Uploaded October 2025 | Updated September 2026, 2 weeks ago
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![The Most Unhinged Pi Approximation there Ever Was
Imagine calculating pi by hand. Its about 3.14 which is why we gather to celebrate it every March 14th for Pi Day. In 1853, amateur mathematician William Shanks published a calculation of pi to 607 decimal places, and by 1873 he had calculated up to 707 decimal places of pi. This was all done by hand, making it one of the most fantastic feats of calculation ever performed. We discuss how William Shanks did it using Machins formula and the Taylor series for arctangent. #maths #piday #mathematics
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[SOURCES]
Pi: A Biography of the Worlds Most Mysterious Number by Alfred S. Posamentier
PI: A Source Book by J. L. Berggren and Jonathan Borwein
https://www.americanscientist.org/article/pencil-paper-and-pi
https://edtechmagazine.com/k12/article/2012/11/calculating-firsts-visual-history-calculators
https://www.craig-wood.com/nick/articles/pi-machin/
http://bit-player.org/2014/the-pi-man
https://www.nationalpiday.org/Pi_History/HISTORY_OF_PI_Desktop_Calculator_Ferguson_and_Pi.htm
https://mathshistory.st-andrews.ac.uk/Biographies/Shanks/
https://www.math.brown.edu/reschwar/M10/machin.pdf
https://proofwiki.org/wiki/Mathematician:D.F._Ferguson
https://engert.us/erwin/miscellaneous/PI.pdf
[MUSIC]
HOME - Resonance
Dire Dire Docks
HOME - Pyxis
Musee Champignon
Stickerbush Symphony
HOME - Were Finally Landing
Reclusas Defeat
0:00 Intro
1:12 Shankss Shadow
2:25 An Intro to Pi
6:17 The arctan Solution
9:03 The Convergence Issue
11:19 Machins Formula
13:23 Walking in his Shoes
17:51 A Legend
19:08 Error and Consequence
21:12 Conclusion The Most Unhinged Pi Approximation there Ever Was](https://i.ytimg.com/vi/t5XOXQqsTvM/mqdefault.jpg)









