Hostname: page-component-77c89778f8-gvh9x Total loading time: 0 Render date: 2024-07-16T21:55:50.149Z Has data issue: false hasContentIssue false

Recent calculations of π : the Gauss-Salamin algorithm

Published online by Cambridge University Press:  01 August 2016

Nick Lord*
Affiliation:
Tonbridge School, Tonbridge, Kent TN9 1JP

Extract

Recent years have seen a marked increase in the tempo of the hunt for digits of the decimal expansion of π as shown in the table below.

Type
Research Article
Copyright
Copyright © The Mathematical Association 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Almkvist, G., and Berndt, B., “Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, π and the Ladies DiaryAmerican Mathematical Monthly, 95, 585608 (1988).Google Scholar
2. Borwein, J.M., and P.B., , “The arithmetic-geometric mean and fast computation of elementary functions”, SIAM Review, 26, 351366 (1984).Google Scholar
3. Borwein, J.M., and R.B., , π and the AGM, John Wiley (1987).Google Scholar
4. Borwein, J.M., and P.B., , “Ramanujan and π", Scientific American, Feb. 1988, 6673.Google Scholar
5. Borwein, J.M., and P.B., , and Bailey, D.H., “Ramanujan, modular equations and approximations to π, or how to compute one billion digits of π”, American Mathematical Monthly, 96, 201219 (1989).Google Scholar
6. Castellanos, D., “The ubiquitous π (Part I)”, Mathematics Magazine, 61, 6798 (1988).Google Scholar
7. Castellanos, D., “The ubiquitous π (Part II)”, Mathematics Magazine, 61, 148163 (1988).Google Scholar
8. King, L.V., On the direct numerical computation of elliptic functions and integrals, Cambridge U.P. (1924).Google Scholar
9. Lawden, D.F., Elliptic functions and applications. Springer (1989).Google Scholar
10. Schoenberg, I.J., Mathematical time exposures. Math. Association of America (1982).Google Scholar
11. Stillwell, J., Mathematics and its history, Springer ( 1989).Google Scholar
12. Wells, D., The Penguin dictionary of curious and interesting numbers. Penguin (1986).Google Scholar
13. Whittaker, E.T., and Watson, G.N., A course of modern analysis (4th edition), Cambridge U.P. (1927).Google Scholar
14. Bruce, J.W., Giblin, P.J., and Rippon, P.J., Microcomputers and mathematics, Cambridge U.P. (1990).Google Scholar