The Discovery That Transformed Pi

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For thousands of years, mathematicians were calculating Pi the obvious but numerically inefficient way. Then Newton came along and changed the game. This video is sponsored by Brilliant. The first 314 people to sign up via brilliant.org/veritasium get 20% off a yearly subscription.

Happy Pi Day! (for a few days ago...)

Arndt, J., & Haenel, C. (2001). Pi-unleashed. Springer Science & Business Media - ve42.co/Arndt2001

Dunham, W. (1990). Journey through genius: The great theorems of mathematics. Wiley - ve42.co/Dunham1990

Borwein, J. M. (2014). The Life of π: From Archimedes to ENIAC and Beyond. In From Alexandria, Through Baghdad (pp. 531-561). Springer, Berlin, Heidelberg - ve42.co/Borwein2012

Special thanks to Alex Kontorovich, Professor of Mathematics at Rutgers University, and Distinguished Visiting Professor for the Public Dissemination of Mathematics National Museum of Mathematics MoMath for being part of this Pi Day video.

Special thanks to Patreon supporters: Jim Osmun, Tyson McDowell, Ludovic Robillard, jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Lyvann Ferrusca, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal

Written by Derek Muller and Alex Kontorovich
Animation by Ivan Tello
Filmed by Derek Muller and Raquel Nuno
Edited by Derek Muller
Music by Jonny Hyman and Petr Lebedev

Additional Music from epidemicsound.com "Particle Emission", "Into the Forest", "Stavselet", "Face of the Earth", "Firefly in a Fairytale"

Thumbnail by Gianmarco Malandra and Karri Denise



15 Mar 2021




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Imagine having a career so illustrious that discovering a groundbreaking way to accurrately find pi is just one of your side achievements
The sheer way humans can do soooooo much with just 10 digits discovered from their fingers is extremely fascinating
Marko Apatović
I've implemented this algorithm in Java, almost solely based on information and formulae from this video. It's really cool, it can basically compute pi to any precision you want, provided you let it run long enough, but with how fast it's converging it's actually surprisingly fast. The biggest roadblock I've actually encountered was printing the whole thing to console.
Sunny Jayaram
Currently a senior in high school. Your channel and 3b1b almost exclusively inspired me to go into math/comp sci in college. The feeling of pure fascination I get from vids like this is unmatched. I have high aspirations in life and you guys led me down a path that can allow me to achieve my goals while working with things that purely astound me. Thank you.
Shawn Anderson
Technically speaking, Newton's method is far superior. However, for me "dissecting polygons" was integral... an epiphany of sorts in visualizing the practical understanding of the math.
John Chessant
What I love about this is it starts with the binomial theorem, which is seemingly totally unrelated to pi. But that's the beauty of math: it's all interconnected and idly playing with patterns can get you meaningful results.
atell Yıl önce
in all honesty, i never realized how much of a genius newton really was. i feel a bit ashamed now, dude practically made hundreds of years worth of discoveries in a few decades and i never cared much for him at all. somehow this is insanely impressive. imagine being this guy.
Steven Robertson
This is so fascinating! I studied the binomial theorem and infinite series years ago (early 1970s) but there was no mention of Newton or the history of bisecting the circle to get π by previous mathematicians. This is so well done, entertaining, and easily understood! Amazing job!
Amanda Penner
I really enjoyed this video. I’m not a mathematician and while I loved algebra I nearly flunked geometry so I never tried physics or calculus. 😭 This has helped me remember I can still learn as a mom of three. Don’t ever give up.
Apple Sauce
I love listening to people this intelligent do their thing. I don't necessarily understand everything being discussed down to a technical level but the graphics/visuals and explanation helps my simpleton brain grasp onto the idea. It makes me feel like a little kid full of wonder learning about the world around me.
A standing ovation. Had this story be there before I had started to learning binomial theorem , I would have been more interested. This is like reading a detective novel.
Newton figured it out looking at a bubble
David John
David John Yıl önce
Newton giving a lecture - "Hi guys, today we're talking about circles. The first thing you wanna do is invent calculus."
Mary Thiel
I've always wondered why 3.14 is so special in calculating things for circles but my math teachers never explained past "just because". Thanks so much for this great explanation!!
Newton was a genius and it's amazing that maths is actually about finding patterns
Vaishnavee verma
I really regret not finding this channel earlier. I used to love math in school but sadly couldn't see that there's more to all those equations and geometry than met the eye. Now that I'm watching your videos I'm realizing a lot more than before and i can see the real essence of mathematics. 💜
Unknown Variable
I've watched this video so many times, and I love it each time. I find Newton's brilliance inspirational in taking a process that everyone thought was well known and, quite literally, rewriting the book. At least here we can all come together to appreciate the beautiful work of a genius expanding humanity's capabilities, instead of hating one another for frivolous things.
Jack RP
I love that this video explains how Newton went through the process of finding a more efficient way of finding the value of Pi by just experimenting and being curious, and just generally playing with maths. It just comes to show how Newton, or any great mathematician/scientist, don't come up with ground-breaking discoveries out of thin air; that would be truly genius. Instead they just let themselves experiment with what's already discovered, and if I were to guess, without focusing so hard on what they're trying to achieve and just letting their mind flow
Mohit Singh
Mohit Singh Yıl önce
Imagine working on something for 25 years only to find out that someone did it while playing with an equation during a pandemic.
Nour Art
I love the storytelling in your videos, even if a subject doesn't interest me, it's still entertaining to watch and in the same time informative. Truly amazing, keep it up.
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