Sherlock Holmes in Babylon: And Other Tales of Mathematical History

Cover 
 Copyright page 
 Title Page 
 Introduction
 Contents
 Ancient Mathematics
 Foreword
 Sherlock Holmes in Babylon R. CREIGHTON BUCK
 Words and Pictures: New Light on Plimpton 322 ELEANOR ROBSON
 1 Introduction
 2 Turning the tables on generating functions
 3 Circling round trigonometry
 4 Words count too: reciprocal pairs
 4 Words count too:reciprocal pairs
 4 Words count too:reciprocal pairs
 References
 Mathematics, 600 B.C.-600 A.D. MAX DEHN
 1 600 B.C.-400 B.C.
 2 400 B.C.-300 B.C.
 3 300 B.C.-200 B.C.
 4 200 B.C.-600 A.D.
 Diophantus of Alexandria J.D. SWIFT
 1 Introduction. 2 The Arithmetic3 Notation
 4 Diophantine algebra
 5 Indeterminate problems
 6 An approximation problem
 7 Transmission of Diophantus
 Bibliography
 Hypatia of Alexandria A.W. RICHESON
 Hypatia and Her Mathematics MICHAEL A.B. DEAKIN
 1 Introduction
 2 The historical background
 3 The primary sources
 4 Life and legend
 5 Hypatia's Philosophy
 6 Hypatia's Mathematics
 7 Apollonius' Conics
 8 The Astronomical Canon
 9 Diophantus' Arithmetic
 10 The astrolabe
 11 The Hydroscope 
 12 Assessment
 References
 The Evolution of Mathematics in Ancient China FRANK SWETZ
 1 Legend and fact. 2 The systematization of early Chinese mathematics3 Trends in Chinese algebraic thought
 4 Conclusions
 Notes
 Liu Hui and the FirstGolden Age of Chinese Mathematics PHILIP D. STRAFFIN, JR.
 1 Introduction
 2 Chinese calculation in the first century A.D.
 3 Nine Chapters on the Mathematical Art
 4 Liu Hui's commentary
 5 The Sea Island Mathematical Manual
 6 The calculation of pi
 7 The volume of pyramids
 8 The volume of a sphere
 9 Conclusion
 References
 Number Systems of the North American Indians W.C. EELLS
 1 Principles of formation
 2 Systems of numeration
 3 Miscellaneous points. 4 NotesReferences
 The Number System of the Mayas A.W. RICHESON
 1 Methods of numeration
 2 Discussion of the numbers
 3 Conclusion
 References
 Before The Conquest MARCIA ASCHER
 1 Introduction
 2 The Incas
 3 The Maya
 4 Conclusion
 References
 Afterword
 Medieval and Renaissance Mathematics
 Foreword
 The Discovery of the Series Formula for pi byLeibniz, Gregory and Nilakantha RANJAN ROY
 1 Introduction
 2 Gottfried Wilhelm Leibniz (1646-1716)
 3 James Gregory (1638-1675)
 4 Kerala Gargya Nilakantha (c. 1450-c. 1550)
 5 Independence of these discoveries
 References. Ideas of Calculus in Islam and India VICTOR J. KATZ1 Introduction
 2 Sums of integer powers in eleventh-century Egypt
 3 Trigonometric series in sixteenth-century India
 4 Conclusion
 References
 Was Calculus Invented in India? DAVID BRESSOUD
 1 Introduction
 2 Greek origins of trigonometry
 3 Trigonometry in classical India
 4 The power series expansion for sine
 5 Conclusion
 Bibliography
 An Early Iterative Method for the Determination of sin 1 FARHAD RIAHI
 1 Background
 2 Al-Kashi's determination of sin 1
 References
 Leonardo of Pisa and his Liber Quadratorum R.B. McCLENON.