How is pi calculated to trillions of digits?
131.1 هزار بار بازدید -
5 سال پیش
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You know 3.14159265... but how
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)
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
https://forms.gle/QJ29hocF9uQAyZyH6
If you want to know more interesting Mathematics, stay tuned for the next video!
SUBSCRIBE and see you in the next video!
If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I will probably reveal how I did it in a potential subscriber milestone, so do subscribe!
#mathemaniac #math #pi #digits #computer #calculation
Social media:
Facebook: Facebook: mathemaniacyt
Instagram: Instagram: _mathemaniac_
Twitter: Twitter: mathemaniacyt
Patreon: Patreon: mathemaniac (support if you want to and can afford to!)
For my contact email, check my About page on a PC.
See you next time!
*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)
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
https://forms.gle/QJ29hocF9uQAyZyH6
If you want to know more interesting Mathematics, stay tuned for the next video!
SUBSCRIBE and see you in the next video!
If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I will probably reveal how I did it in a potential subscriber milestone, so do subscribe!
#mathemaniac #math #pi #digits #computer #calculation
Social media:
Facebook: Facebook: mathemaniacyt
Instagram: Instagram: _mathemaniac_
Twitter: Twitter: mathemaniacyt
Patreon: Patreon: mathemaniac (support if you want to and can afford to!)
For my contact email, check my About page on a PC.
See you next time!
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