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: [ Ссылка ]
2a. A brief history of pi (up to 1996): [ Ссылка ]
2b. A more layman version of the above: [ Ссылка ]
3. Machin-like formula: [ Ссылка ]
4a. BBP algorithm easy derivation paper: [ Ссылка ]
4b. The above adapted into an easy calculus exercise: [ Ссылка ]
5a. Official Google cloud article on breaking record of pi calculation: [ Ссылка ]
5b. A personal blog for the same event (with a bit more technical details): [ Ссылка ]
6. Proof of Chudnovsky formula: [ Ссылка ] (if you are really into this monstrous formula)
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If you want to know more interesting Mathematics, stay tuned for the next video!
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#mathemaniac #math #pi #digits #computer #calculation
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