Pi : a source book

From the contents: Preface.- Acknowledgements.- Introduction.- The Rhind Mathematical Papyrus-Problem 50.- Engles. Quadrature of the Circle in Ancient Egypt.- Archimedes. Measurement of a Circle.- Phillips. Archimedes the Numerical Analyst.- Lam & Ang. Circle Measurements in Ancient China.- The Banu Musa: The Measurement of Plane and Solid Figures.- Madhava's. The Power Series for Arctan and Pi.- Hope-Jones. Ludolph van Ceulen.- Viete. Variorum de Revus Mathematicis Reponsorum Liber VII.- Wallis. Computation of Pi by Successive Interpolations.- Wallis. Arithmetica Infinitorum.- Huygens. De Circuli Magnitudine Inventa.- Gregory. Correspondence with John Collins.- Jones. The First Use of Pi for the Circle Ratio.- Newton. Of The Method of Fluxions and Infinite Series.- Euler. Chapter 10 of Introduction to Analysis of the Infinite.- Lambert. Memoire Sur Quelques Proprietes Remarquables Des Quantites Transcendentes Circulaires et Logarithmiques.- Lambert. Irrationality of Pi.- Shanks. Contributions to Mathematics Comprising Chiefly of the Rectification of the Circle to 607 Places of Decimals.- Hermite. Sur La Fonction Exponentielle.- And much more Our intention in this collection is to provide, largely through original writings, an ex­ tended account of pi from the dawn of mathematical time to the present. The story of pi reflects the most seminal, the most serious, and sometimes the most whimsical aspects of mathematics. A surprising amount of the most important mathematics and a signifi­ cant number of the most important mathematicians have contributed to its unfolding­ directly or otherwise. Pi is one of the few mathematical concepts whose mention evokes a response of recog­ nition and interest in those not concerned professionally with the subject. It has been a part of human culture and the educated imagination for more than twenty-five hundred years. The computation of pi is virtually the only topic from the most ancient stratum of mathematics that is still of serious interest to modern mathematical research. To pursue this topic as it developed throughout the millennia is to follow a thread through the history of mathematics that winds through geometry, analysis and special functions, numerical analysis, algebra, and number theory. It offers a subject that provides mathe­ maticians with examples of many current mathematical techniques as weIl as a palpable sense of their historical development. Why a Source Book? Few books serve wider potential audiences than does a source book. To our knowledge, there is at present no easy access to the bulk of the material we have collected. The aim of this book is to provide a complete history of pi from the dawn of mathematical time to the present. The story of pi reflects the most seminal, the most serious and sometimes the silliest aspects of mathematics, and a suprising amount of the most important mathematics and mathematicians have contributed to its unfolding. Pi is one of the few concepts in mathematics whose mention evokes a response of recognition and interest in those not concerned professionally with the subject. Yet, despite this, no source book on pi has been published. One of the beauties of the literature on pi is that it allows for the inclusion of very modern, yet still accessible, mathematics. Mathematicians and historians of mathematics will find this book indespensable. Teachers at every level from the seventh grade onward will find here ample resources for anything from special topic courses to individual talks and special student projects. The literature on pi included in this source book falls into three first a selection of the mathematical literature of four millennia, second a variety of historial studies or writings on the cultural meaning and significance of the number, and third, a number of treatments on pi that are fanciful, satirical and/or whimsical. In addition to correcting a few minor infelicities, this new edition includes an Appendix in which articles 9 and 12 by Viete and Huygens respectively are translated into English. This Book Documents The History Of Pi From The Dawn Of Mathematical Time To The Present. The Story Of Pi Reflects The Most Seminal, The Most Serious, And Sometimes The Most Whimsical Aspects Of Mathematics. Much Significant Mathematics Originates With Pi, And Many Great Mathematicians Have Contributed To This Story's Unfolding. Mathematicians And Historians Of Mathematics Will Find This Book Indispensable. Teachers At Every Level Can Find Here Ample Resources For Anything From Individual Talks And Student Projects To Special Topics Courses.--jacket. 1. The Rhind Mathematical Papyrus-problem 50 (1̃650 B.c.) -- 2. Engels. Quadrature Of The Circle In Ancient Egypt (1977) -- 3. Archimedes. Measurement Of A Circle (2̃50 B.c.) -- 4. Phillips. Archimedes The Numerical Analyst (1981) -- 5. Lam And Ang. Circle Measurements In Ancient China (1986) -- 6. The Banu Musa: The Measurement Of Plane And Solid Figures (8̃50) -- 7. Madhava. The Power Series For Arctan And Pi (1̃400) -- 8. Hope-jones. Ludolph (or Ludolff Or Lucius) Van Ceulen (1938) -- 9. Viete. Variorum De Rebus Mathematicis Reponsorum Liber Viii (1593) -- 10. Wallis. Computation Of [pi] By Successive Interpolations (1655) -- 11. Wallis. Arithmetica Infinitorum (1655) -- 12. Huygens. De Circuli Magnitudine Inventa (1724). [edited By] Lennart Berggren, Jonathan Borwein, Peter Borwein. Includes Bibliographical References (p. 710-719) And Index. This new edition of the definitive source book on pi aims to provide a complete history of pi from the dawn of mathematical time to the present. The story of pi reflects the most seminal, serious, and sometimes the silliest aspects of mathematics. 82 illus.