Easy Proofs of Some Borwein Algorithms for $\pi$
Abstract
In 1987 Jonathan and Peter Borwein, inspired by the works of Ramanujan, derived many efficient algorithms for computing $\pi$. We will see that by using only a formula of Gauss's and elementary algebra we are able to prove the correctness of two of them.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2008
- DOI:
- arXiv:
- arXiv:0803.0991
- Bibcode:
- 2008arXiv0803.0991G
- Keywords:
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- Mathematics - Number Theory;
- Mathematics - Classical Analysis and ODEs;
- 33E05
- E-Print:
- To appear in The American Mathematical Monthly. (6 pages)