Berggren / Borwein Pi: A Source Book

Erscheinungsjahr 2013
ISBN: 978-1-4757-2736-4
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 716 Seiten, eBook

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 classes: 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.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Berggren, J.L.

Borwein, Jonathan

Borwein, Peter

Inhaltsverzeichnis

Preface. Acknowledgements. Introduction. 1: The Rhind Mathematical Papyrus-Problem 50. 2: Engles. Quadrature of the Circle in Ancient Egypt. 3: Archimedes. Measurement of a Circle. 4: Phillips. Archimedes the Numerical Analyst. 5: Lam & Ang. Circle Measurements in Ancient China. 6: The Banu Musa: The Measurement of Plane and Solid Figures. 7: Madhava's. The Power Series for Arctan and Pi. 8: Hope-Jones. Ludolph van Ceulen. 9: Viete. Variorum de Revus Mathematicis Reponsorum Liber VII. 10: Wallis. Computation of Pi by Successive Interpolations. 11: Wallis. Arithmetica Infinitorum. 12: Huygens. De Circuli Magnitudine Inventa. 13: Gregory. Correspondence with John Collins. 15: Jones. The First Use of Pi for the Circle Ratio. 16: Newton. Of The Method of Fluxions and Infinite Series. 17: Euler. Chapter 10 of Introduction to Analysis of the Infinite. 18: Lambert. Memoire Sur Quelques Proprietes Remarquables Des Quantites Transcendentes Circulaires et Logarithmiques. 19: Lambert. Irrationality of Pi. 20: Shanks. Contributions to Mathematics Comprising Chiefly of the Rectification of the Circle to 607 Places of Decimals. 21: Hermite. Sur La Fonction Exponentielle. 22: Lindemann.