Pi: The Next Generation

1. Computation of π using arithmetic-geometric mean (1976)
Eugene Salamin

2. Fast multiple-precision evaluation of elementary functions (1976)
Richard P. Brent

3. The arithmetic-geometric mean of Gauss (1984)
David A. Cox

4. The arithmetic-geometric mean and fast computation of elementary functions (1984)
J. M. Borwein, P. B. Borwein

5. A simplified version of the fast algorithms of Brent and Salamin (1985)
D. J. Newman

6. Is pi normal? (1985)
S. Wagon

7. The computation of π to 29,360,000 decimal digits using Borweins quartically convergent algorithm (1988)
David H. Bailey

8. Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, π, and the Ladies Diary (1988)
Gert Almkvist, Bruce Berndt

9. Vectorization of multiple-precision arithmetic program and 201,326,000 decimal digits of pi calculation (1988)
Yasumasa Kanada

10. Ramanujan and pi (1988)
Jonathan M. Borwein, Peter B. Borwein

11. Ramanujan, modular equations, and approximations to pi or how to compute one billion digits of pi (1989)
Jonathan M. Borwein, Peter B. Borwein, David H. Bailey

12. Pi, Euler numbers, and asymptotic expansions (1989)
Jonathan M. Borwein, Peter B. Borwein, Karl Dilcher

13. A spigot algorithm for the digits of π (1995)
Stanley Rabinowitz, Stan Wagon

14. On the rapid computation of various polylogarithmic constants (1997)
David H. Bailey, Peter B. Borwein, Simon Plouffe

15. Similarities in irrationality proofs for π, ln 2, ζ(2), and ζ(3) (2001)
Dirk Huylebrouck

16. Unbounded spigot algorithms for the digits of pi (2006)
Jeremy Gibbons

17. Mathematics by experiment: Plausible reasoning in the 21st Century (2008)
David H. Bailey, Jonathan M. Borwein

18. Approximations to π derived from integrals with nonnegative integrands (2009)
Stephen K. Lucas

19. Ramanujan’s series for 1/π: A survey (2009)
Nayandeep Deka Baruah, Bruce C. Berndt, Heng Huat Chan

20. The computation of previously inaccessible digits of π2 and Catalan’s constant (2013)
David H. Bailey, Jonathan M. Borwein, Andrew Mattingly, Glenn Wightwick

21. Walking on real numbers (2013)
Francisco J. Aragón Artacho, David H. Bailey, Jonathan M. Borwein, Peter B. Borwein

22. Birth, growth and computation of pi to ten trillion digits (2013)
Ravi Agarwal, Hans Agarwal, Syamal Sen

23. Pi day is upon us again and we still do not know if pi is normal (2014)
David H. Bailey, Jonathan Borwein

24. The Life of π (2014)
Jonathan M. Borwein, Peter B. Borwein

25. I prefer pi: A brief history and anthology of articles in the American Mathematical Monthly (2015)
Jonathan M. Borwein

Keywords: Mathematics, Computational Mathematics and Numerical Analysis, Number Theory, History of Mathematical Sciences