Calculation of PI with a certain accuracy?

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Need formula/code for the subject.

I read that there is a formula of Gauss (high speed computing), but I couldn't Google it. Generally, it is not so critical that it will be used, but I want to see the implementation of the formula of Gauss.

It will be used in the code in Python3, so I would be grateful if someone will share a ready solution.
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And it's not something?
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Yandex taxis: algolist.manual.ru/maths/count_fast/pi.php
The bottom of the page there is an example in C++ for the formula of Gauss.
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