section introductions that give an overview of each mathematical culture and explanatory notes that put each selection into context. This authoritative commentary allows readers to understand the sometimes unfamiliar mathematics of these civilizations and the purpose and significance of each text. Addressing a critical gap in the mathematics literature in English, this book is an essential resource for anyone with at least an undergraduate degree in mathematics who wants to learn about non-Western mathematical developments and how they helped shape and enrich world mathematics. The book is also an indispensable guide for mathematics teachers who want to use non-Western mathematical ideas in the classroom.

Author Biography

Victor J. Katz is professor emeritus of mathematics at the University of the District of Columbia. His many books include the textbook, "A History of Mathematics: An Introduction, 2nd ed." (Addison-Wesley). He is the coeditor of "Historical Modules for the Teaching and Learning of Mathematics".

Table of Contents

Preface	p. ix
Permissions	p. xi
Introduction	p. 1
Egyptian Mathematics
Preliminary Remarks	p. 7
Introduction	p. 9
Invention of writing and number systems	p. 13
Arithmetic	p. 14
Metrology	p. 17
Hieratic Mathematical Texts	p. 17
Table texts	p. 18
Problem texts	p. 24
Mathematics in Administrative Texts	p. 40
Middle Kingdom texts: The Reisner papyri	p. 40
New Kingdom texts: Ostraca from Deir el Medina	p. 44
Mathematics in the Graeco-Roman Period	p. 46
Context	p. 46
Table texts	p. 47
Problem texts	p. 48
Appendices	p. 52
Glossary of Egyptian terms	p. 52
Sources	p. 52
References	p. 54
Mesopotamian Mathematics
Introduction	p. 58
Mesopotamian mathematics through Western eyes	p. 58
Mathematics and scribal culture in ancient Iraq	p. 62
From tablet to translation	p. 65
Explananda	p. 68
The Long Third Millennium, c. 3200-2000 BCE	p. 73
Uruk in the late fourth millennium	p. 73
Shuruppag in the mid-third millennium	p. 74
Nippur and Girsu in the twenty-fourth century BCE	p. 76
Umma and Girsu in the twenty-first century BCE	p. 78
The Old Babylonian Period, c. 2000-1600 BCE	p. 82
Arithmetical and metrological tables	p. 82
Mathematical problems	p. 92
Rough work and reference lists	p. 142
Later Mesopotamia, c. 1400-150 BCE	p. 154
Appendices	p. 180
Sources	p. 180
References	p. 181
Chinese Mathematics
Preliminary Remarks	p. 187
China: The Historical and Social Context	p. 187
Methods and Procedures: Counting Rods, The "Out-In" Principle	p. 194
Recent Archaeological Discoveries: The Earliest Yet-Known Bamboo Text	p. 201
Mathematics and Astronomy: The Zhou bi suan jing and Right Triangles (The Gou-gu or "Pythagorean" Theorem)	p. 213
The Chinese "Euclid", Liu Hui	p. 226
The Nine Chapters	p. 227
The Sea Island Mathematical Classic	p. 288
The "Ten Classics" of Ancient Chinese Mathematics	p. 293
Numbers and arithmetic: The Mathematical Classic of Master Sun	p. 295
The Mathematical Classic of Zhang Qiujian	p. 302
Outstanding Achievements of the Song and Yuan Dynasties (960-1368 CE)	p. 308
Qin Jiushao	p. 309
Li Zhi (Li Ye)	p. 323
Yang Hui	p. 329
Zhu Shijie	p. 343
Matteo Ricci and Xu Guangxi, "Prefaces" to the First Chinese Edition of Euclid's Elements (1607)	p. 366
Conclusion	p. 375
Appendices	p. 379
Sources	p. 379
Bibliographic guides	p. 379
References	p. 380
Mathematics in India
Introduction: Origins of Indian Mathematics	p. 385
Mathematical Texts in Ancient India	p. 386
The Vedas	p. 386
The SA'ulbasutras	p. 387
Mathematics in other ancient texts	p. 393
Number systems and numerals	p. 395
Evolution of Mathematics in Medieval India	p. 398
Mathematics chapters in Siddhanta texts	p. 398
Transmission of mathematical ideas to the Islamic world	p. 434
Textbooks on mathematics as a separate subject	p. 435
The audience for mathematics education	p. 477
Specialized mathematics: Astronomical and cosmological problems	p. 478
The Kerala School	p. 480
Madhava, his work, and his school	p. 480
Infinite series and the role of demonstrations	p. 481
Other mathematical interests in the Kerala school	p. 493
Continuity and Transition in the Second Millennium	p. 498
The ongoing development of Sanskrit mathematics	p. 498
Scientific exchanges at the courts of Delhi and Jaipur	p. 504
Assimilation of ideas from Islam; mathematical table texts	p. 506
Encounters with Modern Western Mathematics	p. 507
Early exchanges with European mathematics	p. 507
European versus "native" mathematics education in British India	p. 508
Assimilation into modern global mathematics	p. 510
Appendices	p. 51
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