The Discovery That Transformed Pi
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- Опубліковано 15 бер 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!
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 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
The animator is the hidden hero here!
Truth - shout out to Ivàn!
@@veritasium thank you Ivàn!!!!
Ivàn rules
Big up Ivàn!
666 likes
Newton giving a lecture - "Hi guys, today we're talking about circles. The first thing you wanna do is invent calculus."
lmao good one
lol🤣
That is the mathematical equivalent of “welcome to standing up school”
*Fluctions
@@getonthecrossanddontlookba5004 Btw you're not getting into heaven by pretending like that and making effortless youtube comments
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.
or Gauss, that guy had all the answers in the universe but kept them somewhere in his private letters to someone
Nice pfp
@@ker0356what
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.
I did understand all the math and it was even better
That's the Power of Math
maths was nothing just basic calculus
@@KaluaBihari1 people have a hard time with calculus, for some reason
Now imagine actually understanding the math behind it. It immediately becomes revolutionary in terms of new and relevant ways of thinking
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
Woah.
Maybe for veritasium's next video?
You should definitely pin this comment.
@@thethirdjegs Yeah, I would love to know about this series.
And what about Ramanujan Series
Imagine having a career so illustrious that discovering a groundbreaking way to accurrately find pi is just one of your side achievements
Every other guys call themselves real gangsta. If they would have saw Newton, Turing, Euclid they would have shat their pants
And somehow, that grand side achievement is much less attributable to you than a random falling apple :D :D
@@AuliaAF well, falling of an apple gave him the idea of gravity, which in comparison with calculus is way bigger achievement
@@AkshayKumar-kz6zh "You Ain't Gangsta Like Newton"
Would be a dope track. Rofl
@@AkshayKumar-kz6zh so much that no one would think you stealing from your student
There are two mistakes at 14:25 & 14:28.
Firstly there should be x^5/5 in place of x^4/4 and x^9/9 in place of x^9/8 and then 5×8 would be equal to 40 not 4×8 and 128×9 would be equal to 1152 not 128×8.
Just for the mathematical formalism. Else, the video was great.
wow...
Me during quarantine: Plays video games all day
Newton during quarantine: Creates groundbreaking mathematical solutions
Alas, alak.
That’s because he didn’t have video games or other distractions to simulate his brain :)
"Luckily he had just invented calculus" unbelievable
Right? "speed running maths" is complete understatement.
Newton is the equivalent of dropping an atomic bomb on cavemen
You will never find The fun and love in maths. If you don't, "Seek"
Welcome to real numbers in Math
Discovered
@@BlastinRope No, invented
Imagine spending 25 years of your life on something, and then a 23 year old kid comes along and beats you in a week while being in lockdown
Work smarter not harder
I’m literally a 23 year old quarantining and I have done nothing of substance for the world. fml
That's just technology
@@cheesecakelasagna To be fair, most 23 year olds haven't. You'll notice there aren't a lot of Newtons in the world :)
The power of a lockdown
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
Archimedes is almost universally considered the smartest guy alive in the ancient world.
Aryabhatta gave an even more accurate answer
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
What? We learn that in school
Lmao kid is so dumb
You were a bad student.
@@ClintonDawkinsor they had a bad school
@@TaylorfromPapaLouie Bad students never blame themselves.
Hey Derek, i don't know who that guy is, but invite him as much as possible
He is a math-professor.
ok
Alex Kontorovich, Professor of Mathematics at Rutgers University,
it's like u got a thing for him or something
@@Hellmuth4 Hes really happy
Newton was one incredible man
"Newton was a smat cookie"
-- Penny Holfstader
Indeed he was.
Yes indeed he was
@@thebelligerentbostonian7524 smat
Avunu.
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.
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.
Newton’s quarantine: boring. Let’s upgrade human understanding of mathematics.
My quarantine: homemade pizza.
at least they both have pi in common.
My quarantine: Hey I wonder if anti elements has a more interesting name that just "Anti [insert element]"
dont forget the banana bread
But Newton is dead and you aren't so who's the real winner?
@@IdaeChop positron?
Newton schooled himself on Brilliant during the bubonic plague quarantine
I mean brilliant is pretty good. It helps me come up with new topics for my videos
@@DyslexicMitochondria Cool channel
Newton is a Chad bruh
When I start working, I'll sign up for subscription. Currently I'm living off of parent's money for internet etc
@@stereoheart.806 ironically he died a virgin.
This video is an absolute masterpiece of storytelling. The beauty of discovery comes through so well. I watch this every few months, and I'm inspired every single time
The man was so glad to be part of this and talking about it
“Luckily, Newton had just invented Calculus.”
Bruh chill out Newton leave some discoveries for the rest of us.
newton was a massive con artist
Yeah. Newton was a little too smart. The man did enough stuff to help modern physics 100s of years later
Tbf if newton never lived we still would have had calculus, Leibniz has got you covered
@@akashverma8656 Leibnitz fanboy
@@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.
Imagine working on something for 25 years only to find out that someone did it while playing with an equation during a pandemic.
"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.
@@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.
Newton is not just "someone" ...
@@lelouch1722 Was he "something"?
@John Citizen he never said nobody he just most people arent
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.
My most favorite video of all the time on youtube. As many times, as I watch this video, I got to know about and am curious about maths and pi.
Now I understand how my dog feels when I'm talking to it.
That is literally laugh out loud funny.
that would suggest you are barking at your dog, and your dog thinks you are somehow saying long descriptive words that it doesn't understand the meaning for.
you have even overreached with your joke.
@@godsinbox stfu
@@cheesegraters3975 no you
You just need to take second year calculus (where integration will be covered) and probability theory (where factorial notation will be covered).
given a pizza with radius of "z", and thickness of "a", you can calculate its volume using V = pi.z.z.a
we had this written in our school book :D
My dude...love it
Nice
🤣🤣🤣🤣
❤️the video, ❤️ your comment
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.
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
1666: Newton, during quarantine, discovering pi
2020: Me, during quarantine, eating pie
Jim 1999 shagging pie
2354: People, during quarantine looking at pie
Newton copied ancient Indian scriptures
@@shivamnarula1601 ?
@@shivamnarula1601 andddd where did you learned that?
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.
I once read Newton was the smartest human who ever lived. Never saw anyone dispute that.
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
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.
@Alex ' einstein is recognized because he basically revolutionized physics, created what we know as moder physics and because he was right in basically everything, scientists have been trying to break his theories for 100 years and soo far everyone has failed
@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)
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.
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❤
Quarantine : *exists
Newton : guess I'll just invent calculus...
Yep. Quarantine a long time ago.
Leibnitz* but close enough
@@carsonchiem145 Leibniz was the better thinker. But Newton was the better explainer.
him and leibniz
Newton's Achievements:
-- Reflecting telescopes
-- Spectral analysis
-- Calculus
-- Laws of Motion
-- Universal Law of Gravitation
Einstein's Achievements:
-- Brownian Motion
-- Photoelectric Effect
-- Special Relativity
-- Mass-Energy Equivalence
-- General Relativity
My Achievements:
--
I love how mathematicians are almost always so happy to talk about math.
math is his wife
i love to talk about math too even though im not a mathematician
@@lemondigit7309 same with me
Everybody does. Math is beautiful
@@lemondigit7309 I love talking about math, but main stream media told me it is racist. So I count my change silently.
Veritassium videos are always so well and clearly illustrated/animated, kudos!
Nice video, and another contribution to the "Flare-up of Priority Disputes" between Leibniz and Newton. It probably will go on forever.
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.
I failed calculus because it was explained so poorly in class. This video would have helped me ace the class.
@@jasonlandry8685 -- I didn't learn why calc worked until a vid like this came along -- 20 years later.
@@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.
Yeah this video had that 3blue1brown energy
I wish something like this exist 23 years ago, so I don't have to repeat calculus class 3 times, just to get C-🤣
I can easily say, this video is one of the best mathematics video I've ever seen so far.
Great great video. I hope these were available back them in school. Thanks alot for sharing.
"He speed ran pi." Queue Home- 'We're Finally Landing'
TRUE LMAO
Man, i blew water through my nose while drinking it. Lmao 🤣🤣🤣
On point! Thanks for the hearty laugh.
Wow, that is a pretty obscure reference omg
Man, this channel keeps getting better and better. Have my updoot Derrick.
I swear I got goosebumps when he rotated that Pascal's triangle. That was some "protagonist realizes the truth" moment right there. This is how maths should be taught!
If math is taught like like, it feels nothings less than amazing magic tricks!
@@shilpaprajapati4801 this is not how math should be taught. This is purely inspirational presentation. To actually learn you need to do some work yourself to actually understand it. That's why being in a lecture is not enough not matter how good it is.
So if math was taught like this, you'd've never learned any math in the first place. I think these are great as an introduction because they are relatively short and have a great story. But this is not a replacement for proper pedagogy.
@@SiMeGamer so true bro, math should be taught like this. This way of presentation makes even the most complicated topics of math not only easier, but also interesting and fun to watch...
@@shilpaprajapati4801 You just said "so true" and continued agreeing with the point you made previously despite me saying the opposite. It's not how math should be taught. You don't properly learn anything from this.
@@SiMeGamer not true* 😅 I think this is the proper way of teaching
Can someone please shed some light on how that Dutch mathematician was able to calculate the perimeter of a 2^62 side polygon?
Painstakingly.
@@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.
@@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)
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?
@@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.
Beautifully put together! ✨
Veritasium: **explaining how to get Pi**
me just wondering who's gonna eat the pizzas
it's pineapple pizza, so probably no one.
Some videos shouldn't be watched while being high.
@@kennarajora6532, I'd have the pineapple pizza, please.
@@pusingfismat7099 me too
I thought the same as well
"He was quarantining at home due to an outbreak of Bubonic Plague." I felt this
This is his version of learning a new skill during lockdown...dude sat down and calculated pi...
@@sombrero4316 haha tru af, he didnt have netflix tho
Pandemics can be good!
Good thing he had skillshare
IIRC that's also when he came up with his law of universal gravitation and laws of motion, laying the foundation for all of classical mechanics. Maybe that's what you get when you don't have as many distractions as we do these days, I guess, maybe?
I have zero clue what’s happening in this video but it’s somehow keeping me extremely entertained and engaged so good job on that 👍
I keep watching this video again and again. It's just majestic and I want to incorporate this in my mind.
when you aren't looking and mistake Prof. Alex's voice for Sal Khan
Yo
Haha I've listened to sal Khan SO many times that his voice is etched in my brain. His narration is flawless. Whenever I need an idea for a new video, I go to Khan academy. Sal inspired me for my yt channel where i make videos on science
Third to comment on your comment
Oh you're here 🔥👍
hello human
This mans gave me a better understanding of Pi in 2 minutes than 5 years of school
I wish this story was shown to me in ap calc
Yeah.... Only a true seeker can have the power of pure teaching.. 💟
haha school bad, funny
@@sampanna6983 but it's true tho
@@thedirector6297 if schools didn't teach you anything (regardless of how bad they taught), you wouldn't understand half the things in the video, so stop shitting on schools.
coming back to this video when i'm now on university studying calculus and actually understanding all of the integrating part feels soo good
Than guess UA-cam should replace all teachers ...what a waste of money
@@Moodboard39 not as in thanks to this video, but the other sense smh
I have degrees in mathematics, and have never seen anybody explain concepts as well as this channel.
"luckily for us, he had just invented calculus"
as you just casually do, ya know.
Gottfried Leibniz vehemently disagree.
Lol literally the second I looked at the comments he said that and I saw your comment
*unluckily for us dumb shits he invented calculus that will make you suffer your whole university life because it spawns geometry, trigonometry, physics, thermodynamics, hydrodynamics and all that pits of hell
@@overbored617 lol chill math is fun just put time and brain into it
@@andeemengaming5000 not if the amount of work from the other subjects are added
We can all agree that cutting the crust off of pizza is the least ridiculous way to calculate pi.
Yo wsp David
Why don´t use a Pie?
Nevertheless, it makes a great visual. They deserve a 21-gon salute!
The best inside joke in school I've ever had is similar to this, we joke that our (amazing) teacher only eats the crusts of pizzas
@@PastaTurtle
Speaking of college jokes, a friend of mine used to hold up those little square drakes fruit pies and he would say. "Pie are square" (It works better with the pie in hand)
crazy to think such math was discovered so long ago, this inspires me so much
This is probably the coolest maths video i've ever watched. Thanks so much
Van Ceulen; "yeah, so I calculated pi to the 50th integer"
Newton; *"Hold my apple"*
If Newton's apple had landed in a puddle, he would have seen the apple only fell through the air because it was denser then the air, but then floated on top of the water beacause it was less dense than water. Gravity only points direction.
It took him a book three times thicker than the Bible (,,Philosophiae naturalis principia mathematica,,)and he still couldn't finish his equation on how to prove gravity. And it contains so many ,,if,,'s...
Newton's Marvellous Year is 1666 (666 devil's signature...)
i actually audibly laughed at this
@@Politics_is_PUBLIC_TOILET QAnon has taken over your mind, get help
@@NASAFanboy The pressure from that persons skull is so low he's probably floating into space by now
@@Politics_is_PUBLIC_TOILET U ok?
Moral of the story : Newton was hell of a genius.
True
@@madcap9977 he just tried all the possibilities that he know
@@santhoshhbs Look who's talking. You don't even have proper grammer.
@santhoshh bs, you are the type of person to struggle to open pistachios.
@@hijdjf2961 means?
Newton quarantines at home due to a global pandemic and he creates a revolutionary way to solve a mathematical problem.
I do it and I just make some bread and gain weight 😩
Ok, but was the bread good?
You have truly outdone yourself, this is an amazing video.
Ludolph Van Ceulen: “I spent 25 years to calculate pi with extreme precision”
Isaac Newton: *S P E E D R U N*
*dream music starts playing*
*3 . 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0 2 9 7 1 6 9 3 9 9 3 7 5 1 0 5 8 2 0 9 7 4*
@JACOB H uhhh is there any way to cheat in math? that doesn't sound like a thing. but if there is, and someone did it, he'd be that guy
to be fair, Newton was around 24 years old when he discovered how to approximate pi. So essentially Newton only beat Ludolph by 1 year. It took Newton 24 years to get the approximation to more than the current world record at that time.
:^)
@@thenoobthatdied6489 But Newton also did so much more than that during that time. He literally established an entire branch of mathematics--Calculus. Not to mention Newtonian physics, his theory of gravity, his work on light and optics, and few people know this but he actually made huge contributions to theology as well.
"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."
Yeah hate it when that happens
Underrated comment
@@rubenhaug3978 It got 4 likes in 4 days so long after the video was released, so... I'll take it
Hahaha.
@@PunnamarajVinayakTejas I gave you like 100. I made you three digits, my dude! ;)
Amazing.
Have been using these form school time (30 years back) but never realised it the way you explain here. It almost makes me think - why I did not think of it before. 😂😂👍👍
I just noticed today that the integration Derek did at 14:17 is completely wrong... x^4 becomes (x^5)/5, not (x^4)/4. Good video, though!
The integration is correct
@@adwaitpandey2526 no its wrong, watch it again after the 8 times 4 it becomes 40 not 32, and when the 128 times 8 it becomes 1152 not 1024, i calculated the formula, and yeah the integration is wrong from x8 become x9/8 , but just at 14:17, after that it normal again
@@diondidinata5681 Yeah my bad you're correct
"You can say he speedran pi"
So Newton invented speedrunning as well
wow only 31 likes
U are everywhere
Bro lol you have discord??
lol
Yay! I‘m here before this blows up!
Isaac Newton, when the plague hits he discovers gravity, Invented calculus and made his Annus Mirabillis. And here am I getting fatter from quarantine.
i know, right??
Maybe he would be getting fatter if he had UA-cam as well...lol.
@@Shootskas He would have invented UA-cam!
@@darren430 touche
@@Shootskas ;-)
🎯 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 brought back some memories - I came up with the polygon approach myself as a 15yo, but could see that it was not going to be very efficient. Later in life I too used a calculus based approach, but perhaps not as good as Newton's! I worked out the power series for inverse sin, and used it to get estimates for the inverse sin of 1/2, which is of course pi/6. I worked in binary (or sort of in base 4 or 16) and since it was just an indulgent game I didn't waste my time converting to decimal! I was able to hand calculate a value to quite a few places this way.
From just looking at that guy's face you can tell how much in love he is with maths.. He is just so darn happy ❤️
👍👍👍
Kind of
either that, or there is someone under the desk
I’m part of an advanced math progam in MoMath and he’s actually one of the instructors!
He reminded me of my college days studying Math. I used to talk to my Math Major and Non-Math Major friends all about random math history; and wouldn't stop tell someone told me to shut up.
A mathematics professor who was a good friend of mine, and who died recently at 90, told me with haunting conviction that Pascal's triangle has not remotely revealed all of its secrets.
Were gonna break the universe at some point. Or discover the beginning and end. Idk crazy stuff happening
If this much was learnt by just rotating the Pascal's triangle in two dimensions, imagine what could be there if it was in the 3rd dimension
@@movinperera Or even worse, combine Quaternions with Pascals Triangle
@@rs-tarxvfz NO NO NO NO NO! I've spent the last 5 freaking years wrapping my head around quaternions! We DO NOT need to make them any more of an enigma!
@@jessiegashler427 May quaternions explain much more complex phenomenon.
This video is an amazing simplification of several complicated concepts. I have obsessed for years over some of the ideas presented and strongly agree with all ideas presented.
One concept I might have added would be instead of (or in addition to) proving the area of a circle as a rectangle, show it instead as a triangle with Cartesian Coordinates (0,0), (0,2 * pi * r) and (r,0). This triangle is the result of taking the perimeter of a circle and perimeter of each smaller concentric circle until you reach zero. The perimeter of a circle being proportional to each radius of the concentric circles is easily seen on this graph where the value of x is a radius and y is the circumference. The area of the triangle is of course (2 * pi * r^2)/2 = pi * r^2.
Newton was way ahead of his time. The greatest genius ever to be born on Earth ❤
The real question is why Derek bough 6 pizzas when 4 could have done the job.
The naive approach. You don't assume the value you are looking for, you just go and find out. Or maybe pizza cravings?
One of those pizzas was an intruder. It had pineapples
@@RoyBatty81 i ber sir Isaac Newton never ate a pizza with pineapple!
Maybe having some friends over?
He wasn't sure what the ceil of pi is.
Better be safe!
"Newton was quarantining at home due to an outbreak of bubonic plague." Newton was such a recluse, we all know he would've been at home even without the plague haha.
Haha all thanks to his solitude we got this impressive idea!
Haha all thanks to his solitude we got this impressive idea!
Yeah but he would have been too busy with his 'close friend' if he wasn't in quarantine.
Sheeple think SARS-CoV2 is equivalent to the Bubonic Plague.
We now have a generation of insufferable germophobes.
@@noozzoo5152 5 seconds ago, lol
If only I had such videos when I was a bachelor. These are blurring the line between abstract and real. Thanks!
Imma be honest, I don't understand literally any of what's being said in this video but it's nice to listen to.
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. :]
Do it, I never really went on to what pi even is as a student. Not only did he make me understand it litteraly effortlessly, but he made me love it too at the same time
I swear, I'm also a Math teacher at a HighSchool and he only way most of them gets interested is me adding Jokes on numbers, using Food or luxuries instead of Variable(Screw X! I use symbols associated with the formula)
A teacher genuinely wanting to impart knowledge. Well respect. Its rare to see teachers who are genuine
God the students will be even more confused 🔥😂
why is pi > C/D?
I mostly knew Newton as the physics guy but I had no idea he also INVENTED CALCULUS AND BROKE THE BINOMIAL THEOREM TO SOLVE PI THIS MAN WAS INSANE AND DESERVES ALL THE FAME
Newton was the greatest genius who ever lived. Even the great Gauss pays homage to Newton.
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.
@@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
for those who are following the brilliant sequence: @14:19 last term of Pi area calculation, "-5/128 x^9/8" should be "-5/128 x^9/9"
this is so amazing!!! I have never heard this method before
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.
math basically HAS to have many inner patterns, as math is, in a sense, the study of patterns.
@@minecrafting_il and order :)
Math is beautiful
@@hike8932 math folder is blue
@@eggegg6448 Math folder is red, you can't change my mind.
Grienberger: nobody will ever bissect better than me
Newton: I'm gonna do what's called a pro gamer move
hahahahahahaha lolol
Me too
david504 voice: checkmate
This is why mathmaticians have a high suicide rate
Loooooool hahajaha
I really enjoy these videos. Keep up the great work.
Idk if it's Veritasium or volunteers but thanks for making the accurate captions
Newton quarantined at home: figures out pi
Me quarantined at home: screws up making a pie
For some reason I didn’t get the joke on the first read
Maybe because it should’ve been more creative.
haaaa ha ha, and all those series to me are not convincing
@@henk7747 How do u know
Hahaha😆😆😆
Lmao you're one cool dude mate 😊👍🌈🇲🇾🍀
Man, I have just realized something important:
"You would tolerate the complexity of math concept, IF YOU KNEW the story of WHY it was invented"
Or how
Exactly. Schools should play these videos as part of their curriculum.
Man didn't invent math. We simply discovered it
@@cryptopotomus1417 thats an actual philosophical question, did we invented math or did we dicover it?
@@carso1500 2 of an object and 2 more of the same object is 4 objects.
Across all walks of life
It was like that long before humans were around.
It'll be like that long after we're gone and another species discovers it
i love videos like this even i cant understand it.. seeing geniuses talking about something always mesmerizes me.. i really like to open up their head and take a look at their brain.. im so jealous to these genius
Fantastic video so inspiring and eye opening !
he was testing to see if he can write 6 pizzas of on his taxes as a buziness expense
Hopefully the ATO will reprimand him for having pineapple on it.
Now that's a true genius
Damn,
Veritasium stole gus' idea
this video is for a tax write off
@@vigilantcosmicpenguin8721 yeah that one XD
When Mathematics is visualized and explained properly from the beginning it is absolutely beautiful.
It's the language of the universe, the most beautiful thing to ever have been discovered. Everything is based upon it.
You can thank the mathematical genuis God.
@@hamsarris8341 shut up
@@seanmiller8686 ?
@@hamsarris8341 god didn't do anything
@16:08 - again: not how hard you work, but how smart you work - excellent!
I love your table you used with the pizza... The episode was fantastic as usual, but as a woodworker I gotta say that's a nice table 😊
So he figured this out during quarantine. Now I feel even worse about how little I accomplished in 2020.
engineer gaming
anddd he was 24 lol
Lol
And so you should. It isn't as though he had one of the finest creative scientific minds of the last, well, all of history.
He also invented optics and the prism experiment. He was also doing alchemy. As mentioned, he wrote the foundations of calculus.
The sheer way humans can do soooooo much with just 10 digits discovered from their fingers is extremely fascinating
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.
@@decidiousrex base pic would be ideal!
@@decidiousrex base pi*
@@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.
@@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
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
Dude. When you rotated that triangle up into the imaginary I lost my freaking mind. I’ve never had any math concept click that hard. I wish I could relearn all of mathematics in the style of how they were derived. That would be a lot of fun.
Newton during a pandemic: *Solves Pi*
Me during a pandemic: *Sleeps all day*
He didn't just solved the pi, he invented entire calculus in summer break
@@suyogkhadilkar what a monster.
@@suyogkhadilkar Newton was trying to solve Pi and inventing calculus was just a side quest on the way.
Eat a pie if we lucky..
didnt he also found those physic Newton law of motions also? apple thing?
“And no one was bisecting like that ever again” yeah ask my math teacher
I remember using this method in a spreadsheet during my lunch break at work once just out of idle curiosity. It is quite easy if you let a computer do all the grunt work. Got a fair way along before hitting the inevitable integer overflow, couldn't be bothered to compensate to go past that point though since that would have taken a bit of actual effort :)
@@venoltar Just use python. It is epic for math algorithms
Rik kardo MATLAB?
@@Roomsaver not free?
Some people are still living in 1600.
Really good video, keep up the good work
I can feel the happiness on their face when they talk about the new ideas. That's the most beautiful thing about us humans, we love innovation and creativity.
The smile on the professor tells you just how passionate he is about math.
Imagine the intellectual high Netwon was on after accidentally revolutionizing mathematics 4 times while just playing around with an equation out of boredom
Stuck in quarantine no less. Where's our COVID Newton?
@@draco89123 watching Netflix, probably
Just imagine that same Isac Newton spent years decoding the bible and metaphysics that no one talks about today. guess how many mysteries would be unlocked the day we refer to his metaphysical findings.
@@binderchannel9454 The Bible is a bunch of bs made up by primitive men. Half of it seems to be stories adopted from older religions.
@Austin Hernandez
That bunch of bs contains a whole bunch of quarantine measures, ideally suited for disease, plagues, and other outbreaks.
Number one being 'If unclean, or showing symptoms, _don't_ attend your local congregation'.