A Brief History of Pi 1,166,863 viewsMar 14, 2018

A Brief History of Pi 1,166,863 viewsMar 14, 2018 26K DISLIKE SHARE DOWNLOAD CLIP SAVE Simon Clark 425K subscribers Get 10% off Squarespace by following this link: http://squarespace.com/simonclark Check out my new website here! https://www.simonoxfphys.com/ 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 ---------- II ---------- 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. ---------- II ---------- Vlogs from Oxford students - http://www.youtube.com/oxvlog My twitter - http://www.twitter.com/simonoxfphys My facebook - http://www.facebook.com/youtubesimon My insta - http://www.instagram.com/simonoxfphys My goodreads - http://www.goodreads.com/simonoxfphys Thanks to Vlogbrothers for their sponsorship of this video. Money from the Foundation to Decrease Worldsuck contributed to equipment used in this video. 2,175 Comments rongmaw lin Add a comment... Daniel Rutschman Daniel Rutschman 3 years ago One thing I learned from this video is that Simon finds it easier to pronounce long Indian names than short Chinese or French names. Now, you can diagram those names as n-sided polygons where n is the number of syllables in each name, and fit the polygons inside each other such that the polygons with lower values of n are contained within the polygons with higher values of n. Then, by subtracting the highest value of n from the lowest value of n and dividing that by the number of polygons, you can determine that there is an infinite series in which the ease of pronouncing a name progressively increases in proportion to the number of syllables in the name. So a name containing zero syllables would be impossible to pronounce, whereas a name with infinite syllables is absolutely pronounceable. At least in Simon's case. 72 Ajinkya Ajinkya 4 years ago (edited) An interesting fact about Indian Mathematics. Like all other fields, Mathematics in India was documented in the form of Sanskrit poetry ( Easier to learn and remember ). So theorems and formulas including the Madhava infinite series were written as 4 - 8 line 'poems' 731 Tamario Warren Tamario Warren 1 year ago Oh how I love the Ancient Greek legends - "Don't disturb my circles" ... Last words - I love it 193 Michæl Gilbert Clements Michæl Gilbert Clements 2 years ago But wait, the greek letter Pi was first used as a symble to represent the number 3.1415 in 1706 by William Jones. So inthe year 2020, Pi will have been used for 3.14 centuries! 691 Simon Clark #3110 #3110 8 months ago I am more amazed and mind-blown when I realized that Archimedes calculated pi using roman numerals. He's a genius and a hardworking person 52 8-Bit Amit 8-Bit Amit 9 months ago 9:40 Sanghamagrama madhavan His aashrama is 30 minutes from our house. Proud to have a mathematics from our small state Kerala. 50 Krys Kestrel Krys Kestrel 4 years ago This video was made so well, and was actually nice and engaging throughout the entire lesson! Keep up the good work, Simon! 57 clive lewis clive lewis 2 years ago I loved this video. Fascinating and engaging maths with a great dollop of history thrown in! Quite a feat. 10/10 9 baris bilgi baris bilgi 2 years ago History of PI and some other similar concepts like history of trigonometry, derivative, integral etc. should be taught in ordinary public schools to all the students (no matter which subject they will choose in the future). That will help increase the awareness of importance of math and science. Youth will know why we need to trust science. A common sense can be created that way. That will affect how we see life and even our political choices. 17 Colored Screens Colored Screens 3 years ago (edited) Awesome video, but I can't help but to point out one small inaccuracy. At 9:05, you said that "If those contributions keep getting smaller as you go on, then the series converges to a particular value." Though this is often true, there are infinite examples (such as the harmonic series, Σ1/n) where a series consisting of strictly decreasing values diverges. 20 AliasSheep AliasSheep 4 years ago Your science and maths education videos are fantastic, Simon. Can't wait to see what's next! 3 gakaface gakaface 3 years ago Good video Simon. Brings back memories for me. For me, it was the benchmark in mathematics and computer programming. 37 years ago, I programmed a mainframe computer to calculate Pi to 1,000 decimal places - my formula was 4(arctan(1/2) + arctan(1/3)) which converges at a rate of two decimal places per iteration. In those days, it took a whole weekend of the core CPU time. These days, this can be done in a matter of minutes on a laptop. 1 Howard Man Howard Man 4 years ago Despite already having a large chunk of subs, I really think you do deserve more. I feel as though you are one of the few people who are talented in explaining things scientific and mathematical. ; ) 3 Oskar Henriksson Oskar Henriksson 4 years ago (edited) Hmn, I'm not sure Archimedes and Euclid would have agreed that their methods were any less rational, theoretical or based on reason than what the 17th century Europeans were up to :) I guess it fair to say that Leibniz, Gregory et al. had a slightly more abstract and symbolic approach to mathematics -- and they certainly had some really sophisticated concepts (like the notion of a series) that the Greeks didn't have -- but when it comes to theoretical rigor, my impression is that the Greeks had just as solid ground under their feet as the 17th century Europeans, if not more! I haven't read Leibniz's original proof of the series formula, but the way I understand it, it involves quite a lot of infinitesimals being thrown around, which (especially at that early time in the development of calculus) must have been much less clear/rigorous and much more based on intuition/common sense, than the very strict and precise arguments within (an extension of) the Euclidean axiomatic framework that Archimedes made in his "Measurement of a Circle." 8 J. J. Thompson J. J. Thompson 4 years ago Simon this was an awesome pi video! Entertaining, interesting and useful. Thanks very much and looking forward to more stuff!! P. S. Your book recommendation video for studying physics was very useful indeed! I'm currently enjoying Alex's Adventures in Numberland :-) All the best to my fellow science homies out there! 1 Alberto Lema Alberto Lema 1 year ago Great content! Love the tone and how you connect the dots through historic events. Great narratives! 5 Claudia Jade Claudia Jade 4 years ago (edited) Literally no one ever told me that that's what pi is...I just thought it was like an arbitrary number that worked for things. I also thought 'sequences and series' was the most boring topic in maths...I do kinda wish they gave more explanations about things along the way for why different mathematics was important/useful. I was pretty happy to just accept it and do the work, but I certainly would have found it more interesting (and I think would have motivated a bunch of other ppl), to know the context and significance. 35 Gaiboii 2001 Gaiboii 2001 2 years ago Loved this video! On March 14 of this year, my retired physics teacher who came back to teach in an emergency (long story), gave the class some pie! Food for the brain 🧠 6 REME REME 2 years ago Outstanding video and extremely well narrated. Well done! 3 Jeff Wells Jeff Wells 1 year ago A great video, especially since you pronounced Ramanujan's name correctly ;) One mathematical advance that still needs to be done, however, is to lose our clumsy decimal system and switch to duodecimal or "dozenal" counting by twelves instead of tens, mainly because of its factorability. Ten is only evenly divisible by 2 and 5, whereas twelve has even factors of 2, 3, 4, 6 and almost by 8 and 9. We got stuck with tens because we have ten fingers, but if we used the three segments on each of out four fingers we can easily count to twelve (or 24) that way. The symbols for base twelve are the usual 0,1,2,3,4,5,6,7,8,9 plus X and E for ten and eleven, so 10 in dozenal represents twelve, 20 is twenty-four, 100 is 144 and so on. The names proposed for X, E and 10 are currently dek, el and do (rhymes with so). Twelve is why we have twelve months of three seasons each in our calendars and 24 hours in a day, but finer divisions don't fit once weeks, hours, minutes and seconds are randomly crammed in to make decimalizing time a real pain to calculate. This could have been implemented during the French Revolution of 1789 but the chances of it happening now are practically zero, less even than if the United States finally decided to adopt the full metric system. Nelson Swanberg Nelson Swanberg 2 years ago I've often imagined the frustration of using Roman numerals to do engineering calculations. 131 Manu Hernz Manu Hernz 2 years ago Apart from the historical part, I liked the almost philosophical one. What was missing was the futuristic vision of going on with Georg Kantor and his Math of the Infinite. Then one can jump to a conclusion that everything is infinite, even the Higgs Boson. 1 Leon R.M. Auguste Leon R.M. Auguste 4 years ago Great content Dr. Clark! I loved the depth of knowledge you gave us today :D 1 Nathan Whitten Nathan Whitten 3 years ago Well done. If I were to undertake a description of the discover of pi, I'd do something like you did. I have a bit of experience with infinite series. 120 hours of math, 72 of them in grad school. Series were of great interest to me. Thanks for this. Sourkid13 Sourkid13 4 years ago (edited) I love these videos, Simon. You're making great stuff, keep it up 1 Kalpana & Rohit Nain Kalpana & Rohit Nain 1 year ago (edited) Hi! You have explained very well to us. Really, it is an interesting and amazing video. 4 Nick Kartha Nick Kartha 2 years ago 9:37 I was so suprised to see my native language of malayalam in this video. I didn't know Madhava did that, thank you! 11 Ray Kent Ray Kent 4 years ago Great video, thanks. I'd like to throw in a thought for a possible future video. Is the occurrence frequency of single digits necessarily equal or has it only been established experimentally by looking at the enumeration we have so far? Do the digits of pi meet other statistical tests such as recurrence of groups? How does it compare to other pseudo-random generators? Please don't waste your time answering me personally, maybe make a video? Adam Taylor Adam Taylor 4 years ago Great video btw, I love these style of videos looking at the history of maths. It's stuff like this that we never learn at school, but is fascinating. 1 Haridas991 Haridas991 1 year ago Thank you for this informative video. I love your expression of mathematics in such a lighthearted and fun way. 1 Rajarshi Bandopadhyay Rajarshi Bandopadhyay 3 years ago