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 Ivy 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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@betterideas 2 aylar önce
I really like this video because I didn’t understand 99% of the math, yet I was invested. It felt like something important was unraveling before me, and I was excited by that. And that’s the power of good storytelling.
@TheBluePhoenix008 2 aylar önce
I did understand all the math and it was even better
@uncreative369 2 aylar önce
That's the Power of Math
@justanotherbeing4529 2 aylar önce
Ay its my favourite bald guy learning mathematics!
@KaluaBihari1 Aylar önce
maths was nothing just basic calculus
@TheBluePhoenix008 Aylar önce
@@KaluaBihari1 people have a hard time with calculus, for some reason
@endruv_2287 Yıl önce
Newton was the greatest genius who ever lived. Even the great Gauss pays homage to Newton.
@MrTaleth Yıl önce
Regarding inventing calculus it should be noted though that Gottfried Wilhelm Leibniz invited it simultaiously and independently from Newton and Gottfried Wilhelm Leibniz notation was actually superior and the one used later on
@@MrTaleth Newton invented it nearly two decades earlier and kept it for himself. Leibniz is a great mathematician but even he would be embarrassed to be compared with the genius of Newton. Newton is the only human in history who could be arguably called as the greatest mathematician and physicist simultaneously. Newton was something else, no wonder even the incomparable Gauss was in awe of Newton. To me, Newton's genius mind is the pinnacle of human thought.
@MrTaleth Yıl önce
@@critical_analysis I fully agree that Leibnez can't be compared to Newton. Regarding calcus specifically though as I have understood it most historians view the development of it as made by both of them independently of each other. If you have sources of historians pointing to it being the sole invention of Newton please share :)!
oh! he also discovered how your eyes perceiving color works. man was so cool that solving color was just a minor achievement in his career
Moral of the story : Newton was hell of a genius.
@madcap9977 10 aylar önce
@santhoshhbs 8 aylar önce
@@madcap9977 he just tried all the possibilities that he know
@hijdjf2961 8 aylar önce
@santhoshh bs, you are the type of person to struggle to open pistachios.
@santhoshhbs 8 aylar önce
@@hijdjf2961 means?
@ikeatable1 6 aylar önce
If it was anybody but Newton or Euler this would be one of the most iconic moments in mathematical history. The fact that this is one of the least interesting things that Newton discovered is completely insane.
@ker0356 Aylar önce
or Gauss, that guy had all the answers in the universe but kept them somewhere in his private letters to someone
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.
@minecrafting_il Yıl önce
math basically HAS to have many inner patterns, as math is, in a sense, the study of patterns.
@hike8932 Yıl önce
@@minecrafting_il and order :)
@pf6455 Yıl önce
Math is beautiful
@eggegg6448 Yıl önce
@@hike8932 math folder is blue
@almondsai7214 13 gün önce
@@eggegg6448 Math folder is red, you can't change my mind.
@marythiel9447 Yıl önce
I've always wondered why 3.14 is so special in calculating things for circles but my math teachers never explained, saying "just because". Thanks so much for this great explanation!!
@bettercalldelta Yıl önce
To be honest it does get a little "just because" sometimes
@Aldric524 9 aylar önce
@@bettercalldelta It certainly does in the classroom. I think this is partly because to explain beyond "just because" to every single kid in the room would bring everything to a halt. Another reason is teachers get burned out eventually.
@bettercalldelta 9 aylar önce
@@Aldric524 yeah but what I was saying is math sometimes just messes with us and puts pi somewhere just because
@alonso19989 7 aylar önce
Well Pi is 3.14 just because. We compute the relation and it gives that weird number. The best possible answer is "well, that's how the universe works"
@romeohio19 6 aylar önce
And that is exactly why school is a failure. It’s never about actually learning or understanding, it’s just half assing and memorizing to pass a useless test.
@kimi9572 2 yıl önce
Imagine having a career so illustrious that discovering a groundbreaking way to accurrately find pi is just one of your side achievements
@AkshayKumar-kz6zh 2 yıl önce
Every other guys call themselves real gangsta. If they would have saw Newton, Turing, Euclid they would have shat their pants
@AuliaAF 2 yıl önce
And somehow, that grand side achievement is much less attributable to you than a random falling apple :D :D
@arturkarabekov1920 2 yıl önce
@@AuliaAF well, falling of an apple gave him the idea of gravity, which in comparison with calculus is way bigger achievement
@gforcebreakin 2 yıl önce
@@AkshayKumar-kz6zh "You Ain't Gangsta Like Newton" Would be a dope track. Rofl
@yuri-cruiter9676 2 yıl önce
@@AkshayKumar-kz6zh so much that no one would think you stealing from your student
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.
@adeniranye Yıl önce
Real talk. Illustrations like these go a long way for students. Good luck
@maheshnaik8388 Yıl önce
Err..dear..do you go down a path..?...or up a path?..or a path on the same level ??..
@michaelt5459 11 aylar önce
@@adeniranye I'm so glad to have stuff like this today, but at the same time I'm saddened that we don't have more stuff like this in school. I was always really good at math (Like straight A's in AP classes), but it never made me passionate. We would be taught formulas and how to use them, a little bit about what they mean, but nearly nothing about how it was made. I understand they might not have the time for it all the time, but I think they could have incorporated it a bit more. Even if it means they have to cut back on overall content, I think giving in depth insightful stuff like this is much more valuable towards developing a proper math sense.
@leviackerman6598 Aylar önce
​@michaelt5459 totally agreed, one of my mom's brother stopped math js cuz of this, (he was good at it)
Just want a biology related channel now...
@miceyfb 11 aylar önce
Newton was one incredible man
"Newton was a smat cookie" -- Penny Holfstader
@philosophi4911 10 aylar önce
Indeed he was.
@NoLifeDax 10 aylar önce
Yes indeed he was
@74jparralel38 9 aylar önce
@@thebelligerentbostonian7524 smat
@Uma-Bharat-India 4 aylar önce
@harrokrog4707 8 aylar önce
When this man said:“Luckily he just invented calculus“ like its not even that great. I realised what a genius he was. Sadly we dont learn about that in school
@magik97 4 aylar önce
What? We learn that in school
@ClintonDawkins 3 aylar önce
You were a bad student.
@TaylorfromPapaLouie 2 aylar önce
​@@ClintonDawkinsor they had a bad school
@ClintonDawkins 2 aylar önce
@@TaylorfromPapaLouie Bad students never blame themselves.
@advaithbhasi Yıl önce
Can we all take a step back and imagine just how much of a genius Newton was.
@Siberian_Khatru. 10 aylar önce
Absolutely! He's the greatest scientist and the most influential "not a godman" person of all time for me!
​@@Siberian_Khatru.He is more influential than god himself..Jesus himself
@Spectagon-gw7mx 2 gün önce
@@AshikurRahmanRifat Even as someone who is agnostic that is very disrespectful to very religious people
@yt_sricharanp Yıl önce
If only my Math teacher explained it like this back in my college days ...
@joeljustin 11 aylar önce
More like from School itself.
@veritasium 2 yıl önce
Also shout out to Indian mathematician and astronomer Madhava of Sangamagrama, who in the 14th century had a different infinite series for pi that converged as fast as Newton's
@ankeshnand 2 yıl önce
@thethirdjegs 2 yıl önce
Maybe for veritasium's next video?
You should definitely pin this comment.
@ankeshnand 2 yıl önce
@@thethirdjegs Yeah, I would love to know about this series.
@sumitphysics3407 2 yıl önce
And what about Ramanujan Series
@applesauce9982 Yıl önce
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.
@jackrp4713 Yıl önce
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
@Anonymous-sb9uh Yıl önce
That's a simplification. Remember this happened to one of the greatest minds and even then it's not every second. Its like Bolt breaking world record 100m. The fastest man on earth pushes the boundary just a few times. The boundary is the boundary of human achievement by other extreme outliers so not easy by any means.
Newton was the greatest genius who ever lived. Even the great Gauss pays homage to Newton. I don't think anyone comes close to his all-round genius in Math/Physics. One can only be in awe of this gem of human race.
@musaratjahan7954 8 aylar önce
@@critical_analysis there are many that do certainly come close and, I'd argue, surpass him in some key areas.
@critical_analysis 8 aylar önce
@@musaratjahan7954 Never mind many, name one who did pioneering, lasting and original work as Newton simultaneously in both Math and Physics. As I said earlier, he is the only one who could be listed as the greatest mathematician and physicist at the same time. Of course, many geniuses were there like Euler, Guass, Faraday, Maxwell, Einstein etc., but they were more devoted/influential to one field rather than both.
@jimjohnson394 2 aylar önce
huhuhuhuh....you said "hard on"
@Navak_ Yıl önce
It's incredible how many breakthroughs Newton was responsible for.
@user-ut8mt5rj8r Yıl önce
Newton figured it out looking at a bubble On a serious note: loved the way both of you express your passion about the subject. You can feel the guest is actually excited throughout the whole video🔥
@abhilashasinha5186 11 aylar önce
wait your name is j
@user-ut8mt5rj8r 11 aylar önce
@@abhilashasinha5186 nah I wish
@user-im6yc3wg7c 6 aylar önce
@@user-ut8mt5rj8r 🔥
@dufushead Yıl önce
Love it. After 65 years I've finally understood what the teachers were trying to teach me. Odd remembering and piecing together all those fragments of memories largely because they were ajumble of unrelated abstract ideas which you gave coherence, meaning and understanding too. If only you'd been around when my kids were at school. Cheers Prof !
@4tell 2 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.
@ThPaScCo 2 yıl önce
I once read Newton was the smartest human who ever lived. Never saw anyone dispute that.
@anirbanroy5667 2 yıl önce
This is the most unpopular opinion but also aside from all the phenomenol things learned from Newton, Einstein, Euler, Ramanujan, etc, I also learned that there is a different kind of fun in making students stressed out beyond how much peer pressure can
@writershard5065 2 yıl önce
The point isn't about how genius Newton is, but rather that he decided to go against the grain and try things from a different angle, which brought him closer to solving this issue than anyone else did. Innovation and change is just as important as respecting traditions and rules. You need to understand why the latter exists to break it and invent new ways to move forward into the future.
@carso1500 2 yıl önce
@Alex ' knowledge is build on knowledge just because einstein didnt come up with those concepts himself from scratch doesnt mean that he wasnt any less smart or less of a genious thats like saying that newton wasnt smart because he didnt invented mathematics he had thousands of years worth of theory and practice to work from he just moved some numbers around and thats it anyone could have added a -1 its nothing special (which is stupid) einstein started a revolution in many ways that we are still seeing today, and yes his ideas have held up soo far unless you are going to tell me that general or special relativity are wrong, quantum mechanics was always a huge problem for him because he didnt believed in the uncertainty principle since it made him unconfortable and tried really hard to prove it wrong, he failed of course, that doesnt mean that all his ideas are wrong in fact one huge problem modern physics has is that both general relativity and quantum physics are correct, and both theories are basically inconpatible with one another since one is deterministic while the other one is probabilistic (not really incompatible but scientist are having a hard time unifying both theories)
@aelaan12 Yıl önce
To have a brain so brilliant in math is just amazing to me. Imagine being 23 years young and seeing this develop in front of your eyes and your brain sees the solution.
"We should always know the extent to which the rules have a chance of working farther" - I like that phrase
@HeyUtsav 11 aylar önce
Can someone please shed some light on how that Dutch mathematician was able to calculate the perimeter of a 2^62 side polygon?
@nicholasdarrylh.9062 11 aylar önce
@HeyUtsav 11 aylar önce
@@nicholasdarrylh.9062 But still, how is this even humanely possible?! I just want to know how one could construct such shape or make the calculations for it.
@h3xagon488 11 aylar önce
@@HeyUtsav as you can see every shape can be calculated using a formula (which I guess can be done repeatedly until the wanted shape, and as said in the video a 12 sided polygon needs you to extract sqrts in sqrts so imagine you had to do it for like 30 sqrts or something (not sure about the actual number)
@sillyking1991 9 aylar önce
I mean, idk when trigonometry was invented, but since you can divide any polygon into some number of equal right triangles, that you know 1 of the angles for and the length of the hypotenuse...so maybe that way?
@prasoonjha6314 5 aylar önce
@@sillyking1991 Trigonometry is very old. It stretches back to thousands of years. Legend has it that Thales used the ratio of an object's height and it's shadow's length to measure the height of a pyramid (he was basically using tan). Though the earliest form of trigonometry was developed much later by Hipparchus. Trigonometry started looking like it's modern form during India's Golden Age when Aryabhata discovered the sine and versed sine functions (he probably had Hipparchus' works at his disposal but we cannot be sure). Following Aryabhata's lead, Muslim mathematicians discovered the other trigonometric functions and made trigonometry as we know it today during the Islamic Golden Age. At last, the notation to represent trig functions was given by Euler. So, you're probably right that he may have used Trigonometry.
@zrizzy6958 2 aylar önce
🎯 Key Takeaways for quick navigation: 00:00 🍕 Pi can be visualized by cutting pizza slices and calculating the area of a unit circle as Pi. 01:33 🧮 The ancient method to calculate Pi involved inscribing polygons in a circle and using their perimeters to estimate Pi's value. 02:57 📏 Archimedes improved Pi estimation by using polygons with more sides, getting closer to its actual value. 05:00 🤯 Isaac Newton introduced a revolutionary approach to calculating Pi using the binomial theorem, allowing for fractional powers and infinite series. 08:16 🔄 Newton extended the binomial theorem to negative, fractional, and non-integer values, unlocking new mathematical possibilities. 10:40 🪟 Pascal's triangle can be expanded with fractions, creating a continuum of numbers between known rows. 13:38 📐 Newton used his extended binomial theorem to derive an efficient method for calculating Pi by integrating a series from 0 to 1/2. 16:37 🏗️ Newton's approach revolutionized Pi calculation, making previous methods obsolete and showcasing the power of mathematical innovation. Made with HARPA AI
This was one of my childhood mathematical mysteries(that I have not searched for surprise); although pi is irrational how it is calculated.. that I have never come across in my mathematical journey until now. This is really convincing and thank you very much for the video helping me out to educate myself. The production quality, interesting use of graphical diagrams and the curiosity brought through out the video are pieces of art❤. Ps: wondering pi = integral of square root of (1-x^2) is so easy where newton also has come up with, and got convinced still sin inverse(1) is yet to be calculated LOL😅
@Peter_Siri 2 yıl önce
"He was quarantining at home due to an outbreak of bubonic plague." ...what a great time to do math
@Yoctopory 2 yıl önce
While we just watch Netflix..
And 23 years old. My age lol.
@ImBoredToo 2 yıl önce
@@EmmanuelVenturaSilva lol do not compare yourself to Newton. Almost nobody can compare to that much God-tier knowledge and accomplishment
@bestpseudonym1693 2 yıl önce
Thats what happens when you have literally nothing better to do
@@ImBoredToo Hahaha I know bro. Just saying... Lol
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. 💜
@DOSRetroGamer Aylar önce
Veritassium videos are always so well and clearly illustrated/animated, kudos!
@chidieberendukwu 9 aylar önce
Newton was like the final boss in a very difficult FPS game like Doom. I feel as soon as he decided to tackle pi, the Doom boss music started playing in the background.
@pronz72gh85 Yıl önce
It is interesting to note that in Italy, Pascal’s Triangle is called Tartaglia’s Triangle. Niccolò Fontana Tartaglia was a Venetian mathematician. In his General Trattato di Numeri et Misure (General Treatise on Number and Measure), published in 1556, there is an example of the Triangle, and Pascal was not even born at the time! I wonder how many mathematical ideas have been around for so much time, discovered, forgotten, rediscovered or even inspiring new math…
Ok showoff
@MuffinsAPlenty Yıl önce
Yeah, "Pascal's" triangle has come up in civilization after civilization after civilization over the last 2000 years or so. Why do we give credit to Pascal when others like Tartaglia, Yang Hui, Khayyam, and Pingala had the same thing earlier than Pascal?
@dhavalghone9398 Yıl önce
This video is inspirational. Seeing Prof. Kontorovich being amused by math and Newton's genius is amazing because it's amusing in itself that he is appreciating all that
@TheRomichou 2 yıl önce
The animator is the hidden hero here!
@veritasium 2 yıl önce
Truth - shout out to Ivàn!
@robb6560 2 yıl önce
@@veritasium thank you Ivàn!!!!
@thebrahmnicboy 2 yıl önce
Ivàn! We appreciate you!!
@enzoqueijao 2 yıl önce
Ivàn rules
@albertbancroft4507 2 yıl önce
Big up Ivàn!
I'm a year too late to comment. But the most fascinating part of this episode was not how newton made calculating pi easier. He made calculation in general more easier and efficient. And hence developed Calculus, a different branch of mathematics. A guy getting bored in a study room. That's pure fascination 🤯
@Haassan1 Yıl önce
This is absolutely interesting. But I also believe it is essential to develop an understanding of what is means to be a mathematician. Anyway, thank you Veritasium for sharing!
@user-yn9br1uo2q 5 aylar önce
Newton was one incredible man. It's incredible how many breakthroughs Newton was responsible for..
@adarshjadhav3238 4 aylar önce
Newton was way ahead of his time. The greatest genius ever to be born on Earth ❤
@sohamchandratre Aylar önce
I first watched this video like 2 years ago, when i was just starting my engineering. And i have returned to this video a few times because i found it fascinating. But now that I'm in my final year of my engineering diploma, i finally understand the actual math and theory behind it and it makes the video that much more amazing
@mrunfunny 2 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.
@maxschmidt8779 2 yıl önce
"Playing" Perfect. The Best comment here. Not to downplay Newton's genius... but intrinsic learning is a relevant phenomenon. We may be suffering from a from of slight, collective brain damage due to plastics, pesticides and what not, but the genius has not been extinct. I believe that we are just too distracted and demotivated to enjoy searching any more, hence the discrepancy in the willingly educated and the comfortably dumb who almost form the ending points of a spectrum that represents the human intellect. I refuse to believe we have devolved. I just think the dominant majority has long giving up on hope and the joy of discovery itself.
@mrunfunny 2 yıl önce
@@maxschmidt8779 True, makes me say one of the most cliche yet true statement, "Technology has made us more of a stupid than a genius". Majority of people are being motivated only to learn the most basic and inane skills and never grow beyond that. A PhD is rarely likely to earn significantly more than an undergraduate. People are busy learning most insignificant stuff and never allowing their curiosity to take over. Even the smartest people are focusing on wrong things. As Jeff Hammerbacher said, "The best minds of my generation are thinking about how to make people click ads". Although these things might seem to be very important in current state of world but on a larger scale, these never matter. Just think about the covid period and how it made us aware about the importance of scientists and doctors. However there are still people who care about such things and in true sense, they are the only one carrying the whole humanity on their shoulders.
@lelouch1722 2 yıl önce
Newton is not just "someone" ...
@DamirAsanov 2 yıl önce
@@lelouch1722 Was he "something"?
@maazali9604 2 yıl önce
John Citizen he never said nobody he just most people arent
@shrimpbisque Yıl önce
I don't think anybody has yet surpassed the sheer creative genius of Isaac Newton. Imagine being so damn clever that discovering gravity was one of your side projects.
@h0ly208 Yıl önce
It is incredible that Archimedes, over 2,000 years ago, figured out, in any practical sense, pi. Wow.
Lot of civilizations figured it out independentpy 1000's of years ago
@redshirtwookiee 6 aylar önce
This is CRAZY. I didn't realize binomial theorem was used to calculate pi so accurately. Newton was truly a genius. How many of his theorems have been tried and tested millions of times and have come out unscathed? Brilliant.
@user-ey6qd5pe1j 4 aylar önce
It's incredible how many breakthroughs Newton was responsible for.. Newton was one incredible man.
@jesser9134 Yıl önce
it's so hard to imagine being in all of their shoes, taking years to tinker with formulas and discovering unexpected consequences. I feel like hearing about these histories would make math derivations and comprehension much easier
@theknightikins9397 2 yıl önce
I love how mathematicians are almost always so happy to talk about math.
@blmppes9876 2 yıl önce
math is his wife
@lemondigit7309 2 yıl önce
i love to talk about math too even though im not a mathematician
@prajwalsarangi2601 2 yıl önce
@@lemondigit7309 same with me
@innosanto 2 yıl önce
Everybody does. Math is beautiful
@tsadkiel2008 2 yıl önce
@@lemondigit7309 I love talking about math, but main stream media told me it is racist. So I count my change silently.
@levromanov3019 2 aylar önce
This is a very exciting, entertaining and interesting video! Thank you so much for helping me find out more information about fields of science I’m interested in❤
@sm0kei38 Yıl önce
the fact that one man changed how the whole world percieves pi is honestly crazy.
@abdelazizkara2352 6 aylar önce
I can easily say, this video is one of the best mathematics video I've ever seen so far.
@nofvcksgiven 6 aylar önce
3b1b: indeed
@j0shmyg0sh90 Yıl önce
Question: What if you substitute complex numbers into binomial theorem, will you get the third rotation to pascal's triangle?
@ajeetsinghpatel6760 6 aylar önce
It will start expanding in horizontal axis , like positive and negative number expand up and down in vertical axis
@j0shmyg0sh90 6 aylar önce
@@ajeetsinghpatel6760 interesting
This is the most exciting video I have ever watched. It’s like taking all the math I ever learned and putting it into one video. Wish someone had shown me this in 1st grade, so I could have understood the roadmap before me.
@andrewzmorris 2 yıl önce
"Luckily he had just invented calculus" unbelievable
@paxpacis2 2 yıl önce
Right? "speed running maths" is complete understatement. Newton is the equivalent of dropping an atomic bomb on cavemen
@andyc9902 2 yıl önce
You will never find The fun and love in maths. If you don't, "Seek"
Welcome to real numbers in Math
@BlastinRope 2 yıl önce
@paxpacis2 2 yıl önce
@@BlastinRope No, invented
@moistnans1598 Yıl önce
Never thought maths was that interesting until now, amazing. Really enjoyed this and learnt a hell of a lot, have to rewatch this soon
@g-9222 2 aylar önce
Sir Isaac Newton was so brilliant and influenced science so much that he was second only to Sir Winston Churchill as THE Greatest Britton to have ever lived. Imagine his Genius and what he could have achieved if he had of been around in the days of Einstein or Hawking. Imagine those three working together, would have been the ultimate think tank.
@geoffreywilliams9324 4 aylar önce
In the past I was always frustrated as I could not calculate pi. Then about 10 years ago I found this solution for myself. I was so pleased with myself, all that was necessary was the knowledge of Pythagoras and the ability to calculate square roots . .
Love all your stuff. Especially liked your electricity video. However; I would like to request you do a video that explains how power generation actually works in a grid. You see I can't get past the capacity of power needed issue. To me, if you simply think of AC power as electrons moving back and forth (which I now know is wrong) or fields moving outside a wire, then it would seem as long as you have a closed circuit everything should be powered and then the "amount" of power should be infinite - after all we are just oscillating electrons right or fields. Shouldn't we be able oscillate as many as we like. How does capacity figure into the equation.
@anshbeast5934 Yıl önce
The sheer way humans can do soooooo much with just 10 digits discovered from their fingers is extremely fascinating
@decidiousrex Yıl önce
It's unfortunate actually that we have 10 digits and thus created a base 10 system of numerals. If we had instead created, or maybe I should really say normalized, a base 12 system, mathematics as a whole would be far simpler and easier. Base 10 is not really a very good system but because we have 10 fingers it's become the prevailing one.
@lusv4316 Yıl önce
@@decidiousrex base pic would be ideal!
@decidiousrex Yıl önce
@@lusv4316 The only time base pi is ever useful is with circles, and in the very few cases base pi is ever useful it is generally used. For everyday purposes base pi would be absolutely horrendous, and would literally and should literally never be used.
@varshvarsh9486 Yıl önce
@@decidiousrex Not every civilization did that tho. Some counted the space between the fingers and thumb, and measured from a base 8. But ya, base 10 is what we generally use
List of important things Newton has done: - Revolutionizing Optics - Inventing Calculus (Differential / Integral) - Discovering Gravity - Inventing the 3 most important Axioms for Mechanical Physics (f.e. Inertia) - Finding a better way to calculate pi - Generalizing the Binomial theorem - Discovering that light are particles - Contributing to the philosophy of metaphysics and politics
@vikasb8682 Yıl önce
The sheer intelligence behind the simplest and obvious way of solving problems by Newton is simply astonishing...
@tedpop 3 aylar önce
I have degrees in mathematics, and have never seen anybody explain concepts as well as this channel.
@davitti7036 Yıl önce
This has to be the first case of time complexity in action. Algorithm improvement made it possible to do something that took someone 25years to complete to barely day. Newton invented time complexity from literally playing in quarantine.
@AC-bi3bz Yıl önce
Great video to watch … learned something new (everyday’s a school day). I always find it humbling, when I see videos like this, hearing about people / geniuses that were able to discover these things and devise theorems … all without computers, search engines etc.
@boysenbeary 2 yıl önce
This Newton guy seems pretty smart. He should become a mathematician
@googiegress7459 2 yıl önce
IKR instead he wasted his life developing fig-filled cookie cakes
@vasutiwari4187 2 yıl önce
And a physician too
@alrick3000 2 yıl önce
Maybe he should write laws.
@shiveshtuli7608 2 yıl önce
He invented calculus what more math u want from Isaac Newton
@jakethewolfie119 2 yıl önce
Sad he only discovered how light works.
@joshc5613 6 aylar önce
Everyone is talking about how genius Newton is, but really, we need to shout out Archimedes for solving pi to an almost unnecessary level of precision 1800 years before Newton even came along
@rahulzingade99 Yıl önce
Am I the only one who was blown away 1.5 mins into the video just getting to understand the value of Pi, finally?
@kaimarmalade9660 9 aylar önce
Learning, "big boy" math for University and I cannot express how helpful this was. It was like, "omg I get it. I actually get it." Thank you so much.
@daboos8 10 aylar önce
Newton seemed to look for ways of automating mathematical functions. Not sure If I used the right terms there, but he was looking for a tool of getting results faster. And that Pascal’s triangle was perfect for the job.
@jeremenichelli Yıl önce
I've watched this for the fourth time today. What a delight. Thanks for making this!
@themurderofcoke 2 yıl önce
This mans gave me a better understanding of Pi in 2 minutes than 5 years of school
@vexxed8582 2 yıl önce
I wish this story was shown to me in ap calc
Yeah.... Only a true seeker can have the power of pure teaching.. 💟
@sampanna6983 2 yıl önce
haha school bad, funny
@thedirector6297 2 yıl önce
@@sampanna6983 but it's true tho
@PatrickPease 4 aylar önce
It's funny that moving from the 12-gon to the 96-gon is effectively the same as finding the area under a curve using smaller and smaller divisions until you eventually come up with... Integration
Excellent video. But I think there is a mistake when you integrate right at 14:18. The third term must be x to the 5th after the integral, not x to the 4th. Fortunately the mistake was corrected at 15:49
@pravinshingadia7337 4 aylar önce
I studied maths as Uni but never had access to material like this. These videos explain complex ideas in a few minutes that took me weeks of reading in text books to understand.
@Tommy_007 4 aylar önce
If you studied math at university, it should be clear to you that many mathematical details were left out in the video. These details take time to learn - and teach.
@Ggdivhjkjl 6 aylar önce
Pity there's never been any reason to quarantine in our days so someone could discover something like this.
@samimed23 2 aylar önce
Why math isn't taught this way 😢 This was just beautiful 👏
@shubh_1999 2 yıl önce
If maths was taught like this, I would've understood pretty much everything and not develop a phobia towards it.
@PatrickStewarts 2 yıl önce
OMG yes. I struggled for years in school at math (especially algebra) but aced astronomy, baby physics, and statistics course I took. All because of horrible teachers.
@GdotWdot 2 yıl önce
Seriously, I've been watching maths TRvidrs for half a decade now; coincidentally I first started getting those recommendations pretty much the very moment I had finished my formal education. They make all these semesters spent in class, doing pointless computation for no good reason and little gain seem like such a horrendous waste of time.
@tomf3150 2 yıl önce
If only thermodynamic was taugh via statistical physic...
@LongItAll 2 yıl önce
Had a bad algebra teacher in 8th grade that scared me away from any and all math for almost 20 years. Only realized in the past 8 months that I could actually learn it, been doing a bit on Khan Academy almost everyday since then. I love physics and math now again finally and I'm learning more and more everyday, 'tis a wonderful feeling.
@MJ-uk6lu 2 yıl önce
@@test-zg4hv That ain't true. Education got worse. It's likely because people assume that tech is to replace thinking, but tech is only good to extend your own computational power and memorization power. You still have to do thinking. Also culture. Culture worldwide hardly cares about being smart. Most people care more about money and do the simplest things to get it. There's not much point for person nowadays to to do something not for money as many things are already done and way better than one could possibly do. During Newton's era there was no internet, hardly anybody who wanted your money (ads, I mean) and very low amount of distractions. Also culture was different, where human intellect was valued way more and money was less influential on everyday life, especially if you were aristocrat.
@famhwolf5184 Yıl önce
Thank you for filling in so many gaps in my math education. Starting with, why pi*r*r? And, where did all those infinite series they taught us come from? And about the non-whole number extensions to the binomial theorem. And how did people calculate pi, both before and after Newton? And how did square roots get calculated? Sharing this video, for sure.
@ekamsat429 Yıl önce
A good opportunity to remember the work of Mādhava of Sangamagrāma (1340-1425) of the Kerala school of astronomy and mathematics in India. One of the greatest mathematician-astronomers of the Middle Ages, Madhava made pioneering contributions in calculus which included infinite series of trigonometric functions (centuries before any European, e.g., Gregory, Leibniz or Newton). In particular, this famously allowed precise and efficient computation of pi (now known as Madhava-Leibniz series). Madhava was remarkable in also providing correction terms of his infinite series formulations. To know more, his wiki page is a good place to start.
@omers3117 2 aylar önce
not everything in this video is easy to understand but that's what makes inventing new stuff beautifully hard. not everything is easy discovering new pathways to places that always seemed off bound and doing it faster better and more efficient has always led to success
@tornadodex1366 Yıl önce
"This is a story about how the obvious way of doing things is not always the best way" In the wise words of CGP Grey, "Solutions that are the first thing you think of and look sensible and are easy to implement are often terrible, ineffective solutions that, once implemented, will cause mass suffering"
@user-rm2qj2jh4l 4 aylar önce
This is such a great video!! I'm confused though, when you substitute in x = -x^2 and n = 1/2 to (1+x)^n, shouldn't the fourth term be +1/16(x^6) instead of -1/16(x^6)? (0.5)(-0.5)(-1.5) = (-0.25)(-1.5) = +3/8 and (+3/8)/3! = +1/16, and (-x^2)^3 = (x^2)^3 = x^6. Where does the minus sign come from?
@samugolxiii3963 2 yıl önce
I am a mathematician. I have masters in applied statistics, data analysis and all that jazz. I remember when I took the exam from this topic and I learned it. The way it was explained in the book made little sense to me, I always wondered how did anyone come up with it? It was so unintuitive and weird.... I have not seen that theory for years now and yet everything makes sense immediately. I think this is how it needs to be taught at school... well done.
@jasonlandry8685 2 yıl önce
I failed calculus because it was explained so poorly in class. This video would have helped me ace the class.
@timq6224 2 yıl önce
@@jasonlandry8685 -- I didn't learn why calc worked until a vid like this came along -- 20 years later.
@RudyBleeker 2 yıl önce
@@timq6224 Oh boy, the nightmares of highschool calculus. I hope my kids will be taught it differently, because I still believe math is important, even though I was thoroughly turned off of it in school.
@victorzoni4588 2 yıl önce
Yeah this video had that 3blue1brown energy
@latebloomer2 2 yıl önce
I wish something like this exist 23 years ago, so I don't have to repeat calculus class 3 times, just to get C-🤣
@obsolesced Yıl önce
Can't help wondering why stop at integrating up to just 1/2? Since the pi estimate becomes more accurate the smaller the upper integration limit, why not just keep decreasing that? I'm also wondering if one writes the pi estimate as a function of that integration limit, then only retains a few terms in the infinite series, will pi be the limit of that truncated series as the integration limit approaches zero? Would this be another possibly faster way to get better pi estimates?
There is also another way to show the proof of the area of a circle. Simply take a many triangles with a height of dx and a length of r. The area of that triangle it 1/2rdx. Put that into a intergal from 2 pi r to 0. Simplify to get the area of circle.
@googlemustdie Yıl önce
Man you have such a great way of explaining things...lots of hard work there.
@SilverAlex92 7 aylar önce
Wow the guy who spent 25 years of his entire life to calculate pi to 35 decimals was hardcore.
@Lightn0x 7 aylar önce
Before everything we used to calculate pi by running a rope around a big circle, then running a rope through the middle of it and dividing the lengths of the ropes. To get more decimals we just needed to make a bigger circle. True story!
@saddlepiggy 2 yıl önce
“Luckily, Newton had just invented Calculus.” Bruh chill out Newton leave some discoveries for the rest of us.
@gigachad6162 2 yıl önce
newton was a massive con artist
@mdv9831 2 yıl önce
Yeah. Newton was a little too smart. The man did enough stuff to help modern physics 100s of years later
@jhonjacson798 2 yıl önce
Tbf if newton never lived we still would have had calculus, Leibniz has got you covered
@ASLUHLUHCE 2 yıl önce
@@akashverma8656 Leibnitz fanboy
@mdv9831 2 yıl önce
@@jhonjacson798 true. But a lot of other things would've gone undiscovered. The man discovered too many things to count. Also, calculus was discovered earlier in India.
The obvious way of doing things is not always the best way and that it's often a good idea to play around with patterns and push them beyond the bounds where you expect them to work Because a little bit of insight and mathematics can go a very long way - Veritasium -
@rjayde4832 Yıl önce
Being a mathematician in Newton's time must have been crazy when he just turned a difficult process into a simple one. Tho I don't understand the math here, it's clearly much easier than the polygon thing.
@nasalnex 5 aylar önce
I keep watching this video again and again. It's just majestic and I want to incorporate this in my mind.
@josh7035 8 aylar önce
I love the professor he always has a permanent smile on his face.
@daftfaz3a641 5 aylar önce
just imagine where we would be if Newton was alive today. He was so smart and ahead of the game 400 years ago we would be so advanced if he knew what we knew.
@priyam6078 2 yıl önce
If math in schools was taught like this, dearth of STEM candidates in the western world would drop within a decade! Loved it 😊
@AnuragYadav-mr2xv 2 yıl önce
Which class you are
This is because you are an Education Science expert? Or simply because you're unique experience must apply to everyone?
@vilmospalik1480 2 yıl önce
i have never heard the word dearth before in my live
@Dan_Kanerva 2 yıl önce
@@juggiebonebrain3383 based on the overwhelming majority of comments that these type of videos always get... i am gonna go and say because his experience is not so "unique" and it does apply (if not to everyone) to most 😊
@thedofflin 2 yıl önce
To be honest my university physics course had a lot of math stuff taught like this, minus the animations that probably took someone a couple weeks to put together. The historical developments in mathematics are quite important.
Awesome video. Wish I could have seen those patterns drawn in that way when I was a grad student. Math is magical and magic! Thanks for showing it to the world!! I think I've spotted a math mistake, though. At 14:17, when solving the integer, xE4/4 should have gone to xE5/5 and xE9/8 should be xE9/9, shouldn't it? Was that a typo or did I lose something?
At 14:23 it calculates 8x4 and equals 40... so I guess that should have been a 5...
@epicterry6706 Yıl önce
Man just explained the area of a circle formula in 10 seconds better than all of school
@sivakrishnat5471 5 aylar önce
This video should be given as an assignment to all school children. It has blown my mind.
@AdrianCHOY 3 aylar önce
Newton is ridiculously ahead of his time in his time
@patrickfiorito 3 aylar önce
I feel like this guy is the type of math teacher I needed as a kid. I'd ask my math teacher these questions and they would basically tell me to shut up. 😂😂😂😂 . And the way my brain works. I think this made math an ugly subject for me. They keep telling me it works this way and couldn't even begin to explain why. . This would have made a huge difference for me, I think.
The fact that a person actually managed to figure something out like this is amazing. Our brains are actually insane
@System3200 2 yıl önce
@Sonathan1893 2 yıl önce
@@System3200 Sadly you can't expect that from him, if people would notice at which point you're actually smart (and stop generalizing), we would have a lot less problems.
@System3200 2 yıl önce
@@Sonathan1893 I dont get it (which proves my point)
@leonrothier6638 2 yıl önce
@@Sonathan1893 And then I kiss you
@leonrothier6638 2 yıl önce
@@Sonathan1893 😘
@Postntalkmemes Yıl önce
This was immensely enjoyable, Thank you, we need more.
I just love the way the professor is excited talking about this. Maths is really Fun!
@InservioLetum 6 aylar önce
Congrats on your pronunciation of the Dutchman's name, that was not actually even that far off! For a yank that is a VERY impressive achievement!
@Physics369lover Yıl önce
Sir your explanation was really amazing about pi. Maths is just made of some hidden secrets also so netwon did that. Iam a 11th class student and i love doing maths.