Sherlock Holmes in Babylon: And Other Tales of Mathematical History (Spectrum)

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. Part I. Ancient Mathematics -- Sherlock Holmes In Babylon / R. Creighton Buck -- Words And Pictures : New Light On Plimpton 322 / Eleanor Robson -- Mathematics, 600 B.c.-600 A.d. / Max Dehn -- Diophantus Of Alexandria / J.d. Swift -- Hypatia Of Alexandria / A.w. Richeson -- Hypatia And Her Mathematics / Michael A.b. Deakin -- The Evolution Of Mathematics In Ancient China / Frank Swetz -- Liu Hui And The First Golden Age Of Chinese Mathematics / Philip D. Straffin, Jr. -- Number Systems Of The North American Indians / W.c. Eells -- The Number System Of The Mayas / A.w. Richeson -- Before The Conquest / Marcia Ascher -- Part Ii. Medieval And Renaissance Mathematics -- The Discovery Of The Series Formula For [pi] By Leibniz, Gregory And Nilakantha / Ranjan Roy -- Ideas Of Calculus In Islam And India / Victor J. Katz -- Was Calculus Invented In India? / David Bressoud -- An Early Iterative Method For The Determinationof Sin 1° / Farhad Riahi -- 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 -- The First Work On Mathematics Printed In The New World / David Eugene Smith -- Part Iii. The Seventeenth Century -- 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 -- Descartes And The Problem-solving / Judith Grabiner -- René Descartes' Curve-drawing Devices : Experiments In The Relations Between Mechanical Motion And Symbolic Language / David Dennis -- Certain Mathematical Achievements Of James Gregory / Max Dehn And E.d. Hellinger -- The Changing Concept Of Change : The Derivative From Fermat To Weierstrass / Judith V. Grabiner -- The Crooked Made Straight : Roberval And Newton On Tangents / Paul R. Wolfson -- On The Discovery Of The Logarithmic Series And Its Development In England Up To Cotes / Josef Ehrenfried Hofmann -- Isaac Newton : Man, Myth And Mathematics / V. Frederick Rickey -- 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 -- A Contribution Of Leibniz To The History Of Complex Numbers / R.b. Mcclenon -- Functions Of A Curve : Leibniz's Original Notion Of Functions / David Dennis And Jere Confrey -- Part Iv. The Eighteenth Century -- Brook Taylor And The Mathematical Theory Of Linear Perspectives / P.s. Jones -- Was Newton's Calculus A Dead End? : The Continental Influence Of Maclaurin's Treatise Of Fluxions / Judith Grabiner -- Discussion Of Fluxions : From Berkeley To Woodhouse / Florian Cajori -- The Bernoullis And The Harmonic Series / William Dunham -- Leonhard Euler 1707-1783 / J.j. Burckhardt -- The Number E / J.l. Coolidge -- Euler's Vision Of A General Partial Differential Calculus For A Generalized Kind Of Function / Jesper Lützen -- Euler And The Fundamental Theorem Of Algebra / William Dunham -- Euler And Differentials / Anthony P. Ferzola -- Euler And Quadratic Reciprocity / Harold M. Edwards. Edited By Marlow Anderson, Victor Katz, Robin Wilson. Includes Bibliographical References And Index. Ancient mathematics. Sherlock Holmes in Babylon / R. Creighton Buck Words and pictures: new light on Plimpton 322 / Eleanor Robson Mathematics, 600 B.C.-600 A.D. / Max Dehn Diophantus of Alexandria / J.D. Swift Hypatia of Alexandria / A.W. Richeson Hypatia and her mathematics / Michael A.B. Deakin The evolution of mathematics in ancient China / Frank Swetz Liu Hui and the first golden age of Chinese mathematics / Philip D. Straffin, Jr. Number systems of the North American Indians / W.C. Eells The number system of the Mayas / A.W. Richeson Before the conquest / Marcia Ascher Medieval and renaissance mathematics. The discovery of the series formula for [pi] by Leibniz, Gregory and Nilakantha / Ranjan Roy Ideas of calculus in Islam and India / Victor J. Katz Was calculus invented in India? / David Bressoud An early iterative method for the determinationof sin 10 / Farhad Riahi - 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 The first work on mathematics printed in the New World / David Eugene Smith The seventeenth century. 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 Descartes and the problem-solving / Judith Grabiner René Descartes' curve-drawing devices: experiments in the relations between mechanical motion and symbolic language / David Dennis Certain mathematical achievements of James Gregory / Max Dehn and E.D. Hellinger The changing concept of change: the derivative from Fermat to Weierstrass / Judith V. Grabiner - The crooked made straight: Roberval and Newton on tangents / Paul R. Wolfson On the discovery of the logarithmic series and its development in England up to Cotes / Josef Ehrenfried Hofmann Isaac Newton: man, myth and mathematics / V. Frederick Rickey 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 A contribution of Leibniz to the history of complex numbers / R.B. McClenon Functions of a curve: Leibniz's original notion of functions / David Dennis and Jere Confrey The eighteenth century. Brook Taylor and the mathematical theory of linear perspectives / P.S. Jones Was Newton's calculus a dead end? The continental influence of Maclaurin's treatise of fluxions / Judith Grabiner Discussion of fluxions: from Berkeley to Woodhouse / Florian Cajori - The Bernoullis and the harmonic series / William Dunham Leonhard Euler 1707-1783 / J.J. Burckhardt The number e / J.L. Coolidge Euler's vision of a general partial differential calculus for a generalized kind of function / Jesper Lützen Euler and the fundamental theorem of algebra / William Dunham Euler and differentials / Anthony P. Ferzola Euler and quadratic reciprocity / Harold M. Edwards. This book is a collection of 44 articles on the history of mathematics, published in MAA journals over the past 100 years. Covering a span of almost 4000 years, from the ancient Babylonians to the eighteenth century, it chronicles the enormous changes in mathematical thinking over this time, as viewed by distinguished historians of mathematics from the past (Florian Cajori, Max Dehn, David Eugene Smith, Julian Lowell Coolidge, and Carl Boyer etc.) 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#x97;and in particular by mathematics teachers at secondary, college, and university levels