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AuthorBerggren, Lennart. author
TitlePi: A Source Book [electronic resource] / by Lennart Berggren, Jonathan Borwein, Peter Borwein
ImprintNew York, NY : Springer New York : Imprint: Springer, 2000
Edition Second Edition
Connect tohttp://dx.doi.org/10.1007/978-1-4757-3240-5
Descript XIX, 736 p. online resource

SUMMARY

Our intention in this collection is to provide, largely through original writings, an exยญ 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 signifiยญ cant number of the most important mathematicians have contributed to its unfoldingยญ directly or otherwise. Pi is one of the few mathematical concepts whose mention evokes a response of recogยญ 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 matheยญ 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


CONTENT

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. Mรฉmoire Sur Quelques Proprietรฉs Remarquables Des Quantitรฉs 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..


Mathematics Combinatorics Mathematics Combinatorics



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