Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T21:42:19.071Z Has data issue: false hasContentIssue false
  • English
  • Français

88.38 Some observations on the method of arctangents for the calculation of π

Published online by Cambridge University Press:  01 August 2016

Hwang Chien-Lih
Hwang Chien-Lih*
Affiliation:
Dept of Mathematics, National Taiwan University, Taipei, Taiwan, [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Notes
Information
The Mathematical Gazette , Volume 88 , Issue 512 , July 2004 , pp. 270 - 278
Copyright
Copyright © The Mathematical Association 2004

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. Beckmann, P., A history of π (2nd edn), St. Martin’s, New York (1971) pp. 132–133.Google Scholar
2. Shanks, D. and Wrench, J. W. Jr., Calculation of π to 100,000 decimals, Math. Comp. 16 (1962) pp. 76–99.Google Scholar
3. Wetherfield, M., The enhancement of Machin’s formula by Todd’s process, Math. Gaz. 80 (July 1996) pp. 333–344.Google Scholar
4. Lehmer, D. H., On arccotangent relations for π, Amer. Math. Monthly 45 (1938) pp. 657–664.Google Scholar
5. Castellanos, D., The ubiquitous π, Math. Magazine 61 (1988) pp. 67–98 (Part 1) and pp. 148–163 (Part 2).Google Scholar
6. Salamin, E., Computation of π using arithmetic-geometric mean, Math. Comp. 30 (1976) pp. 565–570.Google Scholar
7. Borwein, and Borwein, P. B., Pi and the AGM—a study in analytic number theory and computational complexity, Wiley, New York (1987) pp. 184 and 188.Google Scholar
8. Focus, At the Limits of Calculation, Pi to a Billion Digits and More, Volume 9, Number 5, October 1989.Google Scholar
9. Lord, N., Recent formulae for π: arctan revisited, Math. Gaz. 83 (November 1999) pp. 479–483.Google Scholar
10. Gleick, J., Even mathematicians can get carried away, The New York Times, Sunday, March 8, 1987.Google Scholar
11. Chien-lih, Hwang, More Machin-type identities, Math. Gaz. 81 (March 1997) pp. 120–121.Google Scholar