Uploaded March 2025 | Updated September 2026, 2 weeks ago
Imagine calculating pi by hand. It's 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 Machin's formula and the Taylor series for arctangent. #maths #piday #mathematics
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More math chats: youtube.com/playlist?list=PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO
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[SOURCES]
Pi: A Biography of the World's Most Mysterious Number by Alfred S. Posamentier
PI: A Source Book by J. L. Berggren and Jonathan Borwein
americanscientist.org/article/pencil-paper-and-pi
edtechmagazine.com/k12/article/2012/11/calculating-firsts-visual-history-calculators
craig-wood.com/nick/articles/pi-machin
bit-player.org/2014/the-pi-man
nationalpiday.org/Pi_History/HISTORY_OF_PI_Desktop_Calculator_Ferguson_and_Pi.htm
mathshistory.st-andrews.ac.uk/Biographies/Shanks
https://www.math.brown.edu/reschwar/M10/machin.pdf
proofwiki.org/wiki/Mathematician:D.F._Ferguson
engert.us/erwin/miscellaneous/PI.pdf
[MUSIC]
HOME - Resonance
Dire Dire Docks
HOME - Pyxis
Musee Champignon
Stickerbush Symphony
HOME - We're Finally Landing
Reclusa's Defeat
0:00 Intro
1:12 Shanks's Shadow
2:25 An Intro to Pi
6:17 The arctan Solution
9:03 The Convergence Issue
11:19 Machin's Formula
13:23 Walking in his Shoes
17:51 A Legend
19:08 Error and Consequence
21:12 Conclusion
Imagine calculating pi by hand. It's 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 Machin's formula and the Taylor series for arctangent. #maths #piday #mathematics
Join Wrath of Math to get exclusive videos, lecture notes, and more:
youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join
More math chats: youtube.com/playlist?list=PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO
★DONATE★
◆ Support Wrath of Math on Patreon: patreon.com/join/wrathofmathlessons
◆ Donate on PayPal: paypal.me/wrathofmath
Follow Wrath of Math on...
● Instagram: instagram.com/wrathofmathedu
● TikTok: tiktok.com/@wrathofmathedu
● X: https://x.com/wrathofmathedu
[SOURCES]
Pi: A Biography of the World's Most Mysterious Number by Alfred S. Posamentier
PI: A Source Book by J. L. Berggren and Jonathan Borwein
americanscientist.org/article/pencil-paper-and-pi
edtechmagazine.com/k12/article/2012/11/calculating-firsts-visual-history-calculators
craig-wood.com/nick/articles/pi-machin
bit-player.org/2014/the-pi-man
nationalpiday.org/Pi_History/HISTORY_OF_PI_Desktop_Calculator_Ferguson_and_Pi.htm
mathshistory.st-andrews.ac.uk/Biographies/Shanks
https://www.math.brown.edu/reschwar/M10/machin.pdf
proofwiki.org/wiki/Mathematician:D.F._Ferguson
engert.us/erwin/miscellaneous/PI.pdf
[MUSIC]
HOME - Resonance
Dire Dire Docks
HOME - Pyxis
Musee Champignon
Stickerbush Symphony
HOME - We're Finally Landing
Reclusa's Defeat
0:00 Intro
1:12 Shanks's Shadow
2:25 An Intro to Pi
6:17 The arctan Solution
9:03 The Convergence Issue
11:19 Machin's Formula
13:23 Walking in his Shoes
17:51 A Legend
19:08 Error and Consequence
21:12 Conclusion
