## Section: New Results

### Fast computation of $\pi $

Participant : Yves Bertot.

In the previous year, we studied a proof that $\pi $ could be approximated with a fast converging sequence based on arithmetic geometric means. This year we described a proof that rounding errors during this computation could be guaranteed as small as needed, based on a study of derivatives. This approach provides a fruitful alternative to interval-based approaches. The result was published in [16] .

We also completed a journal paper on various ways to observe and compute the number $\pi $ [7] .