Foreword.- Preface.- Introduction.- Computation of pi using arithmetic-geometric mean.- Fast multiple-precision evaluation of elementary functions.- The arithmetic-geometric mean of Gauss.- The arithmetic-geometric mean and fast computation of elementary functions.- A simplified version of the fast algorithms of Brent and Salamin.- Is pi normal?.- The computation of pi to 29,360,000 decimal digits using Borweins' quartically convergent algorithm.- Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, pi, and the ladies diary.- Vectorization of multiple-precision arithmetic program and 201,326,000 decimal digits of pi calculation.-Ramanujan and pi.- 11. Ramanujan, modular equations, and approximations to pi or how to compute one billion digits of pi.- Pi, Euler numbers, and asymptotic expansions.- A spigot algorithm for the digits of pi.- On the rapid computation of various polylogarithmic constants.- Similarities in irrationality proofs for pi, ln 2, ζ(2), and ζ(3).- Unbounded spigot algorithms for the digits of pi.- Mathematics by experiment: Plausible reasoning in the 21st century.- Approximations to pi derived from integrals with nonnegative integrands.- Ramanujan's series for 1/π: A survey.- The computation of previously inaccessible digits of π2 and Catalan's constant.- Walking on real numbers.- Birth, growth and computation of pi to ten trillion digits.- Pi day is upon us again and we still do not know if pi is normal.- The Life of pi.- I prefer pi: A brief mathematical history and anthology of articles in the American Mathematical Monthly.- Bibliography.- Index.
David H. Bailey currently has two affiliations for his
professional research work. Dr. Bailey is Senior Scientist,
Computational Research Department, Lawrence Berkeley National
Laboratory from which he officially retired in June 2013 but
continues as an active researcher. Since February 2013, Bailey is
also a Research Fellow, Department of Computer Science, University
of California, Davis.
Jonathan M. Borwein is currently Laureate Professor in the
School of Mathematical and Physical Sciences at the University of
Newcastle (NSW) with adjunct appointments at Dalhousie and at Simon
Fraser. He received his Doctorate from Oxford in 1974, and has
published extensively in optimization, analysis, and computational
mathematics, and has received various prizes both for research and
for exposition. He directs the University of Newcastle’s Priority
Research Centre in Computer Assisted Research Mathematics and its
Applications (CARMA).
“Pi: The Next Generation is compiled as a sourcebook on the recent
history of π from 1975 on, and on computational issues. … Reading
the papers in this book I found many aspects on the mathematics and
history of π which I did not know before and I enjoyed reading it
very much. As the older book on π this one will also soon become a
standard reference tool for working mathematicians and historians
of mathematics alike.” (Thomas Sonar, London Mathematical Society
Newsletter, newsletter.lms.ac.uk, November, 2017)
“Each reprinted paper is accompanied by a brief introduction
explaining its significance. The papers range from historical
surveys to popular expositions to research articles. Although I
knew most of the papers already, I still found it delightful to
browse at random. It would make a good selection for a high school
or college library.” (Jeffrey O. Shallit, Mathematical Reviews,
May, 2017)
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