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# The Discovery That Transformed Pi

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- Dipublikasikan tanggal 15 Mar 2021
- 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...)

References:

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

Kimi9511 bulan yang lalu^{+12020}Imagine having a career so illustrious that discovering a groundbreaking way to accurrately find pi is just one of your side achievements

Nezuko Chan23 hari yang lalu@Yuki because it is more scientifically accurate?

Yuki23 hari yang lalu^{+1}@Nezuko Chan why tf are we talking about Star Wars now lmfao

33 Sosa24 hari yang lalu@Greyngreyer its an occultic anecdote. He is the ultimate G in Alchemy. People don't give him credit for that but this man had severe mercury poisoning

pro2go24 hari yang laluU know i wud say that it is his main achievement cuz einsteins theory of gravity wich is a part of the thoery of relativity wich is an improved version of another one of his theories by combining it with newtons gravity theory might be wrong. Dark matter 8s said to exist cuz galaxies and large bodies shudnt have enough matter to generate the gravity to stay attracted so the dark matter theory was made. But ot cud also mean that our laws of physics are incorrect. If so then the relativity theory partially based of of newtons theory is wrong thus meaning this cud be his greatest discovery but only if the gravity theory is wrong ofc

BendikBulan Yang lalu@cdjhyoung Imagine being a grandparent and still fighting someone in a youtube comment section over whether or not you're a virgin, lmao. How have you managed to stay alive so long?

Marko Apatović5 bulan yang lalu^{+632}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.

Harsh Kumar3 hari yang lalu@Leo Franklin Let me try this in C Lang😄

Deal HunterBulan Yang laluNewton > Einstein?

Marko ApatovićBulan Yang lalu@Ameer Abdallah I used BigDecimal, I already addressed that in an earlier reply.

Edit: Unless you're talking about when I implemented Hugh Leyton's algorithm, there I used double knowing it will not work past some precision, but even if using BigDecimal it is kind of flawed to multiply really big numbers and really small numbers to get your terms.

Ameer AbdallahBulan Yang laluif you used something like a double or float for the variable instead of using BigDecimal, your program will not be able to compute pi to a precision you want because of floating point imprecisions. If you used something like BigDecimal though, then you are fine

Marko Apatović2 bulan yang lalu^{+1}@Hugh Leyton So, I implemented your algorithm as well and got 14 correct decimal places in only 29 iterations which is pretty cool. Especially considering how simple it is. But then the terms A and B quickly degraded to 0 since a double variable could not represent them anymore and the algorithm terminated. The flaw is that N quickly explodes to huge numbers and A and B quickly degrade to really small ones, so it's hard to represent them accurately in a computer. What is this algorithm based on?

John Chessant2 bulan yang lalu^{+81}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 #DislikeRebellionBulan Yang lalu^{+3}math basically HAS to have many inner patterns, as math is, in a sense, the study of patterns.

Sunny Jayaram2 bulan yang lalu^{+44}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.

Jerry Ade7 hari yang laluReal talk. Illustrations like these go a long way for students. Good luck

Apple Sauce4 bulan yang lalu^{+27}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.

atellTahun Yang lalu^{+2613}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.

Osama Spin Ladin6 hari yang laluI remember in school wished he never lived and that apple that fall on his head was a big rock instead (idk if it really happened, I mean the apple on the head). But now after watching this video I can fully understand and appreciate what this amazing human did for us

mike dauglashBulan Yang lalunewton is father of physic & mathematics, just like einstin could think the unthinkable, and so do newton, but with ZERO basic in these old era.

David SpencerBulan Yang laluI can't believe I read through that tedious equivalent of Blur vs Oasis.

Neonhueman • 24 yearsBulan Yang laluYes

Anurag GuptaBulan Yang laluEvery person was. Andrew Wiles, Gauss, Euler, Ramanujan etc. and everyone else were equal rivals to him

j4 bulan yang lalu^{+33}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🔥

Mary ThielBulan Yang lalu^{+13}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!!

Jack RPBulan Yang lalu^{+9}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

AnonymousBulan Yang laluThat'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.

Unknown Variable5 bulan yang lalu^{+18}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.

Maps4 bulan yang laluIndians created pi

David JohnTahun Yang lalu^{+5337}Newton giving a lecture - "Hi guys, today we're talking about circles. The first thing you wanna do is invent calculus."

Joseph C.Bulan Yang laluI invented calculus myself!

Stephen WidgerBulan Yang laluNewton was such an introvert and hated people so bad, someone had to persuade him to publish Principia lol

Hugh Leyton2 bulan yang laluMy formular is much simpler.. . The most complicated part is working our Square Roots :

Calculating Pi Program by Hugh Leyton

Formula : Pi = P + Nn * An * Bn for "n" from 2 to infinity

10 PRINT “Calculating Pi” rem Program Title

20 P=0 : N=1 : A=1 : B=1 rem Initial Values

30 O=P : N=N*2 rem Start Loop

40 P=P+N*A*B rem Main Calculation

50 C=(A*A+B*B)/4 : A=SQR(C) rem Next value for An

60 B=1-SQR(1-C) rem Next value for Bn

70 IF P>O THEN GOTO 30 rem Go to next Loop

80 PRINT “ Pi = “ ; P rem Print Answer

Just a random guy8 bulan yang laludiscover

Hugh Leyton8 bulan yang lalu@The lost Tomato Not easy to put it into a text only reply, but lets try : = Sum of 2^n * An * Bn ( those funny boxes simply mean Sum between 1 to infinity. ) I divide the Circle, of any radius, but easiest with a radius of 1 into 4 Triangles. . . So these 1st triangles have sides of 1, so A1 = 1, and B1 = 1. . . . n is just a number from 1 to infinity..

So the first line would be P = 2^1 * 1 * 1 . . . The remaining 4 curved segments then each divided into two more right angled triangles with sides A2 & B2. . . . And so you continue just dividing each remaining segment int ever smaller triangles, doubling the number each time. . . . . .

Then the 2nd line would be P = P + 2^2 * A2 * B2.. . And so the 3rd Iteration would be P = P + 2^3 * A3 * B3.. . . You see how it goes. ? . . . Very simple. . . .. . But since A1 = 1 and B1 = 1, then you have to work out what A2, A3, A4 etc and B2, B3, B4 etc will be. . . . . So I found a way that just slots into a simple Iteration to do that. . . That is what I consider the clever part. . . . A2 = Sq.Rt ( ( A1^2 + B1^2 ) / 4 ) just repeat this for A3, A4 etc. And B2 = 1 - Sq.Rt ( 1 - A2^2 ). . . So you see this is actually very simple, working out Sq.Rt's is the hardest part.

This formula is absolute for Pi, limited only by the accuracy of the computer you can use to do the calculations. . . . You can put these simple formula into a Spreadsheet, or you can put them into a BASIC program.

Basic Program ( n calculated slightly differently, easier for the computer)

10 PRINT “Calculating Pi” rem Program Title

20 P=0 : A=1 : B=1 : N=1 rem Initial Values

30 O=P : N=N*2 rem Start Loop

40 P=P+N*A*B rem Main Calculation

50 IF P=O THEN GOTO 80 rem Final Answer

60 C=(A*A+B*B)/4 : A=AQR(C) rem Next value for An

70 B=1-SQR(1-C) : GOTO 30 rem Next value for Bn

80 PRINT “ Pi = “ ; P rem Print Answer

Al van der Laan2 bulan yang lalu^{+5}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.

Attila Bertok5 bulan yang lalu^{+5}Great video! I've really enjoyed it, but I think it would be very important to mention the radius of convergence for x (=1) because of course the binomial formula stops working for just any number. And... I mean the following comment in a funny way, but I would like to see you doing the integration using Newton's original method with fluxions. That would be a much longer video. It is a bit ironic that for the integral you have used the notation given to us by Leibniz' which is much clearer than the fluxions stuff. Still great work though.

Vaishnavee verma27 hari yang lalu^{+1}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. 💜

Davitti4 bulan yang lalu^{+15}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.

TheRomichouTahun Yang lalu^{+23347}The animator is the hidden hero here!

Michael Rosen17 hari yang laluIvan

The hero we don't deserve

But the hero we need.

Jammiputh19 hari yang laluagree

Meyu20 hari yang laluAll hail Ivàn!

Zahid22 hari yang laluমহিলা ব

HiBulan Yang lalu@HK no

Steverson25 hari yang lalu^{+3}Question:

What if you substitute complex numbers into binomial theorem, will you get the third rotation to pascal's triangle?

Haassan1Bulan Yang lalu^{+1}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!

Dave Jung6 bulan yang lalu^{+2}Learning calc 2 right now and these series expansions are so fascinating. It's refreshing to relate my learning to something tangible like pi.

Fam HwolfBulan Yang lalu^{+1}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.

VeritasiumTahun Yang lalu^{+8306}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

madhav seth10 hari yang laluThanks

Jram the ManBulan Yang lalusHoUtOuT tO sOmE rAnDoM mAtHmAtEtIaN fRoM tHe 14Th CeNtUrY

Krushnadeep SonuBulan Yang laluIt's our pleasure 🙂 Thank you

Ankush KumarBulan Yang lalu@Shripad Krishna so true

Pierce Horton4 bulan yang laluWhat about an equation that took a limited of x as the number of sides on the Pentagons approached infinity?

Moist Nans4 bulan yang laluNever thought maths was that interesting until now, amazing. Really enjoyed this and learnt a hell of a lot, have to rewatch this soon

Stephen SchumacherBulan Yang lalu^{+1}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.

Random Human6 bulan yang lalu^{+3}Breathtaking really. Hiding in plain sight for the right set of eyes. This sort of genius gives hope for mankind.

Advaith BhasiBulan Yang lalu^{+1}Can we all take a step back and imagine just how much of a genius Newton was.

Mohit SinghTahun Yang lalu^{+2506}Imagine working on something for 25 years only to find out that someone did it while playing with an equation during a pandemic.

XonXBulan Yang laluI'd like to know how he calculate polygon with 2^62 sides. Even with a calculator I would have trouble doing this task. Just writing down the intermediate results and not making a mistake is almost impossible.

Anon Emouse4 bulan yang lalu@Footy Tube euler says lol

Matt Z5 bulan yang laluYes and now during covid all we’ve figured out is that masks are useless and transgenderism is a thing.

Max schmidt6 bulan yang lalu^{+1}@Nadarith I totally agree. Although I still consider most of my arguments from back then to be valid, today I feel like I was simply pessimistic. Based on this attitude and my statements, I could almost be accused of disregarding the modern scientific community. It was arguably a narrow-minded look at a world that frustrates me and wasn't entirely fair.

Nadarith6 bulan yang lalu^{+1}@Max schmidt There less people that specialize in more than one field because the fields have grown to such enormous proportion that even a part of it requires a lifetime of study to fully grasp

nowadays any serious paper or discovery involves a team and commonly a supercomputer, with volumes of data that a single person would never be able to process, the easy discoveries have also largely ran out

all the problems you mentioned only affect a portion of humanity, even with them there are much more people on the level of newton in science today than there were centuries before, and newton himself was the type that would be regarded as a pseudoscience fanatic shill in our times

humanity didn't 'stagnate', the current problems simply moved beyond what any single mind, unaided, could possibly tackle, any newton today would just be a part of the team showing once or twice before another newton shows up as one of many names in another paper next year

ro35 bulan yang lalu^{+1}This is very interesting. I was fascinated on how creative Newton linked one thing to another thing that seemed to be unrelated, found a new pattern, found the bigger picture which finally led to a groundbreaking way of doing things. Amazing.

Janan Patel5 bulan yang laluIt's crazy to me that people were really this smart and we just take it for granted these days. Like for myself, I hate calculus, but without it, we would still be missing a lot the technology that we have now days. It's just crazy how a simple Pascal Triangle turned into a formula from integration, which allows you to calculate pi. Just how do people think of these things, WOW

sigil triple seven5 bulan yang laluI have to admit, the way you use the pizza to show what pi is, it’s brilliant. Seriously the best way I’ve ever seen pi explained, so easy to see and understand. Pi should always be taught this way.

Nour Art4 bulan yang lalu^{+5}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.

Just Some Guy without a MustacheTahun Yang lalu^{+9321}"You can say he speedran pi"

So Newton invented speedrunning as well

Lemmi Galgalo3 bulan yang laluBruh Im late 😅

Sven leun4 bulan yang laluthe romans did in the catagory building

Insert Name Here4 bulan yang laluI know everytime I look in the comments, I'll see the damn mustache man.

3.14PI4 bulan yang laluspeedran me

Pedro Paulo Wanderley Júnior4 bulan yang laluSπdrun

Gil Galin5 bulan yang lalu^{+10}if only your explanations would be shown during my schoole years - that would definitely not only produce fascination by the Maths itself but maybe even next level geniuses.

Keep it up, words cannot expess my gratitude for all your work!!!

Best regards, applied maths grad...

Shrimp Bisque4 bulan yang laluI 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.

Andreas CocqBulan Yang laluGreat 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.

Ozquonk6 bulan yang laluThis shows what real genius is, and so powerfully depicted. Young Newton appears to be just enjoying exploring mathematics and then comes up with this. He should have received a lifetime supply of pizzas had they existed in his lifetime! And whatever revolution Einstein heralded, the extraordinary intelligence of Newton cannot be obscured. Both are radiant beacons of intelligence for us to marvel at.

Benjamin MathewTahun Yang lalu^{+2375}1666: Newton, during quarantine, discovering pi

2020: Me, during quarantine, eating pie

Mrutyunjay Mallik 9th C2 bulan yang lalu@INDIAN As for Gravity, people even before Newton knew that things always fall to ground. Well, that was known to everybody. And that was what Indians also knew about gravity. They never knew about it's law, it's application along with calculus and most importantvof all with their concept of gravity they couldn't do anything except saying everything falls to ground.

Mrutyunjay Mallik 9th C2 bulan yang lalu@INDIAN The laws of motion and the concept of gravity was known to even people before Newton. What Newton did, was to totally mathematically formulate those laws, give their correct and entire definition, and show how these laws could account for various things.

Joel Juarez2 bulan yang laluThere's a prodigy in each century

Oahu Hawaii6 bulan yang laluNo, Newton didn't discover pi. It was known for thousands of years. He came up with an efficient way of computing it to many decimal places, reducing what took decades to compute down to a matter of days.

Aryan Sinha10 bulan yang lalu^{+5}@heavenlysf As an indian, we do not claim those toxic people

DaCash5 bulan yang lalu^{+7}I really struggled in calculation (geometry was a breeze but algebra and I had our moments) and then calculus was a weird beast. I always seemed to get the concept clearly and fast enough, could even look at my answer and know if it was right, but the calculation was always painful. So later, when I taught math (as a science teacher), I was so excited to discover manipulatives for teaching binomials (essentially legos to make squares). I thought: why did no one show this to me when I was learning? I feel the same way about your pizza example. The first bit I knew and shared (by diagram) but the second part where you made a rectangle of the slices! Thank you! I no longer teach, but that would have been a beautiful insight. I'm sure I'll use it (and other bits of your video as well) helping someone someday, even if I no longer do it professionally.

Dan M5 bulan yang lalu^{+3}Back in the nineties, circumstances brought a 13 yr old, life-long Chinese citizen to my 7th grade algebra class within a week. Without knowing more than a handful of cursory English words, she understood every concept that I taught the class. More proof that math transcends language and cultures.

GameJBulan Yang lalu^{+3}If our teachers understood maths this way, many students would find in interesting.

Postntalk InfoBulan Yang laluThis was immensely enjoyable, Thank you, we need more.

AJTahun Yang lalu^{+3124}"Luckily he had just invented calculus" unbelievable

Nadarith6 bulan yang lalu@Stevves Even the natural numbers are a construct, an invented extension of fundamental logic of our reality

the universe by itself works purely in unary, there is one stick, then one stick, then one stick, every stick and stone and atom is inherently singular, only by comparing it with others and abstracting them up into a generalised concept of 'quantity' can you say it's three sticks, so really even numbers are an artificial creation

universe doesn't use numbers or equations or quantities, it uses fundamental logic and rules and emergent properties that simply are

Stevves6 bulan yang lalu@Nadarith I mean sure, but its foundations are on things that we intuitively know from our experiences (physical) like the natural numbers are what we count discrete objects with and the real numbers for continuous motion and math built on these rukes

Nadarith6 bulan yang lalu@Stevves What you're talking about is the logic our reality runs on, not math

math is an abstract construct based on it, it's a tool, especially the more advanced it becomes the less to do it has with anything physical

Archives of Fantasy6 bulan yang lalu^{+1}@B.B let’s not forget Leibniz absolutely true. but let’s not forget his quote about Newton either: “Taking mathematics from the beginning of the world to the time when Newton lived, what he had done was much the better half.”

Also look up the story of Newton lion claw it is astonishing.

ZahiTahun Yang lalu^{+1}@Gabriel Silva they all are showing the associative law which is approx equally difficult.

Just do 17×13

Or 17×10+17×3

170+51

221

King Bradley2 bulan yang laluIt's amazing just how much of Newton's work becomes superior as technology improves. He laid basis for numerical methods that have become the backbone of computer calculation. Another famous example is the Newton Raphson method.

Like the polygon method would also improve with technology. However, applying the same tech to Newton's method yields so much more precise values of pi

MuffinsAPlentyBulan Yang lalu^{+1}This is the *real* reason that we credit calculus as being developed in the 17th century. The fundamental core ideas had existed in civilizations for millennia beforehand. But the work of Isaac Barrow, Isaac Newton, and Gottfried Leibniz gave us an easy way to *calculate* with those fundamental core ideas. And that made all the difference.

Shoba DasariBulan Yang lalu^{+1}Could you do a session on difference in the thought processes of the western world vis a vis that of an Indian or Chinese or Japanese with respect to medicine, arthimetic and calculus, or even astronomy. For example: There are a lot of factual differences in textbooks written for western world and those written by russian authors in many areas of science.

Jesse RBulan Yang lalu^{+3}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

Sm0keiBulan Yang laluthe fact that one man changed how the whole world percieves pi is honestly crazy.

themurderofcokeTahun Yang lalu^{+2563}This mans gave me a better understanding of Pi in 2 minutes than 5 years of school

Sampanna11 bulan yang lalu@Daniel Read thank you

Daniel Read11 bulan yang lalu@Sampanna This is a really good point.

Distendedmist5811 bulan yang lalu^{+1}you can say that veritasium speedran teaching pi

Be Prepared For What’s ComingTahun Yang lalu5 years? How old are you?

Kartikay KaulTahun Yang laluI don't buy this statement

Rodrigo ValenteBulan Yang laluAwesome 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?

Rodrigo ValenteBulan Yang laluAt 14:23 it calculates 8x4 and equals 40... so I guess that should have been a 5...

Jesús Ortiz Merodio4 bulan yang laluExcellent 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

Hemu G5 bulan yang laluWow...If I had come across your channel in my engineering days.... I would have enjoyed life and lessons a lot more! Beautifully explained 👏

Nothing Special5 bulan yang lalui am getting that access and feel so good after each of his videos

googlemustdieBulan Yang laluMan you have such a great way of explaining things...lots of hard work there.

Jai ShriRamTahun Yang lalu^{+2019}Newton schooled himself on Brilliant during the bubonic plague quarantine

XonXBulan Yang laluHow come people seems to get dumber with the COVID quarantine?

Nali TikvaBulan Yang lalu@Robert Mitchell Was she really called Karen?

Edit: Just did a quick google search, at least according to Wikipedia his mother had another name, and the Wikipedia page doesn't seem to use the word "flat".

Got a source?

J C2 bulan yang lalu@Smeet Patil which you are now a part of....

Thanga games and music2 bulan yang laluOh bhai

Robert Fan3 bulan yang lalu^{+1}@StereohearT. that's how you know you made it. Even when you're dead people don't say "Newton was" they say "Newton is". Legends never die.

Ekam SatBulan Yang laluA 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.

rJAYdeBulan Yang laluBeing 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.

passenger90005 bulan yang lalu^{+1}Everything looked really amazing and from nowhere calculus entered and broke understandability of the episode.

Ayomikun OsunseyiBulan Yang laluI just love the way the professor is excited talking about this. Maths is really Fun!

Peter SiriTahun Yang lalu^{+3111}"He was quarantining at home due to an outbreak of bubonic plague."

...what a great time to do math

Nadarith6 bulan yang lalu@Jason Arthurs There's thousands, but we ran out of easy discoveries and get so much works and papers yearly that a single person doesn't exactly stand out anymore, it's all slow and steady and done in teams and collaborations

Nadarith6 bulan yang lalu^{+2}@Izzy Aisa lol do not compare god to someone that actually existed

Nadarith6 bulan yang lalu@Unsubtle Major Dictator Language is constantly changing and you just noticed, nothing more

Anonymous7 bulan yang lalu@Tycho Photiou What were you on bruh

Understand The Universe9 bulan yang lalu@Nobody Knows i know

Austin Harding5 bulan yang laluman, taking me back to my college calculus classes, integration is not easy. Another thing cool about Pascals triangle is it can be used to describe the geometry of higher dimensions

Megha SinghBulan Yang lalu^{+1}I was just like woww, it makes sense, it existed in a different light.. you assume and then prove it. It's wild how much creativity and imagination you need in maths, to find unthinkable patterns. WOW

Cameron Smith2 bulan yang laluI love your videos but this one was even more impressive to me. Thanks

Tomkat5 bulan yang laluI haven't counted exactly, but I believe I had watched this video 4 or 5 times now over the last year or so... it is fascinating!

The Knightikins10 bulan yang lalu^{+2535}I love how mathematicians are almost always so happy to talk about math.

Frank Odilon6 bulan yang laluThat is the beauty. It is like a joke everyone considers as lane just to understand it only demands critical thinking

Bellerophon challen6 bulan yang lalu@Thomas Ewing absolutely. There are the scientists and mathematicians who can teach and explain, and there are those like Simon Norton, who live most of their lives inside numbers and equations.

Thomas Ewing6 bulan yang lalu^{+1}@Bellerophon challen Just like Carl Sagan.

7rixee6 bulan yang laluIm not gay but id like to talk about how Newton found out light was gay

BearCubster6 bulan yang laluYes, irritating.

Honey Singh4 bulan yang lalu^{+2}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.

Gianluca VillaBulan Yang laluGreat video! But i think you forget to mention this: the fact that 1/(1+x) = 1-x+x²-x³ .... is true just for x approaching 0, or empirically just for |x|1 the series diverges. But since he integrates from 0 to 1 he got the correct answer anyway.

SUBHAJIT GORAIBulan Yang laluMy respect goes up for Newton after watching this video.

TornadodexBulan Yang lalu"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"

boysenbearyTahun Yang lalu^{+398}This Newton guy seems pretty smart. He should become a mathematician

Ishwor Shrestha7 bulan yang laluU

PowerJetsTahun Yang lalu@Inspector Pelu No you were not put into those two categerories, by deduction just the one you gave yourself.

The video was a fantastic, lets get kids interested in science. Everyone notes how many things Newton did and not just maths. What better than the "last magician", but no we have to have a dig with nationalistic based claims of the past. You seem to be a real expert, but perhaps a few reading tips.

There are a few very short articles about Newton in Quora written by some researchers. Instead of reading all those heavy books.

Of course Newtons work was not accepted overnight and in Germany in particular there was resistance for hundereds of years, based upon nationalistic reasons (science is not well served by nationalism).

One of the biggest German scientists of the time (Goethe) rewrote Newton's optics for example in what he regarded as his greatest achievment. Of course ultimately a German did revise Newtons work, only he was a jew and never wanted to be German, Swiss or American. He said he did not stand on the shoulders of Newton either, but someone elses.

But just the book for an inspector, the hint I gave in the thread: Newton and the Counterfeiter by Thomas Levenson.

PowerJetsTahun Yang lalu@Inspector Pelu Ah nationalism again (this was all part of the school stuff in Germany in the 1930s). There could be a reason why there is a lack of physics teachers in Germany. You need to phone the car garage to get someone who knows the name. As for James Clerk-Maxwell forget it. I think Einstein might have said something about that guy though. You might want to read something other than Wikipedia in German.

MartinO MendocinOTahun Yang lalu^{+2}@Muhammad Soleh Ehhh. Newton WAS in fact a guy who lived over 400yrs ago and

he was the great grandfather of psychics

Muhammad SolehTahun Yang lalu^{+2}me: Waiting for someone who didn't get the joke

Martin BlakeBulan Yang laluEngineer guy here with a PhD in Physics. I can say for a fact that almost all people doesn't realize that Newton actually paved the way for the industrial age, electrical age, computer age, and all other technological ages that will come up in the future just because of his curiosity about Pi and the insane intellect to craft a mathematical equation to do something about it. I was always fascinated with math as a child and upon learning Calculus and it's history, I was amazed at how that mathematical calculation revolutionized science and technology bringing us closer to becoming a space-faring civilization. Many scientists even Einstein calls him the greatest that has ever lived.

IR gEEK4 bulan yang laluI love this channel so much! Blows my mind every time I watch!

Joseph A. Muniz4 bulan yang laluAmazing! I just finished with Calc 2 and this made sooooo much sense! Friggin Awesome!

silas kuira3 bulan yang laluVeritasium blows my mind every time! And so does Newton...

saddlepiggy | The Purple PigTahun Yang lalu^{+4533}“Luckily, Newton had just invented Calculus.”

Bruh chill out Newton leave some discoveries for the rest of us.

Giga Chad5 bulan yang lalu@Col Br Dude he ordered innocent people killed for “counterfeiting” money and that’s the only reason why he was knighted.

Col Br5 bulan yang lalu@Giga Chad I love how it's so easy to judge people without having any clue what was going on with them, or what state their physical or mental health was in.

Nadarith6 bulan yang lalu@SnakeVenom 49 Not knowing about things he couldn't possibly know about isn't making a mistake wtf?

also citation needed on that wireless power harming people

Nadarith6 bulan yang lalu@highend custom design car audio Nobody here is talking about your ancient middle eastern myths here so stop interjecting

pardeep garg11 bulan yang lalu@Philka lemon boiler

POOF BE GONEBulan Yang laluI feel like "Newton goes even further" should be the quote that gives the motivation to the greatest of people

Aries Lau2 bulan yang laluCan'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?

M. Venkadesen4 bulan yang lalu^{+1}Learning maths via knowing about history of math is amazing

Prakul Sharma2 bulan yang laluI'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 🤯

ASHA K.VTahun Yang lalu^{+1127}C'mon, Newton is the most ridiculous person in the world. Three- quarters of what I'm studying was made by that single man.

Stephen OlanTahun Yang lalu@Tu Ut

Ask random people who Newton was a percentage of them will say he invented a fig cookie.

Tomos HalseyTahun Yang lalu@dekippiesip Fresnel, Lagrange, Lovelace the list goes on.

Felipe BrunettaTahun Yang lalu@Anaformia abalatus dispositium. I appreciate the Von Neumann love. Dude is just criminally underrated

anomTahun Yang lalu^{+1}@2 Nep8id6 idc.. its just a documentary feel free to dislike it.

anomTahun Yang lalu^{+1}@Tu Ut the Victor's write history? I'm sure in many cases the losers do too unless they were totally wiped out.

Orbnotacus5 bulan yang laluThis reminds me of a moment in middle school when I asked the teacher if you can put decimals into fractions (as numerator or denominator, not conversions) and she broke.

Wissle6 bulan yang lalu^{+13}Starting this video with Pizza was brilliant, I watched all of it after that intro

Interesting stuff, Newton was such a genius it's really mindblowing

Matthew Firestone4 bulan yang laluYou could also think about it as rotating the triangle around 0, based on the power you use.

Beth Carroll5 bulan yang lalu^{+2}"which is to break the formula." Love it. March straight through someone's brick wall and find that it isn't really there at all!! Thanks for the video!

Punnamaraju Vinayaka TejasTahun Yang lalu^{+5163}"Kids these days depend too much on the binomial expansion to calculate pi. Back in our day we used to bisect polygons. Sure, it was hard work, but it built character. Now we have entitled brats who think the fastest way of calculating pi is the right way of doing it."

IrokoSalei9 bulan yang lalu"It will be terrible for the economy"

Kenn Tollens9 bulan yang laluYou are talking about kids from way back, kids these days google it. Why use your brain when you don't have to.

Sunil Naidu9 bulan yang lalu^{+1}@Canadian Hobo yes we were taught about the area of circle as πr^2 . But our teachers didn't say the meaning of π. Even now a days you can find the children who knew the value of π didn't the meaning of it.

Tracer Hobbes9 bulan yang lalu@Chopin I'm really not sure what your point is. Is there a place on Earth that requires people to learn 16 years of math?

David Máximo9 bulan yang lalu^{+1}@Chopin what you said is nothing like what I said, I never said people who don't know math will hate it, I said people who are ignorant are in risk of disregarding the importance of a subject just because of their ignorance in it. The analogy would be more like: "people who hated ELA are likely to disregard the importance of Shakespeare's influence on English literature". And they would do that without a clue on what they're talking about, which is why education is important.

RezaN2 bulan yang laluMy teacher started teaching us binomial theorem 3 days ago and I randomly got this video recommended really cool to know about its contribution and history

Konrad Palm3 bulan yang laluAmazing video. Though I have to say, saying I understood half of it would be an overstatement.

Dokja26 hari yang laluThank you for the video, it helped me get a better understanding of uses of bionomial series…

Also I wanna address at 14:17 the calculations were little off after integration but gets corrected after few next steps…

igoretskiHari Yang laluYes. I just saw that too. There should be x5/5 instead of x4/4.

James Simmons IIBulan Yang laluWithout the aid of a calculator or computer! Truly amazing!

Anshbeast8 bulan yang lalu^{+2084}The sheer way humans can do soooooo much with just 10 digits discovered from their fingers is extremely fascinating

Nebula_Wolf11 hari yang lalu@Ms Moon Boo -_-

Ms Moon Boo12 hari yang laluGiggity

decidiousrex26 hari yang lalu@Nebula_Wolf I'm not a historian but from what I know time and base 60 were developed in Mesopotamia before the Egyptians. I can't really comment though, I don't know

decidiousrex26 hari yang lalu@Karyuu Correct, for anything above everyday math it makes absolutely no difference

Nebula_Wolf26 hari yang lalu^{+1}@decidiousrex didnt the egyptians count in base 12? or someone, and thats the reason we measure days in multiples of 12 hours, and hours in multiples of 12 minutes, and minutes in multiple of 12 seconds and such?

BEASTO4 bulan yang laluJust a minute in the video and I already gave a like your really explained a lot in a way that I'll never forget

Thank you.

Epic Terry3 bulan yang lalu^{+1}Man just explained the area of a circle formula in 10 seconds better than all of school

MSM5 bulan yang lalu^{+1}A circle in 3 dimensions is a sphere. In 4 dimensions it is a tube shaped like a Mike and Ike candy. When applied to a gravitational field the tube takes the shape of an innertube. When applied to an ever expanding but ultimately repetitive universe (big bangs repeating over and over eternally) the innertube becomes a larger hollow tube rising into the infinite sky.

Vance McCarthy6 bulan yang laluA method which, 350 years later, could be plugged into a computer to calculate PI to one million decimal places.

James BatleyTahun Yang lalu^{+613}Derek, I'm a math instructor at a university. Your teaching methods are seriously starting to make me question my own. I want to teach like you in the classroom. :]

Xen XanderTahun Yang laluConfucius says:

"He who keeps the old a kindle, and adds new knowledge, is fit to be a teacher."

I can't add new things to mathematics, I'm a teacher of math to H.S. but I'm not a math professor.

The only way I can keep up this saying as true, is to try and find new angles to teach old curriculum.

Arkodyoti ChoudhuryTahun Yang laluBest wishes for ur future..💟 I hope u get curious, seeking students....

Jack RainfieldTahun Yang laluDefinitely bring pizza to class when you teach Pi....

Ivory ASTahun Yang laluJames Batley

Well, he seems to be in a bit of a different game, but I'm not even a teacher (I'm an undergrad in engineering) and I'm glad to hear that!

Bill KieleTahun Yang lalu^{+1}@Nice Guy The circle as drawn circumscribes the hexagon. The area of the hexagon is exactly that of the six equilateral triangles that form the hexagon. The hexagon "cuts corners" going once around the hexagon (perimeter), which means there are six pieces of the circle cut by the shortcuts that have positive area. Hence, the inequality.The details are left to the reader.....whenever I saw those last words in any of my grad textbooks, I knew some blood, sweat, and tears were about to happen while I tended to the details. Enjoy your weekend.

Sidra Tul Muntaha2 bulan yang laluThat's amazing amazing. Let me to say veritisium doesn't stop surprising me.

Incredible job 👏

Andras VagoBulan Yang laluLove Math! Thanks for this wonderful video!

John Mcpherson5 bulan yang lalu^{+1}Okay, so all I learned watching this was that Isaac Newton was far better at math than I will or could ever be. Same for the two fellas rambling on throughout this clip.

transformer8896 bulan yang laluI remember we used to use binomial series to solve the boundary conditions, not just playing with numbers

Shubhankar DeshmukhTahun Yang lalu^{+311}If maths was taught like this, I would've understood pretty much everything and not develop a phobia towards it.

MJTahun Yang lalu@test 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.

MattTahun Yang lalu^{+2}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.

Tom FTahun Yang laluIf only thermodynamic was taugh via statistical physic...

G. W.Tahun Yang lalu^{+6}Seriously, I've been watching maths IDclipsrs 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.

Patrick StewartTahun Yang lalu^{+8}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.

CGMe5 bulan yang lalu^{+5}He invented this, calculus (alongside Gottfried Leibniz), the three laws of motion, and made discoveries in the science of light (I.e., optics).

Hugh Leyton5 bulan yang laluNot easy to explain, perhaps someone could put my simple formula into a video.. . My formula starts with 4 right angled squares in the circle. Each iteration doubles the number of right angled triangles.. . Very easy to calculate their area.. . My formula can go on for ever, getting increasingly accurate... It is totally accurate and faster than many or all others.

Gero Krüger6 bulan yang laluThis is a wonderful video! Thank you very much!

Pratishtha BajracharyaBulan Yang laluI really wish my calculus teacher taught things like these instead of just making us solve 2 pages of questions. But that's how the education system is