# The Borwein brothers, Pi and the AGM.

@article{Brent2018TheBB, title={The Borwein brothers, Pi and the AGM.}, author={Richard P. Brent and Richard P. Brent}, journal={arXiv: Number Theory}, year={2018} }

We consider some of Jonathan and Peter Borweins' contributions to the high-precision computation of $\pi$ and the elementary functions, with particular reference to their book "Pi and the AGM" (Wiley, 1987). Here "AGM" is the arithmetic-geometric mean of Gauss and Legendre. Because the AGM converges quadratically, it can be combined with fast multiplication algorithms to give fast algorithms for the {$n$-bit} computation of $\pi$, and more generally the elementary functions. These algorithms…

## One Citation

### The Art of Modern Homo Habilis Mathematicus, or: What Would Jon Borwein Do?

- ArtHandbook of the Mathematics of the Arts and Sciences
- 2021

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