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Note that there's a huge amount about pi that I didn't cover in this video due to time - I didn't even mention proofs of it being irrational and transcendental, or why we call it pi! I chose to focus on the development of its approximation as a hook to teach the broader history of mathematics, rather than make this video an exhaustive list of facts. The wiki is a great place to learn more about the rest of the number's history and applications in maths and physics: https://en.wikipedia.org/wiki/Pi#History
A few nitpicky things:
- I made mistakes distinguishing between 'digits of pi calculated' and 'decimal points of pi calculated' in some sections, so it is possible that this error is elsewhere without me knowing.
- Archimedes didn't do his approximation with squares, he started with hexagons and then increased the order of the polygon. I chose to present the zeroth order version of his algorithm using squares for simplicity, but note that this is not what he did.
- Something which got lost from the final version of this video is my argument that during the Age of Enlightenment pi shifted from being a physical (measured) constant to a purely logical (theoretical) one. This then embodies the philosophical shift in society at the time. This is hinted at but not fully explained, so I thought I'd put this here.
- Lastly, I am truly sorry for the pronunciations which I doubtlessly completely murdered in this video. At least I spared you my attempt at Chinese.
I am hugely indebted to Alex Bellos and his excellent book Alex's Adventures in Numberland for the inspiration to make this video. There is an entire chapter of the book devoted to a broader but shallower discussion of pi and its history, which I highly recommend.
You can support the channel by donating at http://www.patreon.com/simonoxfphys
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Huge thanks to my supporters on Patreon: Dan Hanvey, David Efird, Elliot Conway, Robert Eldon, Syafiq Kay, Xavier Chesterfield, Jay Wright, Myles Kornfeld, Louis Gillet, Michael Phillips, Neudys Almonte, Fraser Birks, Martin Hermes, Anh Duong, Luca Schumann, Rhys Rickard-Frost, Cameron Matchett, Lachlan Woods, Tim Boxall, Simon Vaes, Gabriele Mozzicato, Jawad Alalasi, Gaia Frazao Nery, Kodzo, Josh Ruby, Claire Anthony, Eve Dillon, Rowan Gow, Matthias Loos, James Bridges, James Craig, Angela, Sanaa Al Derei, Mark Anthony Magro, Liam, Theresa Wang, Kieran Kelly, Wendover Productions, Kendra Johnson, Caitlin Louise.
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Thanks to Vlogbrothers for their sponsorship of this video. Money from the Foundation to Decrease Worldsuck contributed to equipment used in this video.