Pi And The Agm


Pi And The Agm
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Pi And The Agm


Pi And The Agm
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Author : Jonathan M. Borwein
language : en
Publisher: Wiley-Interscience
Release Date : 1998-07-13

Pi And The Agm written by Jonathan M. Borwein and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-13 with Mathematics categories.


Critical Acclaim for Pi and the AGM: "Fortunately we have the Borwein's beautiful book . . . explores in the first five chapters the glorious world so dear to Ramanujan . . . would be a marvelous text book for a graduate course."--Bulletin of the American Mathematical Society "What am I to say about this quilt of a book? One is reminded of Debussy who, on being asked by his harmony teacher to explain what rules he was following as he improvised at the piano, replied, "Mon plaisir." The authors are cultured mathematicians. They have selected what has amused and intrigued them in the hope that it will do the same for us. Frankly, I cannot think of a more provocative and generous recipe for writing a book . . . (it) is cleanly, even beautifully written, and attractively printed and composed. The book is unique. I cannot think of any other book in print which contains more than a smidgen of the material these authors have included.--SIAM Review "If this subject begins to sound more interesting than it did in the last newspaper article on 130 million digits of Pi, I have partly succeeded. To succeed completely I will have gotten you interested enough to read the delightful and important book by the Borweins."--American Mathematical Monthly "The authors are to be commended for their careful presentation of much of the content of Ramanujan's famous paper, 'Modular Equations and Approximations to Pi'. This material has not heretofore appeared in book form. However, more importantly, Ramanujan provided no proofs for many of the claims that he made, and so the authors provided many of the missing details . . . The Borweins, indeed have helped us find the right roads."--Mathematics of Computation



Pi And The Agm


Pi And The Agm
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Author : Jonathan M. Borwein
language : en
Publisher:
Release Date : 1987

Pi And The Agm written by Jonathan M. Borwein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Computational complexity categories.




Pi A Source Book


Pi A Source Book
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Author : J.L. Berggren
language : en
Publisher: Springer
Release Date : 2014-01-13

Pi A Source Book written by J.L. Berggren and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-13 with Mathematics categories.


This book documents the history of pi from the dawn of mathematical time to the present. One of the beauties of the literature on pi is that it allows for the inclusion of very modern, yet accessible, mathematics. The articles on pi collected herein fall into various classes. First and foremost there is a selection from the mathematical and computational literature of four millennia. There is also a variety of historical studies on the cultural significance of the number. Additionally, there is a selection of pieces that are anecdotal, fanciful, or simply amusing. For this new edition, the authors have updated the original material while adding new material of historical and cultural interest. There is a substantial exposition of the recent history of the computation of digits of pi, a discussion of the normality of the distribution of the digits, and new translations of works by Viete and Huygen.



Pi Unleashed


Pi Unleashed
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Author : Jörg Arndt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Pi Unleashed written by Jörg Arndt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.


In the 4,000-year history of research into Pi, results have never been as prolific as present. This book describes, in easy-to-understand language, the latest and most fascinating findings of mathematicians and computer scientists in the field of Pi. Attention is focused on new methods of high-speed computation.



Pi A Source Book


Pi A Source Book
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Author : Jonathan M. Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Pi A Source Book written by Jonathan M. Borwein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.


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.



Pi Unleashed


Pi Unleashed
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Author : Jörg Arndt
language : en
Publisher: Springer Science & Business Media
Release Date : 2001

Pi Unleashed written by Jörg Arndt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Computers categories.


Never in the 4000 year history of research into Pi have results been so prolific as at present. In their book Jörg Arndt and Christoph Haenel describe the latest and most fascinating findings of mathematicians and computer scientists in the field of Pi. Attention is focussed on new methods of computation whose speed outstrips that of predecessor methods by orders of magnitude. The book comes with a CD-ROM containing not only the source code of all programme described, but also related texts and even complete libraries.



From Analysis To Visualization


From Analysis To Visualization
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Author : David H. Bailey
language : en
Publisher: Springer Nature
Release Date : 2020-03-16

From Analysis To Visualization written by David H. Bailey and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-16 with Mathematics categories.


Students and researchers from all fields of mathematics are invited to read and treasure this special Proceedings. A conference was held 25 –29 September 2017 at Noah’s On the Beach, Newcastle, Australia, to commemorate the life and work of Jonathan M. Borwein, a mathematician extraordinaire whose untimely passing in August 2016 was a sorry loss to mathematics and to so many members of its community, a loss that continues to be keenly felt. A polymath, Jonathan Borwein ranks among the most wide ranging and influential mathematicians of the last 50 years, making significant contributions to an exceptional diversity of areas and substantially expanding the use of the computer as a tool of the research mathematician. The contributions in this commemorative volume probe Dr. Borwein's ongoing legacy in areas where he did some of his most outstanding work: Applied Analysis, Optimization and Convex Functions; Mathematics Education; Financial Mathematics; plus Number Theory, Special Functions and Pi, all tinged by the double prisms of Experimental Mathematics and Visualization, methodologies he championed.



Turning Adversity To Advantage


Turning Adversity To Advantage
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Author : Nancy McGown Minor
language : en
Publisher: University Press of America
Release Date : 2009-10-05

Turning Adversity To Advantage written by Nancy McGown Minor and has been published by University Press of America this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-05 with History categories.


This book tells the story of the Lipan Apaches, once one of the largest and most aggressive tribes of the Rio Grande region. The story of the history of the Lipan Apaches is a tale of survival and preservation in the face of incredible challenges.



Pi The Next Generation


Pi The Next Generation
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Author : David H. Bailey
language : en
Publisher: Springer
Release Date : 2016-07-19

Pi The Next Generation written by David H. Bailey and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-19 with Mathematics categories.


This book contains a compendium of 25 papers published since the 1970s dealing with pi and associated topics of mathematics and computer science. The collection begins with a Foreword by Bruce Berndt. Each contribution is preceded by a brief summary of its content as well as a short key word list indicating how the content relates to others in the collection. The volume includes articles on actual computations of pi, articles on mathematical questions related to pi (e.g., “Is pi normal?”), articles presenting new and often amazing techniques for computing digits of pi (e.g., the “BBP” algorithm for pi, which permits one to compute an arbitrary binary digit of pi without needing to compute any of the digits that came before), papers presenting important fundamental mathematical results relating to pi, and papers presenting new, high-tech techniques for analyzing pi (i.e., new graphical techniques that permit one to visually see if pi and other numbers are “normal”). This volume is a companion to Pi: A Source Book whose third edition released in 2004. The present collection begins with 2 papers from 1976, published by Eugene Salamin and Richard Brent, which describe “quadratically convergent” algorithms for pi and other basic mathematical functions, derived from some mathematical work of Gauss. Bailey and Borwein hold that these two papers constitute the beginning of the modern era of computational mathematics. This time period (1970s) also corresponds with the introduction of high-performance computer systems (supercomputers), which since that time have increased relentlessly in power, by approximately a factor of 100,000,000, advancing roughly at the same rate as Moore’s Law of semiconductor technology. This book may be of interest to a wide range of mathematical readers; some articles cover more advanced research questions suitable for active researchers in the field, but several are highly accessible to undergraduate mathematics students.



The Light Gray People


The Light Gray People
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Author : Nancy McGown Minor
language : en
Publisher: University Press of America
Release Date : 2009-10-05

The Light Gray People written by Nancy McGown Minor and has been published by University Press of America this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-05 with History categories.


Although Lipan Apache culture was studied by one of the most eminent anthropologists of the twentieth century, many important questions remain. What is the meaning of the tribal name Lipan? Did Morris Opler's 1935 study of historical Lipan culture conform to practices seen by eighteenth century Spaniards? Only four in situ observations of Lipan Apache culture survive - observations made by a Spanish priest, a Spanish military officer, a Swiss botanist and an Anglo captive. Each source reveals fascinating insights into a hitherto unseen world of Lipan beliefs and practices. The sources reported, for example, that the Lipans were able to predict both solar and lunar eclipses, a practice which went far beyond the vision quest posited by Opler. The Light Gray People seeks to complete a comparative analysis of traditional Lipan Apache culture, as seen through the eyes of four eighteenth and nineteenth century observers and Morris Opler's theories.