Spectrum : Sherlock Holmes in Babylon: and Other Tales of Mathematical History.

Front 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 -- 5 In search of an author -- 6 Conclusions -- 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 Arithmetic -- 3 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 mathematics -- 3 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 Notes -- References -- 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. KATZ -- 1 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 -- The Algorists vs. the Abacists: An Ancient Controversy on the Use of Calculators BARBARA E. REYNOLDS -- Sidelights on the Cardan-Tartaglia Controversy MARTIN A. NORDGAARD -- Reading Bombelli's x-purgated Algebra ABRAHAM ARCAVI and MAXIM BRUCKHEIMER -- 1 Bombelli's method -- 2 Bombelli's method and continued fractions -- 3 Bombelli's method in the classroom -- 4 Final comments -- References -- The First Work on Mathematics Printed in the New World DAVID EUGENE SMITH -- 1 General description -- 2 Typical problems not listed under algebra -- 3 Typical problems listed under algebra.

Afterword -- The Seventeenth Century -- Foreword -- An Application of Geography to Mathematics: History of the Integral of the Secant V. FREDERICK RICKEY and PHILIP M. TUCHINSKY -- Some Historical Notes on the Cycloid E. A. WHITMAN -- 1 Introduction -- 2 Early history of the curve -- 3 The work of Roberval -- 4 Construction of the tangent -- 5 Pascal's mathematical contest -- 6 The brachistochrone problem -- References -- Descartes and Problem-Solving JUDITH GRABINER -- Introduction -- A first look at Descartes' Geometry -- The background of Descartes' Geometry -- Descartes' method in action -- Beyond the Greeks -- The power of Descartes' methods: tangents and equations -- Conclusion -- References -- René Descartes' Curve-Drawing Devices: Experiments in the Relations Between Mechanical Motion and Symbolic Language DAVID DENNIS -- 1 Introduction -- 2 Apollonius regained -- 3 Conchoids generalized from hyperbolas -- 4 Conclusion -- References -- Certain Mathematical Achievements of James Gregory MAX DEHN and E. D. HELLINGER -- 1 The ``Taylor's series'' -- 2 The interpolation formula -- 3 The binomial series -- 4 Gregory's Vera Quadratura -- 5 Conclusion -- References -- The Changing Concept of Change: The Derivative from Fermat to Weierstrass JUDITH V. GRABINER -- The seventeenth-century background -- Finding maxima, minima, and tangents -- Tangents, areas, and rates of change -- Differential equations, Taylor series, and functions -- Lagrange and the derivative as a function -- Definitions, rigor, and proofs -- Historical development versus textbook exposition -- References -- The Crooked Made Straight: Roberval and Newton on Tangents PAUL R. WOLFSON -- 1 Introduction -- 2 What Roberval knew -- 3 What Newton thought -- 4 Conclusion -- References.

On the Discovery of the Logarithmic Series and Its Development in England up to Cotes JOSEF EHRENFRIED HOFMANN -- 1 Nicolas Mercator (1620-1687) -- 2 James Gregory (1638-1675) -- 3 Isaac Newton (1642-1727) -- 4 The methodological expansion -- References -- Isaac Newton: Man, Myth, and Mathematics V. FREDERICK RICKEY -- 1 Newton's education and public life -- 2 Newton's mathematical readings -- 3 Newton's works -- 4 Conclusion -- References -- Reading the Master: Newton and the Birth of Celestial Mechanics BRUCE POURCIAU -- Newton as an Originator of Polar Coordinates C. B. BOYER -- Newton's Method for Resolving Affected Equations CHRIS CHRISTENSEN -- Newton's method for approximating roots -- Resolution of affected equations -- Extensions -- Appendix I. Portion of the Epistola prior -- Appendix II. Portion of the Epistola posterior -- References -- A Contribution of Leibniz to the History of Complex Numbers R. B. McCLENON -- Functions of a Curve: Leibniz's Original Notion of Functions and Its Meaning for the Parabola DAVID DENNIS and JERE CONFREY -- Afterword -- The Eighteenth Century -- Foreword -- Brook Taylor and the Mathematical Theory of Linear Perspective P. S. JONES -- Was Newton's Calculus a Dead End? The Continental Influence of Maclaurin's Treatise of Fluxions JUDITH GRABINER -- 1 Introduction -- 2 The standard picture -- 3 The nature of Maclaurin's Treatise of Fluxions -- 4 The social context: The Scottish Enlightenment -- 5 Maclaurin's Continental reputation -- 6 Maclaurin's mathematics and its importance -- 7 Other examples of Maclaurin's mathematical influence -- 8 Why a Treatise of Fluxions? -- 9 Why the traditional view? -- 10 Some final reflections -- References -- Discussion of Fluxions: from Berkeley to Woodhouse FLORIAN CAJORI -- The Bernoullis and the Harmonic Series WILLIAM DUNHAM.

Leonhard Euler 1707-1783 J. J. BURCKHARDT -- 1 The legacy of Euler's writings -- 2 Number theory -- 3 Analysis -- 4 ``Applied'' mathematics (physics) -- 5 Astronomy -- 6 Correspondence -- 7 Postscript -- Reference -- The Number e J. L. COOLIDGE -- 1 The Greek beginning -- 2 Grégoire de St. Vincent -- 3 The introduction of logarithms -- 4 Mercator, Newton, Leibniz -- 5 Leonhard Euler -- References -- Euler's Vision of a General Partial Differential Calculus for a Generalized Kind of Function JESPER LÜTZEN -- 1 The algebraic function concept -- 2 Euler's generalized functions -- 3 Euler's vision of a generalized calculus -- 4 The fate of Euler's vision -- 5 Concluding remarks -- References -- Euler and the Fundamental Theorem of Algebra WILLIAM DUNHAM -- Epilogue -- References -- Euler and Differentials ANTHONY P. FERZOLA -- Euler and the 18th century -- Differentials as absolute zeros -- Computations with elementary functions -- The total differential -- Differentials in multiple integrals -- Conclusion -- References -- Euler and Quadratic Reciprocity HAROLD M. EDWARDS -- Afterword -- Index -- About the Editors -- Back cover.

Covering a span of almost 4000 years, from the ancient Babylonians to the eighteenth century, this collection chronicles the enormous changes in mathematical thinking over this time as viewed by distinguished historians of mathematics from the past and the present. Each of the four sections of the book (Ancient Mathematics, Medieval and Renaissance Mathematics, The Seventeenth Century, The Eighteenth Century) is preceded by a Foreword, in which the articles are put into historical context, and followed by an Afterword, in which they are reviewed in the light of current historical scholarship. In more than one case, two articles on the same topic are included to show how knowledge and views about the topic changed over the years. This book will be enjoyed by anyone interested in mathematics and its history - and, in particular, by mathematics teachers at secondary, college, and university levels.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.