The Discovery That Transformed Pi

32 255 Shikime 3,3 mln

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 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 -
Dunham, W. (1990). Journey through genius: The great theorems of mathematics. Wiley -
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 -
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 "Particle Emission", "Into the Forest", "Stavselet", "Face of the Earth", "Firefly in a Fairytale"
Thumbnail by Gianmarco Malandra and Karri Denise


  1. David Williams
    David Williams
    4 orë më parë

    Pi/2=90° which is one fourth of a circle

  2. genesis
    6 orë më parë

    Now we have to learn different laws , theorems , postulate in order to find something we could invent 😂

  3. megamanexe4
    10 orë më parë

    What if each room could fit an infinite number of people

  4. Savoundaria Latchoumy
    Savoundaria Latchoumy
    11 orë më parë

    Why don't we divide 22 by 7

  5. Spade
    11 orë më parë

    Veritasium, I have to know, where did you get those pizzas? They looked delicious.

  6. Syed Hussain
    Syed Hussain
    12 orë më parë

    Invitation code shahjamal111 For Pi Network

  7. BBCAT -
    BBCAT -
    12 orë më parë

    What a great video. Really mind blowing what deductive reasoning can do.

  8. Dan Ellwein
    Dan Ellwein
    13 orë më parë

    thank you for this ... really appreciate it ...

  9. Nivyan
    14 orë më parë

    Newton revolutionized math in 5 different ways doing his isolation. What have you done since Covid started?

  10. Ideenlos
    14 orë më parë

    nice, now Im hungry :(

  11. Vojtech Pilar
    Vojtech Pilar
    16 orë më parë

    Who else is proud of themselves to follow the video all the way to the pizzas? 🍕🍕🍕

    19 orë më parë

    Ludolph van Ceulen: I spent my 25 years to calculate 35 digits of π Newton: Hold my APPLE🍎

  13. Daniel_
    19 orë më parë

    So just asking.. *For the big round ass, is that infinite number also applied?* 😀

  14. Jaime Duncan
    Jaime Duncan
    Ditë më parë

    3.14 is not all the precision that we need, it's pretty clear that the autor is not an engineer 😃

  15. Aditya Since 2006
    Aditya Since 2006
    Ditë më parë

    was parker on time ? PIZZA TIME !

  16. Sem
    Ditë më parë

    didn't know tom morello was into pi

  17. Bruce Chan
    Bruce Chan
    Ditë më parë

    Thank you! It's really helpful.

  18. José Barría
    José Barría
    Ditë më parë

    What would happen if n is a complex number?

  19. Mike Seguin
    Mike Seguin
    Ditë më parë

    The expansion of the universe is time. Without expansion you don't have infinite, the same reason why you can always ad a decimel point. You can do this because of the expansion of the universe. In the future, future civilizations won't understand theorys like the big bang because they can't see evidence of it. Could be the same reason we don't understand what was before the big bang. Because their is no data before that moment

    1. Mike Seguin
      Mike Seguin
      Ditë më parë

      Dark energy is also time

  20. Jack Johnson
    Jack Johnson
    2 ditë më parë

    I'm not gonna pretend I'm smart enough to understand all of this

  21. Caracalla
    2 ditë më parë

    No pizzas were harmed in the making of this video*

  22. Tiddybearkush
    2 ditë më parë

    Pi are square but square is in.

  23. Gamer Blank
    Gamer Blank
    2 ditë më parë

    Im an indian , and i hate self proclaim proud petty indians who brag to feel superior (fill their insecurities) , just becuz someone with a great mind lived 2000 yrs ago within 2000 km radius from his home . None of the guys here said "Our European Newton "

  24. Tiddybearkush
    2 ditë më parë

    I like pi it taste good.

  25. Nick Hermans
    Nick Hermans
    2 ditë më parë

    pineapple pizza -> UNSUBSCRIBED.

  26. Brewed Meditation
    Brewed Meditation
    2 ditë më parë

    Wonderful! I don't understand how newton caught that

  27. 4Nonym0u5
    2 ditë më parë

    Why did you circumsise that pizza?

  28. Ultralon
    2 ditë më parë

    Awsome Channel - evan the Advertising is interesting. Thats the way youtube should be. Thanks

  29. Tanya Sharma
    Tanya Sharma
    2 ditë më parë

    Last night I was thinking how the circle's area formula been made? and youtube show this in my recommendation😁

  30. OniZenMaster
    2 ditë më parë

    Geez lol. And what did WE all do during lockdown?

  31. Ria Ed
    Ria Ed
    3 ditë më parë

    I hate Math and I watched this in full attention... that's how good Derek's videos are 😅

  32. Abk Khan
    Abk Khan
    3 ditë më parë

    Don't waste pizzas

  33. Ivan M
    Ivan M
    3 ditë më parë

    didn't know that Newton do speedruns

  34. ft55555
    3 ditë më parë

    This is the type of ingenious stuff you can come up with if you don't spend all day thinking about getting tail. I'll never be a genius.

  35. HYDRA Gaming
    HYDRA Gaming
    4 ditë më parë

    PI pi full form is P=perfect people - I involve inside information... that is meaning of pi.. now.. new reason create pi meaning.. )( is create three meaning.. 3-6-9 9 is top art 3 is first art 6 is last art.. three in one meaning 3in1 3=1...1=3 3+3(1)' 3+3+1 =7 ........let's gooooooooooo pi create the human-beings pi=picture of living beings-living things p=peace living create I=involved non living living thing non living thing pi art is give reason of whole beings walking in pi solve Bsqure now.. 2 hand finger=10 +namaste namaste is=1 10+1=11 2 legs=10 2legs=10 2hand=10 20...teen endinnn. meditation stage..1 hole body.. 7 chakra meditation time 108 reason of life.. 1(0)+8 =9 than~0 so reason know 0-9 value of 0 to 9 in count..around times is..human arts stand to pose of namaste... 10finger of hand 10legs pose of namaste 1 hole body is 1 10+10+1+1 22 # then 22/7 Bsquare proofs Health.. I am SOS-303 save our soul 333 save soul spirits S.S.S i am processing human civilization.. 8 types.. 8wonder... Healthy Body healthy life processing healthy habit good habit-good result healthy life style daily routine.. food vegetable fruits.. water and medicine.. cure all disease.. 100% vegetarian life process make disease resistant. .100 out of hundred guaranteed.. mortals soul and spirits immortal life.. ..big mestrious reason.. aquatic life processing.. starting ULTRA arts.. land arts and forest arts is Anti-clock ice land is aromatic arts human civiliZation is ULTIMATE ARTIFICAL POWER ENERGY=1. .. the 3 arts is exist world and another world.. exist world=○ another world= - middle world=| ................. exist world is= Time another world is =LiGht=1,speed=1 middle world is=machine Artifical.. AVATAR..... A star.. I am star BoY.. goinin shine Diomond.. like diamond in the sky.. but I am earth son. I am PLUTO BOY.. COMin earth to burn to find the reason of life of everything.. I am born to burn blood.. V.Born.. a cure a pure= a square B purest B curest= B square a square Bsqure proofs.. Sign-heart boy going=NON BoY.. I am null I am nothing I am never never never born again .. past and future.. I am present.. I am dies and I am rise.. rising sun..I am.. I am MAN..and the.. I AM REAL MAN... now.... PSYCHIATRIC BOB.B Bsqure proofs ###

  36. HYDRA Gaming
    HYDRA Gaming
    4 ditë më parë

    I am give some calculation example..of PI 22/7 22+7=29 .......The moon one revolvin process in earth. 7×4=28 is calculation in human theory... but 1 is exists .. 7×3=21.......21+1=22 7 is 1 week 1=week 7=days 7+1 is 8 8 is (2+2)×2 2+2=4+1=5.. now the game times slovenian.. 22/7 (22+7)=2+2+7=11 ok..11=1+1=2 29=2and9 9 is higher of exists 3-6-9 2 is 1+1=11 11=one of one: 1 is null~1 is neutral. . the solo art is begin.... 22/7 divide 2 11/3.5 divide 2 5.5/1.75 divide 2 2.75/0.375 =2:75~375 2=7+5~3+7+5 2=27=27+2=29 but... 2:27 =2+2+7 =11 Bsquare proofs 22/7=11 thank you..

  37. HYDRA Gaming
    HYDRA Gaming
    4 ditë më parë

    I am not talented.. I am simple anything.. I am give some example is PI MEDITATION(M)=11 that is 1=1 spiritual energy=1 holy heart is=1 so..1+1=11 this is TiMe artificial machine that is Time machine.. TIME full form=True inside mind energy.. that is convert T.I.M.E mind Feelings(MF)=11 brain parts is=1 Feeling imagine create=1 they are LiGht=1,speed=1 light speed =1+1=11 Time-LigHt-Speed=Artifical machine.. 11+11=22 ................... Lucky(L)=7 week of days=7 meditation energy create..7 wonder work.. but 8 WONDER WORK COMING SOON.. B.B-4Bsqaure proofs.. that is Bsqure times 2+2=5.. 0.25 .M.A.(N)... Making artificial arts nation Nest.. that is MAN...MAN was=1, that is=I I was man, man is only one who exists everywhere... B.B know everthing.. HE(S) is G.O.D.. great..originally...Development...Human-beings revolvin.. He's 11=1.1 Peri-lion Boy.. True spiritual truth trust..everything ok.. silent is best reason of make self development. . sound love you.. you find the reason of you want..and you aim ..dream... you are B.B=believe-beautiful= best brave works.. you are one who is exists.. you are 1-Trillions.. B.B......Bsquare proofs.. psychiatric Bob.b..0.25...

  38. Вадим Владимирович Тимофеев
    Вадим Владимирович Тимофеев
    4 ditë më parë

    Lyagulyalyulin made boom 💥 in blogging

  39. Raghevendra Rajput
    Raghevendra Rajput
    4 ditë më parë

    Well This kids doesn't know about Ramanujan 😎

  40. Ly Minh Hoang
    Ly Minh Hoang
    4 ditë më parë

    NOT fair when comparing Newton's method with bisecting the polygons. The crux in Newton's method is that he's invented Calculus, which is not only a powerful tool but also a new branch of Mathematics.

  41. Karl Davis
    Karl Davis
    4 ditë më parë

    I tried evaluating just one term, not performing any of the subtractions, and got 3.4. One digit was right, the leading 3. It looks like you get about one digit per term, very roughly. I can't believe how fast that converges. Just one subtraction term, and you're at 3.152 (vs. 3.1416). Wow!

  42. Manuel Bourgault
    Manuel Bourgault
    4 ditë më parë

    The tombstone has an error at the 5th digit, this is kinda sad..

  43. Pascal Manuel
    Pascal Manuel
    5 ditë më parë

    Great video. At 14:20, shouldn't it be x5/5 rather than x4/4 ?

  44. 20BEMEG027_Shivansh Rai
    20BEMEG027_Shivansh Rai
    5 ditë më parë

    Instead of inscribing polygons in circles, they should have tried dividing 22 by 7 :)

  45. Polite Cat
    Polite Cat
    5 ditë më parë

    Ludolph Van Ceulen: “I spent 25 years to calculate pi with extreme precision” Isaac Newton: *S P E E D R U N*

  46. Ryker Edits
    Ryker Edits
    6 ditë më parë


  47. Yash Kumar
    Yash Kumar
    6 ditë më parë

    Why couldn't they just divide the circumference by diameter

  48. Ben Levy
    Ben Levy
    6 ditë më parë

    Weird thing about Pi and reality: As far as modern physics goes, there is no meaning to lengths smaller than the Planck Length. It's not even theoretically possible to measure a smaller length. It's about 10^-35 meters. On the other end, it is not theoretically possible to observe sizes larger than the observable universe. That's about 10^26. This means 62 digits of pi are enough to calculate the circumference of the entire observable universe- the largest possible thing- to the precision of the smallest possible measurement. Digits of pi past the 62nd can never apply to an actual field measurement, not even theoretically. If, for some reason, the actual circumference of circles* differs from calculations at the 63rd digit or beyond, we would never be able to know. Those digits not only have no practical use, according to physics as we know it, they can't. *Possible in a curved universe!

  49. Hugo Clarke
    Hugo Clarke
    6 ditë më parë

    You might laugh at the dude who spent 25 years of his life calculating Pi with an inefficient method, but he isn't the one wasting good pizza

  50. Drew Jarrell
    Drew Jarrell
    6 ditë më parë

    This is poggers

  51. Dream
    7 ditë më parë

    My boy Kontorovich using a Greenscreen. Perhaps his sense of home is very private.

  52. Thaís Frutuoso
    Thaís Frutuoso
    7 ditë më parë


  53. Samiul Karim
    Samiul Karim
    7 ditë më parë


  54. Jim DeCamp
    Jim DeCamp
    7 ditë më parë

    Errata @14:17 Third term on the bottom sequence should be x^5/5, not X^4/4, and last term should be x^9/9, not x^9/8. These corrections are consistent with the expression @15:58. I implemented this in Excel. After 17 terms it runs out of dynamic range (significance), but does computes π with full double precision. I sum the terms from the bottom up (Horner's rule), but the 18th term is: -7.41982E-16 and the sum of terms 29 through 18 is -1.13986E-14. In Excel 3.1415926535898000 -1.13986E-14 = 3.1415926535898000 and =PI() evaluates to 3.1415926535898000.

  55. Rediljan
    7 ditë më parë

    The crain and the brick analogy was simply a poor choise and bad

  56. Jordan Adkins
    Jordan Adkins
    7 ditë më parë

    I wonder if pi is a dimensional constant; that is, for instance, in your dreams if you were to work out pi would it still be 3.141592.....?

  57. D Wayne
    D Wayne
    7 ditë më parë

    14:19 why is x^9 divided by 8, shouldn't it be divided by 9 cause he said you multiply by x and divide by the new power, which is 9

  58. ShrimpMage
    7 ditë më parë

    Who else had their mind absolutely blown by the beginning pizza segment??

    8 ditë më parë

    That's awesome even be ı'm enginnering..

  60. John Boze
    John Boze
    8 ditë më parë

    Do Photons Have Mass? YES... I Sincerely Beg You To PROVE ME WRONG! ... and the Answer To The Universe Is -42 !!! The Mass of a Photon is Given by: m = (h/cλ) (kg) where, m = mass of a single photon c = speed of light, λ = wavelength of photon “Bozeon Constant” b is as follows: b = h/c (kg m) b =6.62607004x10^(-34) (kg m^2/s) / (299792458) (m/s) b = 2.210219x10^(-42) (kg m) The Mass of a Photon Is: m = b/λ (kg) or, m = 2.210219x10^(-42) / λ (kg) A typical Red photon with a wavelength of 700nm has the following mass: m = 2.210219x10^(-42) (kg m) / 7x10^(-7) (m) Mass of a 700 nm Red Photon: m = 3.1574557x10^(-36) (kg ) PROVE ME WRONG OR… Join The TTOE Team At BRAVE and Help Save Physics From Those With Warped Spacetime Minds: @BozeonResearchAndAEtherVerificationEtaireia Notes To Aid Understanding of what EM Dipoles Particles Are … The “Bozeon constant” “b” converts photon wavelength into the sum of all the masses of the “bozeons” or “God particles” that form the “quantum superfluid” in all particles. “Bozeon” is Polish for “God Particle”, the ethnicity of the Conceivor of EM Kinetic Dipole Theory, aka The Theory of Everything. There are trillions upon trillions of dipoles in a single photon. (more on the exact number later). Everything including all elementary particles are made of complex flows of EM Kinetic Dipoles. A Kinetic Dipole is a somewhat symmetric particle with one end that has more mass than the other. Bozeon’s are Electromagnetic Kinetic Dipole Particles that form the EM field. For better understanding you can pretend for now that the Planck Length is the RMS distance between kinetically colliding EM Dipoles (“Bozeons”). You can also pretend that the “size” of a EM Dipole is about 10^(-42) meters in length. The Dipole Mass Density Gradient in Vacuum determines the local force of gravity. Big “G” simply converts Dipole Mass Density Gradients into Acceleration. All forces EM, Gravity, Weak, Strong, are all calculated from the momentum transfers between kinetic collisions of these EM Dipole Particles. EM Dipoles in Vacuum are in a gaseous state and the “quantum superfluid” in all particles is liquefied EM Fields and are technically a Bose-Einstein Condensate of EM Kinetic Dipole Particles. Black holes are supersolids of EM Dipole Particles. Copyright 2021 John E. Boze

  61. Alex Mercer Turzo
    Alex Mercer Turzo
    8 ditë më parë

    why dont people just divide the circumference with diameter?

    1. JeffDunhamVEVO
      6 ditë më parë

      We don't know the circumference

  62. Hardik Nandha
    Hardik Nandha
    8 ditë më parë

    The Way of Presentation of This Video and Visuals are Just As Amazing as content!!!!

  63. Jose Manuel Lizardi
    Jose Manuel Lizardi
    8 ditë më parë

    Newton stole calculus from Leibniz

  64. rahul garg
    rahul garg
    8 ditë më parë

    Which software do you use to make animation?

  65. Nirmal Singh
    Nirmal Singh
    8 ditë më parë

    I am pretty sure newton was high 24/7...

  66. Gilberto Francisco
    Gilberto Francisco
    8 ditë më parë

    U got me a little hungry

    8 ditë më parë

    Do a video on ramanujan infinity series please ❤️❤️

    8 ditë më parë

    6:45 sanskrit (india)

  69. 『Ѷ』
    8 ditë më parë

    so anybody eating those pizza?

  70. steveshadforth
    9 ditë më parë

    It’s not „on“ it’s OVER ie 1 over 3, not 1 ON 3

  71. Rangel Ramos
    Rangel Ramos
    9 ditë më parë

    I don't understand it 😵

  72. Abhinav
    9 ditë më parë

    after learning differentiaition and integration, i finally understand it i love pure mathematics

  73. jack russell
    jack russell
    10 ditë më parë

    In reality, there is no such thing as a circle. Only approximations to circles. That's because in the material world, any circle you make or is made, is made up of particles with finite size. They may be extremely small, but are still finite. even when speaking of electromagnetic fields, there are quantum nodes that are distinct entities. Thus all figures that look like circles are really polygons of n sides where n < infinity. That means the ratio of perimeter to radius is not fixed, but varies as n. The fact that pi is an irrational number should have been a clue from the beginning. Mathematics, in fact, is only a simplified model of reality. There are no infinitely small objects called points, or lines made up of these imaginary objects of zero size, etc. Our math is a very good approximation that of course has been extremely useful to us, but sometimes when we slip into thinking that it is absolutely precise, we can get into difficulties.

  74. Pieter Geerkens
    Pieter Geerkens
    10 ditë më parë

    At 4:48 Did the poor mason who inscribed "1415926**3**35" instead of "1415926**5**35" have to refund any of the purchase price for that error?

  75. Mr.Bill.Fold
    10 ditë më parë

    I was just wondering, what happened to all those pizzas?

  76. roebi
    10 ditë më parë

    Excellent video! However, way more than a transformation of Pi... great explanation of Newton's expansion / insight into the binomial theorem and Pascal's triangle =)

  77. Sarthak Vishwakarma
    Sarthak Vishwakarma
    10 ditë më parë

    That's why ,we say smart work is better than hard work !

  78. Shraboni Pal
    Shraboni Pal
    10 ditë më parë

    *People talk about Newton cause he labelled hisname on science, but no one talks about Bhaskaracharya, because he worshipped science...*

  79. Muhammad Ahsan Khan
    Muhammad Ahsan Khan
    10 ditë më parë

    This is magical

  80. Levi Matthews
    Levi Matthews
    11 ditë më parë

    Each and every one of us deserves a pizza for watching this

  81. Kevin Luo
    Kevin Luo
    11 ditë më parë

    pineapple pizza is great. fight me.

  82. David Sutton
    David Sutton
    11 ditë më parë

    Mind blown!

  83. Mehmet A.
    Mehmet A.
    11 ditë më parë

    Pizza's just gone cold.

  84. Mr Steele
    Mr Steele
    11 ditë më parë

    At 23 I was just trying to work out a formula to pay my student debt...

  85. S
    11 ditë më parë

    How do you know how many decimal places it is correct to if that’s the best algorithm it came out during that time? Does that mean there was another algorithm that’s even better?

    1. S
      11 ditë më parë

      @MuffinsAPlenty thank you so much for your explanation. I understand now

    2. MuffinsAPlenty
      11 ditë më parë

      For the Archimedean method (polygons inside and outside of the circle), well... Archimedes didn't have decimal notation, so he didn't use decimal places. (Decimal notation as we know it today didn't really exist until the 16th century CE.) However, if you were to try to do it, you would do it like this: the polygon _inside_ the circle has a smaller perimeter than the circle, and the polygon _outside_ the circle has a larger perimeter than the circle. Therefore, you get an upper bound and a lower bound for pi. If both your upper bound and lower bound agree to 3 decimal places, for instance, then you know pi must have those same 3 decimal places. Now, for Newton's technique, that's a little bit trickier! What it essentially boils down to is checking how big later terms in the series are and understanding that the series "converges". If the later terms could only add up to give you a value of, say, 0.00002, then you know your approximation is correct up to 3 decimal places. If you want to learn more about this technique, you can look up the "Alternating Series Estimation Theorem" which is one test for a certain type of series. But there are other estimation theorems for different types of series.

  86. Aniket Singh
    Aniket Singh
    11 ditë më parë

    I found a way to calculate value of pi with increasing precision. The formula is Pi = Lim{(n/2).sin(360/n)} as n -> infinity. For variety, I have another formula:- Pi = Lim{n.sin(180/n)} as n -> infinity. Both these formulae don't give same results for a specific value of but they give values closer to the Pi given by calculators if you keep increasing the value of n.

    1. Aniket Singh
      Aniket Singh
      10 ditë më parë

      @Релёкс84 Still, we can use a calculator 😋. Even though most calculors give the value of pi but using a formula to find it is more satisfying.

    2. Релёкс84
      11 ditë më parë

      But then you run into the problem of calculating sin with precision. It's very easy to calculate powers of x, but sin(x) is much harder.

  87. T
    11 ditë më parë


  88. PowerKing
    12 ditë më parë

    Great video...Love from India

  89. Conner
    12 ditë më parë

    Pi's round, cornbread's square..

    12 ditë më parë


  91. yakety yak
    yakety yak
    12 ditë më parë

    now they discovered that math is racist... how about that

    1. yakety yak
      yakety yak
      12 ditë më parë

      @nothing to see here move along loll just look it up lol

    2. nothing to see here move along
      nothing to see here move along
      12 ditë më parë

      lol what

  92. Patrick Prafke
    Patrick Prafke
    12 ditë më parë

    lol, my Grandpa to the rescue again!

  93. 51er
    12 ditë më parë

    Didn’t know I’d need to know that but now I’m smarter, thank you 👍

  94. Lucifer X
    Lucifer X
    12 ditë më parë

    how comes zero??????????????????????

  95. Vicevilla
    12 ditë më parë

    that pizza lookd good af ngl

  96. David Spain
    David Spain
    12 ditë më parë

    So great... Such a simple thing he did but so many ramifications to it! When I was younger I could have followed you easily but I'm going to have to go back and study the video again. We were told these infinite series in math class but nobody ever explained why they did what they did... I thought it was so amazing that someone did this, had such insight, but all they were doing was "playing" with the binomial theorem...

    12 ditë më parë

    Holy moly I’ve got to learn math, this looks so cool.

  98. Suchetan Majhi
    Suchetan Majhi
    12 ditë më parë

    Dhin terekete dhum tanana

  99. Félix Bélair
    Félix Bélair
    12 ditë më parë

    Theres a mistake at 14:17. the x^9 term should be divided by 9 and not over 8. reverse power rule

  100. greggy A
    greggy A
    12 ditë më parë

    I wonder...How many of the more than 3 million viewers....Really understand this