How is pi calculated to trillions of digits?

Описание: You know 3.14159265... but how do we calculate these digits in the first place? Measure it? Well, definitely not up to trillions of digits of accuracy, and Archimedes' method is insanely slow for trillions of digits to be calculated. Here is a simple explanation of Machin-like algorithms, which only requires high school knowledge of complex numbers.

*REFERENCES AND FURTHER READINGS*:

1. A comprehensive history of pi and its computation: http://www.cecm.sfu.ca/~jborwein/pi-s...

2a. A brief history of pi (up to 1996): https://www.davidhbailey.com//dhbpape...
2b. A more layman version of the above: https://en.wikipedia.org/wiki/Chronol...

3. Machin-like formula: https://en.wikipedia.org/wiki/Machin-...

4a. BBP algorithm easy derivation paper: https://www.jstor.org/stable/3620961?...
4b. The above adapted into an easy calculus exercise: https://drive.google.com/open?id=1yuH...

5a. Official Google cloud article on breaking record of pi calculation: https://cloud.google.com/blog/product...
5b. A personal blog for the same event (with a bit more technical details): http://www.numberworld.org/blogs/2019...

6. Proof of Chudnovsky formula: https://arxiv.org/pdf/1809.00533.pdf (if you are really into this monstrous formula)

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