Imagine calculating pi by hand. It's about 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: More math chats: ★DONATE★ ◆ Support Wrath of Math on Patreon: ◆ Donate on PayPal: Follow Wrath of Math on... ● Instagram: ● TikTok: @wrathofmathedu ● X: [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 : [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