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Pi: The Next Generation
David H. Bailey, Jonathan M. Borwein (Gebundene Ausgabe, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
05.08.2016
Sprache
Englisch
EAN
9783319323756, 9783319323756
Herausgeber
Springer International Publishing
Sonderedition
Nein
Autor
David H. Bailey, Jonathan M. Borwein
Seitenanzahl
507
Auflage
1
Einbandart
Gebundene Ausgabe
Buch Untertitel
A Sourcebook on the Recent History of Pi and Its Computation
Schlagwörter
Catalan's constant, Euler numbers, approximations to pi, arithmetic-geometric mean Gauss, asymptotic expansions, computation pi, ladies diary, pi normal, proofs pi, spigot algorithms
Thema-Inhalt
PBKS - Numerische Mathematik
PBH - Zahlentheorie
PBX - Geschichte der Mathematik
Höhe
254 mm
Breite
17.8 cm
Transparenz & Sicherheit
Hersteller: Palgrave Macmillan, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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