A [computer program](http://nezumi-lab.org/blog/?cat=11) ouputs the digits of $\pi$ by evaluating the recurrence relation


$a\_{n+1} = a\_n + sin \ a\_n$


with $a\_0 = \frac{6}{5}$


Does the sequence actually converge or is this just coincidence?




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I would like to answer this by rewriting it as a differential equation.


Can I write $\frac{dy}{dx} = sin \ x$ and solve this?



Verifying a sequence that converges to pi
Regarding the second question, no.


But you can write $\Delta a\_x=\sin a\_x$.


