ฝัง
- เผยแพร่เมื่อ 3 มิ.ย. 2024
- View full lesson: ed.ted.com/lessons/making-sens...
Like many heroes of Greek myths, the philosopher Hippasus was rumored to have been mortally punished by the gods. But what was his crime? Did he murder guests or disrupt a sacred ritual? No, Hippasus's transgression was mathematically proving the hitherto unprovable. Ganesh Pai describes the history and math behind irrational numbers.
Lesson by Ganesh Pai, animation by Anton Trofimov.
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.
😭😂
Same
Took me a while to make this connection too
Peter Griffin moment
WTF! Same
Hippasus' colleagues punished him for discovering irrational numbers? Wow, that's truly irrational!
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.
Peek comedy
314 likes nice
SUS HIPPO
No, he deserves it!!!
This should've been titled "Rationalizing Irrational Numbers".
lol
Omg what a missed opportunity
2/sqrt(2)=sqrt(2)
@@trevorallen3212 0_o
@@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)
> "Are you the square root of 2?"
> "Because I feel irrational around you."
How to flirt. :D
Meow
+Cat Are you hungry?
+Stray Pay Or, they will think you are calling them fat.
howard wallowitz,
+cortster12 Definitely. I guess it would only work with mathematicians. :P
_"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)
best part of that movie :D
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 😊
(clapping )
David S. Cats eyes nebula.. nice
whoa
Hippasus: *discovers irrational numbers*
God: wait that’s illegal
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
@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.
@@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)
He couldn't have because "irrational numbers" don't exist in mathematics. Chuckle.
@@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.
the lesson by "Ganesh Pi"
+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
Meow
Good one Aditya! I will make sure our founder reads this comment :)
Illuminati confirmed
Ganesh 3.141592653589
Great explanation.
I have a degree in applied mathematics and have never heard this pontificated so well.
Thank you.
@@harshitabhagat8467 ig cbse has it in 9th also
@@tarunkumarcs2374 ICSE in 7th grade.. I was like wait I've proved that!!!
Nice proof and illustration/animation
Meow
Thank you Vikas, our founder collaborated with TED-Ed to create this lesson :)
Why is Hippasus's time shown as 8 BC? He belonged to 5th Century BC.
Don't Memorise wierd flex but ok😂😂
Not their proof.
“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
It's pretty much all of Reddit at this point tbh
Sriram Radhakrishna Yeah, mostly dankmemes tho
Can't help but agree
"instead of adhering to norms decided to prove it was something new" In that world at that time doing this would take immense courage!
even in our world now tbh(:
Meow
In any world at any time actually
For all humans always actually
Good, now cover negative numbers, imaginary/complex numbers, hyperreals, surreals, and split octonians!
Well square root of a negative number should be quite obvious to realise
What is a split octonian?
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.
+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 TH-camr that combines drawing and math named Vihart, in a video explaining why 0.9(repeating) is equal to 1.
Puggalug That was a very good video, yes. Glad to see another fan.
Please, never stop doing this videos, they are too good
“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
Great abstract video 🙂 please make more of them, they are the juice for my brains!
I'm feeling a little…irrational now
+Ropsana Khanom
HA HA HA HA HA HA.
Punny.
Meow
Have some Pi and you can be transcendental.
I'll give you a 3.1415926535897932.
Same here
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 :)
Great to hear that Rajat. Our founder was the educator for this lesson. Thank you :)
Great! finally another narrator!
wow. the animation is amazing. really great for visual learners.
Well played, Hippasus.
Meow
Hippasus was NOT punished by any god, but by his fellow Pyrhagoreans.
SUS
@@XenophonSoulis when u lidering a cult, ppl see u as god, lol, ask donnald duck 'bout his trip in mathmagic land
0:27 The man has blonde hair is doing the floss
really well made video, was hoping for a geometrical proof though seeing as algebra wasn't discovered in 5 BC
Lovely video, clear, concise and with subtle humour.
Thank you!
These lessons never dissapoint!
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
Meow
+Cat Irrational cat is here again! Want some pi?
Thank you :)
@@ASOUE miaou
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.
That was a really great TED-Ed, loved the animation on this one :) (and the topic)
Great job guys! I have a much clearer understanding of irrational numbers now! Wish all my classes were like this:)
Making *sense* of *irrational* numbers
. . . . . I see what you did there
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
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!
WOW! I never really understood irational numbers this well! Animation is a powerfull thing
Thank you for making this so easy to understand, it was very helpful!
The Animation was so Dope!
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.
Meow
Well... You could technically plot it it would just be not exactly perfect
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.
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.
@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.
Narration is done in a very good and clear way
This is really cool! We're learning about Pi in class and I'm going to show this to my teacher!
I have such a bad relationship with math and feel sorry for it
Meow
+Cat Woof
+sara meachel At least you know what you lose (unlike others who don't know that).
does it remind you about your "x" since you don't know "y" she left you?
very awesome animations, I really learned somehting today that 13 years of school didn't teach me
Meow
Woof
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
@@iceenderman-fm4kb "as q^2 times 4 is p^2 we can say that p=4a" no, that is false
This was so beautiful to watch. Thank you!
Wow, incredible animations! I'd love to learn to animate mathematics like this someday.
3:26 Ohhh!! That Activity did in School 👍🏼
Discrete mathematics at its finest.
Meow
What is discrete math?
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.
This whole video has nothing to do with discrete mathematics.
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
thank you another great video from TED ED It's amazing and irrational how much you make maths easy
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!
So I have finally found one of the inventors of math
*discreetly adds him to hit list *
@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
@MthYsdAsd throw him with statue of numbers
Only Indian students will know that we have the proof of this in our class 10 syllabus.
Exactlyyyy!!!!!
I love this video!! The style it is made of and the narrator are very nice :) Plus the explanation also made it very clear how this all happened ^^
This is a great channel, I'm very glad I found it.
3:44 Ooh, the golden ratio.
I think it's called The Spiral Of Theodorus.
Love this
Meow
Love you
+Cat omg i love your account ahaha
+Don Draper lmao ily too
+polaroidstyles Meow! (that mean ily 2)
Finally finally finally.... a good explanation if irrational numbers. Well done.
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.
I watch all these ted-ed videos but never really understand them
try to "split" every explication to understand the video
Great animation
Meow
This is such an awesome way to teach irrational numbers
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.
conclusion doing math = you go to hell , to hell with math "literally"
Meow
i believe if u dont do maths then u go to hell😝😝
Math is fun
Sickness!
be careful!!!! I think there are still people who believe in maths as a religion!!!!
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!
Me Mine im first befor that *CAT*
Thank you for the knowledge beyond textbooks.
Such amazing animation
The irony That the person who made this videos is ganesh Pai(pie)
Meow
how is that irony?
His surname seems a bit irrational
Yes, and Ganesh Pai/Pie/Pi loves math :)
We also proved this
I am a 10th standard student from India
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.
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.
Everything is making sense. Great explanation.
Came here for a Math’s video ,
Got a history lecture instead
video: anything times 2 is even
me: 2.5 x 2
video; wait thats illegal
awesome animation! !! thank you ted ed !!!
The number "e", aka Euler's Number: "A M I A J O K E T O Y O U?"
When does Life of Ganesh Pai come out?
Soon! :)
Never*
How simple and smart is that? Great video, as always.
Finally a comprehensible class🙄 Thnx 😁
can we appreciate the fact that the lesson is by ganesh 'Pi' :P
I didn't notice that! :0
This is a cool version of the proof, but it's not how Hippasus concluded this... there was no algebra in his time
The video was informative :D
Please make a video on the idea behind complex numbers
Beautifully explained!!
I love pretending that I understand these videos!
🤣🤣🤣🤣🤣🤣
now i know where the word rational comes from
Seriously dude? You should go back prep
+Jordan Tan
It comes from ur mum because she was telling me to talk mathematical to her
Meow
Rational comes from the Latin, "ratio," meaning reason. How the heck did you figure that out just by watching this video?
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
This is exactly what I learnt in school !!!!! Thanks Ted!
I feel clever now cause I knew the answer lol
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/
@@NewCalculus shut up
Where is Anthony Anderson? I can't watch without his voice!!!
Awesome animation and expalined very well
This is so fascinating 🤯
"Two times any number = an even number" what about 0.3 for an example
Whole number
can we get 1000 subscribers without content
All decimals are even
Because
0.3/2 = 0.15
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?
+Baga Jr I saw it too. You are talking about the Fibonacci Sequence :)
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?
+Baga Jr you're not thinking of complex numbers and how you can multiply them and find the product graphically using triangles are you?
It's the Spiral of Theodorus :)
Baga Jr I made a mistake. I totally forgot of what Don't Memorise said! The Spiral of Theodorus.
I'll have to watch it over and over again
Great work 👏👏👏👏💐
Narrator: "Don't be afraid to explore the impossible."
Me: *fails Math test*
Kayline Alsen same 😭
Me too. Oh! I hate Maths...
- Ganesh PAI
Why has nobody commented about it?
Dude loads of people have commented about it.
This was informative. Loved it.
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.
please don't upload any video without subtitles ! please please please :(
LagiNaLangAko23 but i don't understand all show .I am a novice in learning english
you can check the subtitles by clicking the 'CC' button. It is found where you see three dots on top of each other
Mikel Arenas but "CC" not available
it's not available on this video.
Oh, then that should put it on
We learned this in school, and so I proved *Root 4* is irrational using the same method...
...my teacher was not pleased
Substitute p to 4 and q to 1 through the video
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)
root 4 is 2
Loved the last line 👌
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.
I agree.
Hey guess you can say a lot in this world is made by numbers, specifially 1 and 0
Meow
Actually everything is.
Woof
@@XenophonSoulis +Ξενοφώντας Σούλης
+Cat
Why are you guys writing the same meow woof thing on every comment? Are you bots?
@@alisonlaett9625 I'm trying to scare him/her, 'cause cats are afraid of dogs.
Until you try to divide by 0.
Meow
already did, the answer i got was...
Can't tell if joking or serious. Please confirm.
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.
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.
😊😊😊😊..thank you very much ted...i finally got this rational and irrational number idea 😊
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.
It's simple 2÷root 2 = root 2 lol 😁
My God...he's done it...
+Money Jatt I'm even more confused now.
then what about that root 2 in denominator....???
false. 2/sqrt (2) =/= sqrt (2)
+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)
Realy good explanation...thanks