Making sense of irrational numbers - Ganesh Pai

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  • Опубликовано: 23 дек 2024

Комментарии • 1,3 тыс.

  • @milyon8910
    @milyon8910 5 лет назад +4154

    oh my goodness i just realized that "rational" means it can be expressed in ratios. I thought mathematicians just didn't think the numbers made sense.

    • @sheena_.
      @sheena_. 5 лет назад +78

      😭😂

    • @santripta
      @santripta 5 лет назад +60

      Same

    • @Boog1137
      @Boog1137 4 года назад +59

      Took me a while to make this connection too

    • @IMVeer0072
      @IMVeer0072 4 года назад +19

      Peter Griffin moment

    • @Its_Pritam_
      @Its_Pritam_ 4 года назад +15

      WTF! Same

  • @XxUginxX
    @XxUginxX 5 лет назад +1093

    Hippasus' colleagues punished him for discovering irrational numbers? Wow, that's truly irrational!

    • @commmander64
      @commmander64 5 лет назад +14

      Honestly if i where during that time i would think of the gods and their believers a bit LESS in value since they can't handle the truth of Hippasus's work. Ironically that would make me have the same impiety i guess.

    • @noammosek1319
      @noammosek1319 3 года назад +11

      Peek comedy

    • @quantumbracket6995
      @quantumbracket6995 3 года назад +2

      314 likes nice

    • @buzyparticals3753
      @buzyparticals3753 2 года назад

      SUS HIPPO

    • @randompoop1565
      @randompoop1565 2 года назад

      No, he deserves it!!!

  • @-.._.-_...-_.._-..__..._.-.-.-
    @-.._.-_...-_.._-..__..._.-.-.- 8 лет назад +546

    _"I'm sure that I will always be_
    _A lonely number like root three_
    _The three is all that's good and right,_
    _Why must my three keep out of sight_
    _Beneath the vicious square root sign,_
    _I wish instead I were a nine-_
    _For nine could thwart this evil trick,_
    _with just some quick arithmetic_
    _I know I'll never see the sun, as 1.7321_
    _Such is my reality, a sad irrationality_
    _When hark! What is this I see,_
    _Another square root of a three_
    _As quietly co-waltzing by,_
    _Together now we multiply_
    _To form a number we prefer,_
    _Rejoicing as an integer_
    _We break free from our mortal bonds_
    _With the wave of magic wands_
    _Our square root signs become unglued_
    _Your love for me has been renewed"_
    -Harold & Kumar Escape from Guantanamo Bay (2008)

    • @sophiejones7727
      @sophiejones7727 8 лет назад +9

      best part of that movie :D

    • @rahulshah9993
      @rahulshah9993 8 лет назад +28

      Sorry to disappoint you but square root of 3 isn't lonely at all , infact there are infinitely many numbers as close to it as you want 😊

    • @somebodyonce6063
      @somebodyonce6063 5 лет назад +7

      (clapping )

    • @allenaegarcia3635
      @allenaegarcia3635 5 лет назад +4

      David S. Cats eyes nebula.. nice

    • @TurnipBoy666
      @TurnipBoy666 5 лет назад +3

      whoa

  • @xmaxwell7987
    @xmaxwell7987 8 лет назад +2765

    This should've been titled "Rationalizing Irrational Numbers".

    • @dragosdragos3961
      @dragosdragos3961 6 лет назад +13

      lol

    • @flamingpi2245
      @flamingpi2245 4 года назад +24

      Omg what a missed opportunity

    • @trevorallen3212
      @trevorallen3212 4 года назад +10

      2/sqrt(2)=sqrt(2)

    • @theobserver314
      @theobserver314 4 года назад +2

      @@trevorallen3212 0_o

    • @trevorallen3212
      @trevorallen3212 4 года назад +1

      @@theobserver314 2/(cubicroot(4))=cubicroot(2)
      2/(4throot(8))=4throot(2)...
      I can go on but, it be pain to type so here is formula for equivalent irrational numbers of nthroots.
      Base/(nthroot(Base^(n-1)))=
      nthroot(base)

  • @FlyAVersatran
    @FlyAVersatran 5 лет назад +112

    Great explanation.
    I have a degree in applied mathematics and have never heard this pontificated so well.
    Thank you.

    • @tarunkumarcs2374
      @tarunkumarcs2374 2 года назад +1

      @@harshitabhagat8467 ig cbse has it in 9th also

    • @NOOBCRASTINATOR69
      @NOOBCRASTINATOR69 2 года назад +1

      @@tarunkumarcs2374 ICSE in 7th grade.. I was like wait I've proved that!!!

  • @Stray0
    @Stray0 8 лет назад +3928

    > "Are you the square root of 2?"
    > "Because I feel irrational around you."
    How to flirt. :D

    • @ASOUE
      @ASOUE 8 лет назад +94

      Meow

    • @ThomasNimmesgern
      @ThomasNimmesgern 8 лет назад +54

      +Cat Are you hungry?

    • @cortster12
      @cortster12 8 лет назад +12

      +Stray Pay Or, they will think you are calling them fat.

    • @rishovmondal1524
      @rishovmondal1524 8 лет назад +8

      howard wallowitz,

    • @stellalpina
      @stellalpina 8 лет назад +6

      +cortster12 Definitely. I guess it would only work with mathematicians. :P

  • @FrancisACNH
    @FrancisACNH 5 лет назад +231

    “The gods did not appreciate being contradicted”
    They’re just like parents and r/dankmemes members: They destroy whoever disagrees with them, even when losing an argument

    • @sriramradhakrishna878
      @sriramradhakrishna878 4 года назад +10

      It's pretty much all of Reddit at this point tbh

    • @FrancisACNH
      @FrancisACNH 4 года назад +3

      Sriram Radhakrishna Yeah, mostly dankmemes tho

    • @Blurrybob
      @Blurrybob 4 года назад +2

      Can't help but agree

    • @edwardcap7
      @edwardcap7 27 дней назад

      "heresy"

  • @adamn7409
    @adamn7409 5 лет назад +1353

    Hippasus: *discovers irrational numbers*
    God: wait that’s illegal

    • @iceenderman-fm4kb
      @iceenderman-fm4kb 4 года назад +10

      Let √4=p/q(here,p and q don't have common factor)
      q√4=p
      4(q^2)=p^2
      So,as q^2 times 4 is p^2 we can say that p=4a
      4(q^2)=(4a)^2
      4(q^2)=16a^2
      q^2=4a^s
      Does, this means√4 is irrational number

    • @thesushi1947
      @thesushi1947 4 года назад +11

      @Agrim Verma
      Assume √4 = p/q where p and q are coprime and are both integers
      q√4 = p
      4q² = p²
      Already we can find two coprime integers, with q = 1 and p = 2 (or any pair where p =2q for that matter), to prove it so we can conclude that √4 can be written as 2/1 as those numbers satisfy our modified equation and so confirm the original assumption. Another variable wouldn't be needed to solve the equation like you had, but one was used in the video to illustrate that p was even rather than specifically a multiple of the radicand.
      This same reasoning can't work with √2 because no coprime integers can satisfy 2q² = p², and the same method can be applied to √n by finding (or proving that there aren't) any coprime integers to satisfy nq² = p².

    • @Muhammed_English314
      @Muhammed_English314 4 года назад +15

      @@iceenderman-fm4kb what you have done wrong is: 4(q^2)=p^2 means (p) is even but what you have done is assuming that p=4a since (a) is an integer 4a CANNOT be equal to 2 which means that you eliminated the only possible answer (2) what you must do instead is: let p=2a(a is an integer) then 4(q^2)=(2a)^2 => 4(q^2)=4(a^2) => q^2=a^2 => q=a => √4=p/q=2a/a=2 notice that you can't prove that q is odd or even since it's equal to an integer (a) which can be either even or odd and it turns out that it's odd(1)

    • @NewCalculus
      @NewCalculus 4 года назад +2

      He couldn't have because "irrational numbers" don't exist in mathematics. Chuckle.

    • @MrTeen-ul7yc
      @MrTeen-ul7yc 4 года назад +2

      @@iceenderman-fm4kb Absolutely not! The implication from Step 3 to Step 4 is incorrect. 4(q^2)=p^2 does not imply p=4a. Consider values p = 6 and q = 3. Then q^2 = 9 and 4(q^2) = 36 = p^2. But p is 6, which is not divisible by 4. Notice how q itself became a factor of p which already contradicts the initial assumption. In general if the square of a number is divisible by 4 then that does not necessarily imply that the number is also a multiple of 4. Any number that is congruent to 2 or 0 mod 4 will become congruent to 0 mod 4.
      What you've proved is not that √4 is irrational. Interestingly, the contradiction you've arrived at proves that the first assumption is false. That is p and q must have common factors specifically in this case that either p | q or q | p. which can then be reduced to the trivial form where the denominator is 1, at which point you're just saying n = n/1.

  • @VikasVJois
    @VikasVJois 8 лет назад +693

    Nice proof and illustration/animation

    • @ASOUE
      @ASOUE 8 лет назад +5

      Meow

    • @InfinityLearn_NEET
      @InfinityLearn_NEET 8 лет назад +20

      Thank you Vikas, our founder collaborated with TED-Ed to create this lesson :)

    • @YathishDhavala
      @YathishDhavala 8 лет назад +4

      Why is Hippasus's time shown as 8 BC? He belonged to 5th Century BC.

    • @sauceaddict9569
      @sauceaddict9569 5 лет назад +1

      Don't Memorise wierd flex but ok😂😂

    • @elee2968
      @elee2968 5 лет назад

      Not their proof.

  • @AnantMall
    @AnantMall 8 лет назад +304

    "instead of adhering to norms decided to prove it was something new" In that world at that time doing this would take immense courage!

  • @adityakhanna113
    @adityakhanna113 8 лет назад +1528

    the lesson by "Ganesh Pi"

    • @salehsalem9638
      @salehsalem9638 8 лет назад +147

      +Wizard Johnson I don't think that was the reference or joke there. The original commenter spelled the last name wrong deliberately to show the irrational... I don't even know why I'm explaining this

    • @ASOUE
      @ASOUE 8 лет назад +40

      Meow

    • @InfinityLearn_NEET
      @InfinityLearn_NEET 8 лет назад +106

      Good one Aditya! I will make sure our founder reads this comment :)

    • @kronk5866
      @kronk5866 8 лет назад +18

      Illuminati confirmed

    • @RoyalDog214
      @RoyalDog214 7 лет назад +42

      Ganesh 3.141592653589

  • @igb5551
    @igb5551 8 лет назад +62

    Please, never stop doing this videos, they are too good

  • @Puggalug
    @Puggalug 8 лет назад +2451

    Good, now cover negative numbers, imaginary/complex numbers, hyperreals, surreals, and split octonians!

    • @rnyjizzle
      @rnyjizzle 8 лет назад +40

      Well square root of a negative number should be quite obvious to realise

    • @ptyamin6976
      @ptyamin6976 8 лет назад +46

      What is a split octonian?

    • @GoldenKingStudio
      @GoldenKingStudio 8 лет назад +132

      Something he most likely read on Wikipedia. You don't need to worry about it, I doubt he could explain it to you. (If the guy actually knows it, I don't mean to offend him, I was just making a joke because he rattled off a list of semi-related math terms that all happen to be linked together in Wikipedia. I wouldn't have known about many of those concepts without Wikipedia, so I am not trying to sound better.)
      An octonion (he spelled it incorrectly) is an extension of complex numbers into an 8 dimensional number line, like how real numbers are on one number line, and complex numbers have two number lines, octonions have 8 that represent them. They have lots of special properties that make them interesting to mathematicians, and split octonions are similar to octonions in that they are 8 dimensional, but they are made by different rules, to put it simply. Like how complex numbers have a + bi, where i is the square root of 1, split octonions have 8 parts to them. I don't really know that much about them or why these particular definitions are useful, but there is a basic rundown. There is a method of construction that allows for the generation of lots of arbitrary algebras, but this particular one must have some special properties.

    • @Puggalug
      @Puggalug 8 лет назад +73

      +GoldenKingStudio Yes, you're partially right. I did spell octonion wrong, and I wouldn't have been able to explain them. But I didn't get those concepts from Wikipedia - I got them from an awesome RUclipsr that combines drawing and math named Vihart, in a video explaining why 0.9(repeating) is equal to 1.

    • @GoldenKingStudio
      @GoldenKingStudio 8 лет назад +37

      Puggalug That was a very good video, yes. Glad to see another fan.

  • @minhaslpu
    @minhaslpu 8 лет назад +5

    I am a tutor and was teaching number systems to my students. They couldn't understand much and then TED made this Video(so GLAD) and i showed this video to them and believe me, they understood everything :)
    Thanks TED for making our life easier :)

    • @InfinityLearn_NEET
      @InfinityLearn_NEET 8 лет назад +1

      Great to hear that Rajat. Our founder was the educator for this lesson. Thank you :)

  • @margaretbonassar709
    @margaretbonassar709 4 года назад +45

    “The gods cursed a human for a proof of contradiction” was not the geometry hot take I was expecting today but it is welcome nonetheless

  • @JoseAngelC
    @JoseAngelC 8 лет назад +15

    Great! finally another narrator!

  • @dsc4178
    @dsc4178 7 лет назад +9

    It's an interesting paradox: the length of the hypotenuse is always a set, specific length, and the diameter and circumference of a circle are too; yet irrational numbers are not in any real way a specific length.

  • @BugCatLove
    @BugCatLove 8 лет назад +116

    Well played, Hippasus.

    • @ASOUE
      @ASOUE 8 лет назад +2

      Meow

    • @XenophonSoulis
      @XenophonSoulis 6 лет назад +3

      Hippasus was NOT punished by any god, but by his fellow Pyrhagoreans.

    • @syncradar
      @syncradar 10 месяцев назад

      SUS

    • @kfarbarata
      @kfarbarata 7 месяцев назад

      @@XenophonSoulis when u lidering a cult, ppl see u as god, lol, ask donnald duck 'bout his trip in mathmagic land

  • @RK-ep8qy
    @RK-ep8qy 8 лет назад +680

    I'm feeling a little…irrational now

  • @nuetralkitty58
    @nuetralkitty58 2 года назад +2

    3:43 That's a square root spiral right? I had an art integration activity in maths for that. It's seriously amazing how numbers can be connected to concepts like art, music, cosmology etc. I wonder if we will ever find a way to define irrational numbers? There IS a lot of freedom in maths after all.

  • @VEROTIKAA
    @VEROTIKAA 8 лет назад +117

    wow omg really so beautifully put and explained in such simplistic mode that never once had i even thought to put it like that but now that i see it it makes sense wow gteat video thank you from the bottom of my heart even my 7 yearr old understood thank you

  • @jonbenge2383
    @jonbenge2383 8 лет назад +6

    This made so much more sense than when I was in high school. I wish my teacher had explained concepts like this much more clearly instead of saying "Because they are not rational"; probably would have gotten a better grade...
    Thanks Ted!

  • @Piyushks02
    @Piyushks02 7 лет назад +89

    The Animation was so Dope!

  • @Rav3r916
    @Rav3r916 8 лет назад +6

    wow. the animation is amazing. really great for visual learners.

  • @TheGamerzXChannel
    @TheGamerzXChannel 8 лет назад +6

    Great abstract video 🙂 please make more of them, they are the juice for my brains!

  • @lazybacon5282
    @lazybacon5282 5 лет назад +22

    0:27 The man has blonde hair is doing the floss

  • @W.M.-
    @W.M.- 7 лет назад +10

    really well made video, was hoping for a geometrical proof though seeing as algebra wasn't discovered in 5 BC

  • @lexinaut
    @lexinaut 8 лет назад +2

    Quite nicely presented and relevant. As an educator, I still find that irrational numbers make people . . . nervous! However, from my reading, no one apparently knows precisely which irrational number Hippasus either proved was irrational, or revealed was irrational (if someone else proved it). Root 2, of course, is a very likely candidate, since it is present in a simple unit square. For this reason, I commonly call Root 2 "the Monster in the Unit Square (with comical yet serious intent). I agree! We should appreciate the adventure of irrational numbers rather than excessively fearing them! Mathematics is a great adventure indeed! Have a great day!

  • @djr5995
    @djr5995 8 лет назад +148

    Making *sense* of *irrational* numbers
    . . . . . I see what you did there

    • @iceenderman-fm4kb
      @iceenderman-fm4kb 4 года назад +1

      Let √4=p/q(here,p and q don't have common factor)
      q√4=p
      4(q^2)=p^2
      So,as q^2 times 4 is p^2 we can say that p=4a
      4(q^2)=(4a)^2
      4(q^2)=16a^2
      q^2=4a^s
      Does, this means√4 is irrational number because here ,
      2q=p
      And
      q=2a
      And this means both p and q are even and have as common factor which cannot be true since contradicts the fact that p and q cannot have a common factor

  • @Saj1037_
    @Saj1037_ 4 года назад

    It’s insane how smart one would have to be so long ago to figure this out. Creating/discovering math is one of the most fascinating things mankind is capable of.

  • @legofan431
    @legofan431 8 лет назад +30

    very awesome animations, I really learned somehting today that 13 years of school didn't teach me

    • @ASOUE
      @ASOUE 8 лет назад +1

      Meow

    • @XenophonSoulis
      @XenophonSoulis 6 лет назад

      Woof

    • @iceenderman-fm4kb
      @iceenderman-fm4kb 4 года назад

      Let √4=p/q(here,p and q don't have common factor)
      q√4=p
      4(q^2)=p^2
      So,as q^2 times 4 is p^2 we can say that p=4a
      4(q^2)=(4a)^2
      4(q^2)=16a^2
      q^2=4a^s
      Does, this means√4 is irrational number because here ,
      2q=p
      And
      q=2a
      And this means both p and q are even and have as common factor which cannot be true since contradicts the fact that p and q cannot have a common factor

    • @eladidu3
      @eladidu3 3 года назад

      @@iceenderman-fm4kb "as q^2 times 4 is p^2 we can say that p=4a" no, that is false

  • @oferzilberman5049
    @oferzilberman5049 4 года назад +1

    I was in a group of 3 more friends and we called ourselves "3 guys and the square root of negative 2" (me being referred to as the square root of negative 2) and we all just loved this name, It was awesome.

  • @Supremebubble
    @Supremebubble 8 лет назад +46

    Even more interesting is that it is impossible to plot the number pi on the real number line with only using ruler and compass. Same goes for the number e. These are called transcendental numbers however the proof is rather complicated.

    • @ASOUE
      @ASOUE 8 лет назад +1

      Meow

    • @hawkecrail5186
      @hawkecrail5186 8 лет назад +4

      Well... You could technically plot it it would just be not exactly perfect

    • @hyrekandragon2665
      @hyrekandragon2665 8 лет назад +10

      It has to be exact though. If you can't do it with absolute and exact precision using a straight edge and a compass, then it is transcedental.

    • @Arkalius80
      @Arkalius80 7 лет назад +4

      It's not hard to prove pi is transcendental after you prove e is (which is quite hard). It is known that a transcendental number raised to an algebraic power other than 0 will produce a transcendental number. We know that e ^ (i * pi) = -1, and we know e is transcendental and -1 is algebraic. So, that means i * pi must not be algebraic. Since i is algebraic, pi must be transcendental.

    • @martind2520
      @martind2520 7 лет назад +4

      @Alex Chuoy
      That is incorrect. the cube root of 2 is not transcendental but cannot be constructed using compass and straight-edge either.
      All transcendental numbers cannot be constructed but that does not mean that all numbers that cannot be constructed are transcendental.

  • @hrag03
    @hrag03 2 года назад +1

    Wow, really so beautifully, clearly put and explained in such simplistic way. My teachers used to tell me that I should always "remember" that sqrt(2) is irrational and cannot be shown in a rational way. But after watching the proof, now everything started to make sense. I wonder if every problem has a solution, then why can't this irrational numbers have solutions too? Also there may be other numbers in the infinite set that are in a similar condition to sqrt(2) that cannot be proven.

    • @Grizzly01-vr4pn
      @Grizzly01-vr4pn Год назад

      There certainly are.
      At present, it is not known (and therefore unproven) if π + e, πe, π/e, π^e, π^√2 or ln π are irrational or not.

  • @V3nky_
    @V3nky_ 3 года назад +3

    3:26 Ohhh!! That Activity did in School 👍🏼

  • @thompson5085
    @thompson5085 7 лет назад +2

    This is really cool! We're learning about Pi in class and I'm going to show this to my teacher!

  • @niory
    @niory 8 лет назад +34

    I have such a bad relationship with math and feel sorry for it

    • @ASOUE
      @ASOUE 8 лет назад +2

      Meow

    • @XenophonSoulis
      @XenophonSoulis 6 лет назад +1

      +Cat Woof
      +sara meachel At least you know what you lose (unlike others who don't know that).

    • @joshua50101
      @joshua50101 6 лет назад +6

      does it remind you about your "x" since you don't know "y" she left you?

  • @BangMaster96
    @BangMaster96 6 лет назад +1

    I wish school taught us math this way, it's so much more fun to learn this way, and now i actually want to learn about square roots and irrational numbers.

  • @nabila7628
    @nabila7628 5 лет назад +26

    So I have finally found one of the inventors of math
    *discreetly adds him to hit list *

    • @Morningstar_37
      @Morningstar_37 3 года назад

      @QuantumRat2005 Legends say they already have a time machine. And I believe these legends because they come from extinct cultures all around the world, with millenials old stones spelling the name "Nabila" in English

    • @verdessence
      @verdessence 3 года назад

      @MthYsdAsd throw him with statue of numbers

  • @BagaJr
    @BagaJr 8 лет назад +3

    3:42 When all of those triangles are drawn showing all the roots of integers, it kind of reminds me of something, but I can't quite remember what... is that from some other important math concept or am I just crazy?

    • @ArmandoMachado92
      @ArmandoMachado92 8 лет назад +2

      +Baga Jr I saw it too. You are talking about the Fibonacci Sequence :)

    • @BagaJr
      @BagaJr 8 лет назад

      Armando Machado I know each hypotenuse is the square root of a whole number and the outside edges are all 1, but I don't see where the fibonacci numbers come into play. What am I missing here?

    • @morethejamesx39
      @morethejamesx39 8 лет назад

      +Baga Jr you're not thinking of complex numbers and how you can multiply them and find the product graphically using triangles are you?

    • @InfinityLearn_NEET
      @InfinityLearn_NEET 8 лет назад

      It's the Spiral of Theodorus :)

    • @ArmandoMachado92
      @ArmandoMachado92 8 лет назад

      Baga Jr I made a mistake. I totally forgot of what Don't Memorise said! The Spiral of Theodorus.

  • @basicnpcc
    @basicnpcc 8 лет назад +209

    Discrete mathematics at its finest.

    • @ASOUE
      @ASOUE 8 лет назад +2

      Meow

    • @ptyamin6976
      @ptyamin6976 8 лет назад +1

      What is discrete math?

    • @basicnpcc
      @basicnpcc 8 лет назад +34

      PT Yamin A sub-set of mathematics like trigonometry or algebra. Discrete math is where the proofs come from for our mathematical equations. In math, we need to prove everything that we do. Through methods like induction proofs, we can do this. For example, you can prove that the square root of two is irrational like in the video. If you want to be a Computer Science major in college or maybe a Math major, this class will probably be required.

    • @willnewman9783
      @willnewman9783 7 лет назад +14

      This whole video has nothing to do with discrete mathematics.

    • @hewhomustnotbenamed5912
      @hewhomustnotbenamed5912 7 лет назад

      Lord Gaben is that you if so please answer my prairs release left 4 dead 3 half life 3 and the pyro update for tf2

  • @TrueInvisible
    @TrueInvisible 8 лет назад +309

    conclusion doing math = you go to hell , to hell with math "literally"

  • @imaan2164
    @imaan2164 3 года назад +1

    3:59 i am pretty sure pi is how many times the RATIO goes into the circumference and NOT diameter as she said

    • @Anon101sss
      @Anon101sss 3 года назад +2

      You're wrong. π=c/d

  • @memine226
    @memine226 8 лет назад +7

    irrational number like square root 2 is fine. but the real problem is Transcendental number. it is NOT a root of a non-zero polynomial equation with rational coefficients. We can't use a nice simple formula to express it. Except using a symbol like pi or e, not really much we can do... Yet they are so useful and powerful!

    • @mmae8266
      @mmae8266 6 лет назад +2

      Me Mine im first befor that *CAT*

  • @garydunken7934
    @garydunken7934 8 лет назад

    Finally finally finally.... a good explanation if irrational numbers. Well done.

  • @LeHoangBac
    @LeHoangBac 6 лет назад +5

    3:44 Ooh, the golden ratio.

    • @crweewrc1388
      @crweewrc1388 Год назад

      I think it's called The Spiral Of Theodorus.

  • @BlackStarrSoul
    @BlackStarrSoul 8 лет назад +2

    3:44
    I almost fell out of my chair. That is so amazing!! I didn't expect that, to be honest.

    • @InfinityLearn_NEET
      @InfinityLearn_NEET 8 лет назад +1

      It's called the Spiral of Theodorus. Sounds scary doesn't it?

  • @experienceeverything4841
    @experienceeverything4841 3 года назад +12

    Only Indian students will know that we have the proof of this in our class 10 syllabus.

  • @seshasayeesudharsan7938
    @seshasayeesudharsan7938 4 года назад +1

    This is such an awesome way to teach irrational numbers

  • @cletuslopes159
    @cletuslopes159 8 лет назад +11

    The irony That the person who made this videos is ganesh Pai(pie)

    • @ASOUE
      @ASOUE 8 лет назад

      Meow

    • @ankurama42
      @ankurama42 8 лет назад +5

      how is that irony?

    • @hijack69
      @hijack69 8 лет назад +8

      His surname seems a bit irrational

    • @InfinityLearn_NEET
      @InfinityLearn_NEET 8 лет назад

      Yes, and Ganesh Pai/Pie/Pi loves math :)

  • @jonahcarter196
    @jonahcarter196 6 лет назад

    2 points response to Making sense of irrational numbers-Ganesh Pai The things I learned from this video is the history of irrational numbers and better ways to solve irrational numbers. the message the narrator was trying to send out was decimals and ratios are only ways to express numbers. What I was thinking about while watching this video are ways to solve irrational numbers and how I can understand it. I likes that at the very beginning she mentioned the philosopher Hippasus and his discovery towards mathematics.

    • @terrariaman8454
      @terrariaman8454 5 лет назад +1

      Your comment has been posted 4 times. Stop it.

  • @diba4707
    @diba4707 5 лет назад +3

    Came here for a Math’s video ,
    Got a history lecture instead

  • @alfonsogarcia608
    @alfonsogarcia608 2 года назад +1

    Lovely video, clear, concise and with subtle humour.
    Thank you!

  • @hithere-nk1ee
    @hithere-nk1ee 5 лет назад +7

    I watch all these ted-ed videos but never really understand them

    • @channel-wf1ev
      @channel-wf1ev 4 года назад

      try to "split" every explication to understand the video

  • @paerpo9577
    @paerpo9577 3 года назад +1

    Finally a comprehensible class🙄 Thnx 😁

  • @canilogin1730
    @canilogin1730 4 года назад +3

    The number "e", aka Euler's Number: "A M I A J O K E T O Y O U?"

  • @isaacdemoorea
    @isaacdemoorea 8 лет назад

    Did anyone at 3:43 thought about Tool, Lateralus? Anyone?

  • @BoredatroundSI
    @BoredatroundSI 8 лет назад +27

    can we appreciate the fact that the lesson is by ganesh 'Pi' :P

    • @nadiaxantho
      @nadiaxantho 8 лет назад +1

      I didn't notice that! :0

  • @YBouty
    @YBouty 6 лет назад

    Ted ed best RUclips channel ever I mean ever

  • @davidribosome4326
    @davidribosome4326 4 года назад +4

    video: anything times 2 is even
    me: 2.5 x 2
    video; wait thats illegal

  • @chronic295
    @chronic295 8 лет назад

    These lessons never dissapoint!

  • @abhijeettalukdar5004
    @abhijeettalukdar5004 3 года назад +3

    We also proved this
    I am a 10th standard student from India

  • @prof.einsteindarcy3951
    @prof.einsteindarcy3951 8 лет назад +2

    Great job guys! I have a much clearer understanding of irrational numbers now! Wish all my classes were like this:)

  • @polaroidstyles9348
    @polaroidstyles9348 8 лет назад +4

    Love this

  • @yuhyunlee1095
    @yuhyunlee1095 6 лет назад

    This video is much more interesting and attractive than mathematic classes i've got in korea. I wanna show it to my friends who is unfamiliar with mathematics.

  • @jordantan2543
    @jordantan2543 8 лет назад +29

    now i know where the word rational comes from

    • @religionbuster7180
      @religionbuster7180 8 лет назад

      Seriously dude? You should go back prep

    • @eugenekudlanov3128
      @eugenekudlanov3128 8 лет назад +1

      +Jordan Tan
      It comes from ur mum because she was telling me to talk mathematical to her

    • @ASOUE
      @ASOUE 8 лет назад +1

      Meow

    • @BionicKing
      @BionicKing 8 лет назад +3

      Rational comes from the Latin, "ratio," meaning reason. How the heck did you figure that out just by watching this video?

    • @soggytoasty
      @soggytoasty 8 лет назад

      LOL SAME. i always thought rational came with the word ration and ration means a portion of food so i thought its just a unique word of its own

  • @varadakolkar229
    @varadakolkar229 3 года назад +1

    "Instead of giving up finding ratio, he decided to prove it couldn't be done.. "
    I am now inspired

  • @Cloiss_
    @Cloiss_ 7 лет назад +9

    This is a cool version of the proof, but it's not how Hippasus concluded this... there was no algebra in his time

  • @victoriawomack6512
    @victoriawomack6512 6 лет назад

    2 points response to Making Sense Of Irrational Numbers-Ganesh Phi
    What I took from this video is about ratios and irrational numbers and how they differ. The narrators message from this video is that decimals and ratios are the only ways to express numbers . I was thinking about how to solve irrational numbers. I liked the beginning when the narrator mentions The philosopher Hippsaus and his discovery towards mathematics:

  • @kaylinealsen2651
    @kaylinealsen2651 5 лет назад +3

    Narrator: "Don't be afraid to explore the impossible."
    Me: *fails Math test*

    • @d.akiehs
      @d.akiehs 5 лет назад +2

      Kayline Alsen same 😭

    • @ucbinhcam3871
      @ucbinhcam3871 5 лет назад +2

      Me too. Oh! I hate Maths...

  • @antontonable
    @antontonable Год назад

    @3:44 that extenuation of triangles looks like a fibonacci spiral... is it?

  • @chris_tzikas
    @chris_tzikas 8 лет назад +13

    I feel clever now cause I knew the answer lol

    • @NewCalculus
      @NewCalculus 4 года назад

      I bet you didn't!
      www.linkedin.com/pulse/%25CF%2580-%25CE%25B4%25CE%25B5%25CE%25BD-%25CF%2583%25CE%25B7%25CE%25BC%25CE%25B1%25CE%25AF%25CE%25BD%25CE%25B5%25CE%25B9-%25CE%25B1%25CF%2581%25CE%25B9%25CE%25B8%25CE%25BC%25CF%258C%25CF%2582-john-gabriel/

    • @brainded653
      @brainded653 3 года назад

      @@NewCalculus shut up

  • @D0GBOOT
    @D0GBOOT 5 лет назад +2

    Thank you for making this so easy to understand, it was very helpful!

  • @rachanabaditha9618
    @rachanabaditha9618 7 лет назад +29

    We learned this in school, and so I proved *Root 4* is irrational using the same method...
    ...my teacher was not pleased

    • @joijoi8782
      @joijoi8782 6 лет назад

      Substitute p to 4 and q to 1 through the video

    • @devanshkamra5652
      @devanshkamra5652 6 лет назад +3

      I know what you did......but there is one mistake.... You may have came across a result where you got 4q^2=p^2, from here you may have deduced that p must have 4 as its factor. But this law only applies to prime numbers. If p^2 has x as factor then p also has x as factor ONLY IF x is a prime number (try it out yourself)

    • @RahulMaru3507
      @RahulMaru3507 6 лет назад

      root 4 is 2

  • @scitwi9164
    @scitwi9164 7 лет назад +1

    It only takes one look into Euclid's "Elements" to ascertain that the Pythagoreans indeed knew all well about the existence of irrational numbers and they didn't treat is as something that derails their philosophy. They also used ratios in a different way than we do nowadays: more like algebraic ratios than ratios of whole numbers only. And Hippasus's death was not a punishment for him discovering irrational numbers, but for leaking the secret to wider public.

  • @jeromeorji1057
    @jeromeorji1057 8 лет назад +3

    When does Life of Ganesh Pai come out?

  • @fatgamer919fan4
    @fatgamer919fan4 3 года назад

    This was a lesson by ganesh pai, he was built for this video

  • @CsVipar4
    @CsVipar4 8 лет назад +3

    Great animation

    • @ASOUE
      @ASOUE 8 лет назад

      Meow

  • @cjfdnqkn4374
    @cjfdnqkn4374 3 года назад

    Let's stop and admire this wonderful lesson

  • @leonardohelveciodeoliveira5233
    @leonardohelveciodeoliveira5233 5 лет назад +3

    "Two times any number = an even number" what about 0.3 for an example

    • @samueltong8061
      @samueltong8061 5 лет назад +1

      Whole number

    • @maryroserivera7946
      @maryroserivera7946 5 лет назад +1

      can we get 1000 subscribers without content
      All decimals are even
      Because
      0.3/2 = 0.15

  • @finalislytan8342
    @finalislytan8342 6 лет назад

    Narration is done in a very good and clear way

  • @anveshasingh8672
    @anveshasingh8672 3 года назад +3

    I love pretending that I understand these videos!

  • @khai96x
    @khai96x 8 лет назад +2

    I always consider numbers (as well as other math concepts such as Infinity) as mathematical symbols which help us to caculate things. They don't really exist in reality but in our mind.

  • @spencerpoore5805
    @spencerpoore5805 8 лет назад +3

    Where is Anthony Anderson? I can't watch without his voice!!!

  • @pandora5560
    @pandora5560 5 лет назад +2

    to me math is complicated and hard and i cant do it. but i find it really *extremly* interesting is so interesting how everything relates to...EVERYTHING!

  • @catalonyking
    @catalonyking 8 лет назад +9

    please don't upload any video without subtitles ! please please please :(

    • @catalonyking
      @catalonyking 8 лет назад +2

      LagiNaLangAko23 but i don't understand all show .I am a novice in learning english

    • @babyfingers9874
      @babyfingers9874 8 лет назад

      you can check the subtitles by clicking the 'CC' button. It is found where you see three dots on top of each other

    • @catalonyking
      @catalonyking 8 лет назад

      Mikel Arenas but "CC" not available

    • @sophiejones7727
      @sophiejones7727 8 лет назад

      it's not available on this video.

    • @babyfingers9874
      @babyfingers9874 8 лет назад

      Oh, then that should put it on

  • @min11benja
    @min11benja 8 лет назад

    WOW! I never really understood irational numbers this well! Animation is a powerfull thing

  • @shrutigupta250
    @shrutigupta250 6 лет назад +3

    - Ganesh PAI
    Why has nobody commented about it?

    • @terrariaman8454
      @terrariaman8454 5 лет назад

      Dude loads of people have commented about it.

  • @___xyz___
    @___xyz___ 6 лет назад +1

    1:48 Wait, what? A Greek mathematician/philosopher in the 5th century BCE used letters from Latin to prove irrationality algebraically using expressions from common core math? Sounds legit.

  • @midnightshaddow7612
    @midnightshaddow7612 8 лет назад +10

    Hey guess you can say a lot in this world is made by numbers, specifially 1 and 0

    • @ASOUE
      @ASOUE 8 лет назад

      Meow

    • @jeromeeuler168
      @jeromeeuler168 8 лет назад +1

      Actually everything is.

    • @XenophonSoulis
      @XenophonSoulis 6 лет назад

      Woof

    • @alisonlaett9625
      @alisonlaett9625 6 лет назад

      @@XenophonSoulis +Ξενοφώντας Σούλης
      +Cat
      Why are you guys writing the same meow woof thing on every comment? Are you bots?

    • @XenophonSoulis
      @XenophonSoulis 6 лет назад

      @@alisonlaett9625 I'm trying to scare him/her, 'cause cats are afraid of dogs.

  • @shubhamg9495
    @shubhamg9495 4 года назад +2

    I know that even *π* can be *expressed* as a *ratio of irrationals just like Phi.* I can *visualise* this in my mind and I always got that the result to be *a sum of very complex numbers.* The only *problem* is that I am in *10th grade* so my *knowledge* is very *limited* but still I have a *theory* that *states* :-
    _Every number which can be geometrically constructed can be written in the forms of numbers either rational or irrational_
    _Just like Phi (1/2 + √5/2) and the diagonal of a square as √2_

  • @OmnipotentO
    @OmnipotentO 8 лет назад +18

    Until you try to divide by 0.

    • @ASOUE
      @ASOUE 8 лет назад +1

      Meow

    • @khorps4756
      @khorps4756 8 лет назад

      already did, the answer i got was...

    • @blabbityblah
      @blabbityblah 8 лет назад +1

      Can't tell if joking or serious. Please confirm.

    • @ESL1984
      @ESL1984 7 лет назад +2

      blabbityblah You can't divide by 0. Because if you could then let's assume it gives us a value like 3/0=a ok, then lets say 4/0=b so we move zero to the other side of each equation and we get that 4=0xb and 3=0xa we know that 0x(any number)=0 so 4=0 and 3=0 both don't make sense and also it implies that 4=3. All of this is nonsense, don't try to divide by 0 unless you are dealing with limits, that's completely another story.

    • @Multibe150
      @Multibe150 7 лет назад

      JoSe74248 However, there is a number that you can safely divide by 0: 0. If you divide 0/0, your ecuation becomes 0x=0, and any number can fill this requirement.

  • @aarthykanagarajan7912
    @aarthykanagarajan7912 8 лет назад

    how elegant and simple is this proof ?

  • @MoneyXJatt
    @MoneyXJatt 8 лет назад +3

    It's simple 2÷root 2 = root 2 lol 😁

    • @DekuStickGamer
      @DekuStickGamer 8 лет назад +14

      My God...he's done it...

    • @Heropadopa
      @Heropadopa 8 лет назад +1

      +Money Jatt I'm even more confused now.

    • @omkarchavan5940
      @omkarchavan5940 8 лет назад

      then what about that root 2 in denominator....???

    • @mouradqqch1767
      @mouradqqch1767 8 лет назад

      false. 2/sqrt (2) =/= sqrt (2)

    • @dirfgiS
      @dirfgiS 8 лет назад +4

      +Mourad Qqch Of course it is, it can also be written as 2^1/2^(1/2) = 2^(1-1/2) = 2^(1/2) = sqrt(2)

  • @danielclark1313
    @danielclark1313 6 лет назад +1

    Just like to point out that as beautiful as this proof is, this isn't a proof that the ancient Greeks would have known, as they didn't have algebra. Nor did they in fact use numbers like we think of today, rather they thought in terms of a given unit length, and numbers were simply the possible lengths of line segments (for example, 2 is exactly twice the length of the unit length)

  • @The_Green_Man_OAP
    @The_Green_Man_OAP Год назад

    So, if I have the expression: -
    Z=exp(i¼π)+exp(-i¼π)= √½(1+i)+√½(1-i)=√2
    - Is it "rational" or not ?
    Note, have: 1/√2= 1/Z = 1/(√½)(2+i-i)=√2/2
    But both complex numbers have magnitude 1, so √2=sum( 1 at 45°, 1 at -45°)
    Depends on what you mean by "irrational".
    1.exp(i¼π)+1.exp(-i¼π)
    = (cos+cos)(¼π) +i(sin-sin)(¼π)
    =√(½)(2)+i(0)
    =√2
    i.e. {√2}→= {1}↗+{1}↘
    Whereas: {2}→= {1}→+{1}→; {2}↑= {1}↑+{1}↑.

  • @sunwicked
    @sunwicked 8 лет назад +1

    We need these videos inside classrooms.

  • @kietpham4635
    @kietpham4635 4 года назад

    I'll have to watch it over and over again

  • @ahra5476
    @ahra5476 8 лет назад +1

    Omg only if this video came out when i was studying this at school it would've made my life so much easier

  • @Unknown10446
    @Unknown10446 Год назад +1

    My class 9th syllabus got revised. Thank you. 🙂