All possible pythagorean triples, visualized 

I scrolled down to the comments just to see if anyone caught that.

Hey 3Blue1Blue, thanks for another great video! For fun I've tried out to make Randolph smile (self.play(randy.change_mode, "happy")), but for some reason it wouldn't let me. Any idea why that would be? Moving works fine. Also, I'm gonna do videos on functional programming and logic foundations (no animations) and was wondering how I could do life LaTeXing, as I want to avoid handwriting. Do you have any idea how to approach this? Thanks for your math content!

Shame on the second blue pi creature.

Names of the other three pi creatures, please?

What are the other ones' names?

Oof, just oof

Up

"i'm four parallel universes ahead of you"

PedrivoGamer 3,14 Up what?

@Mark Smith Teacher would give that kid an F for copying haha

For me it's a Dutch essay lol

Lmfao

I swear

Why is maths interesting when you have other things

Lmao how'd you know??

yuki nagato

You’re... you’re what?

Yeah Build it in front of my school examination hall

Oh cool Wait hold up...

Can you pm me a photo of what it looks like as an architectural drawing? I’m pursuing civil engineering.

I couldn't agree more with that last sentence!

Truth.

onlynamelefthere hey. If you get an already pythagorean triple and Square them, why don't you get a "fermat's triple for n=4"?

Agreed😊💐💐💐💐👍

Claudia Assis Say a,b,c satisfy : a^2 +b^2 = c^2 Squaring both sides : (a^2 + b^2)^2 =c^2 Or, a^4 + b^4 + 2*(a*b)^2 = c^4 Whereas Fermat's triplet for n=4 satisfy: a^4 + b^4 = c^4

one day, someone will write french names correctly

René please

And whoever made that tablet in 1800 bc

@@Targeted_1ndividual actually that was Pythagoras his great-great-great-... grandfather ;)

3European1American

경례...

치직,,,

이거 이해한분 설명좀..ㅠㅠ 경례

반쯤 지나고부터는 자막이 안나와서 뭐라는지 모르겠음

🇰🇷 경례

He studies the topic that provides fund. Many scientists study global warming, not because it delights. They know that's a bunch of lies, but that's easiest to get money from.

@@seanleith5312 climate change denier? 99% of scientists, especially climate scientists, believe in climate change. AND, climate science by far does not make the most money... What about medical science (doctors, pharmaceuticals) or engineering (especially for companies like Boeing and Lockheed Martin that get military contracts)?

@@pranaygupta6688 All you know is repeat the propaganda from your school and liberal media. Do you have a brain to think for yourself?

@@seanleith5312 And why don't you believe in climate change ? Have you any proof to sustain your belief ?

@@Hobbit_libertaire Who said I don't believe climate change? Climate change happened since the earth existed, it's always changing, it will be forever. What I don't believe is: Man-made CO2 is the driver for climate change. There is no evidence to CO2 plays any meaningful way. And it is theoretically close to impossible that CO2 play any meaningful role. You are indoctrinated to believe in this religiously. It is disgusting to use science as a political tool.

It seems that the meme-arrow trend I started last week has carried over to this video as well! Good, good, muahahaha

Faculty of Khan What? Greentext arrows have been around for years, lol

I meant using meme-arrows in the comment section on 3b1b's videos. I made a comment last week on the pi/prime irregularities video using meme-arrows, and was (rightly) made fun of for it. It's amusing to see the trend continue here.

Further Maths right

don't kid yourself, you didn't start shit

John Rickert Doctor, i'm interested in your profession since i'm going to study and become an applied mathematician and I wanted to know how it has been to be a mathematician :), greetings

Thank you for your reply. Well, I was in Pure Mathematics instead of Applied. I believe that Applied Mathematics would give you very great flexibility. Academia may or may not be the best environment to be in. Even though I no longer work as a mathematician professionally, I still study mathematics and find it fascinating. I have never regretted the time and effort I have put into it. I hope that you find it rewarding.

@@danielwylliel.rodrigues1015 you know we are both a year late. RU-vids recommendation algorithm is retarded

@@nucleartree8159 even more for me

Would you mind sharing what you wrote your doctorate about? Thanks!

I'd honestly love for 3b1b to talk about hyperbolic geometry

@@glitchy9613 ikr, hope he notices how many people that have liked this comment so that he makes a series

@@theseal126 Wait shouldn't it be called "Essence of geometry"? most of those topics relate more closely to geometry than they do topology.

@@glitchy9613 Oh, true!! Essence of geometry sounds better. Though maybe some people might get the wrong idea so maybe essence of non euclidean geometry

@@theseal126 this sounds like a beutiful idea, I need this

Yes, I thought the Pythagorean triples from Sumerian times (1,000 years before Pythagoras lived) were found by trial and error. I never guessed that there could be an algorithm for it, let alone a simple(?) algorithm as described by this video.

i also love the fact that is in 60fps so thank you

Why? Do you watch in 0.5x speed?

It's subjective, not axiomatic

60 FPS / 1080 P MATH WHAT THE FUUUUUUUUUUU

Higher framerate means more data. Also, at a certain point, some people can't tell the difference. Barely any humans would be able to tell the difference between 1000Hz and 2000Hz, so doubling the amount of data used serves no purpose.

This is exactly what schools should be doing but a lot of them don't.

That is awesome and good for you! I’m replying in English because I know RU-vid has a translate function, so I hope you can understand this message clearly. Math can truly be a beautiful subject to explore, and videos and visualizations like this make it possible for everyone to experience it. I get excited just thinking about the future of math education, since I know that people like this will be able to make even the most esoteric topics approachable.

Exactly Dude. I hope google translates this correctly. But really math is crazy because of the way that hundreds of equations can make such organic and natural shapes

한국인이다!!

I like math, I listen to math every night to cure insomnia.

@@samgrattan5465 Bad news: Google is really bad at translating English to Korean, and idk why. Anyways, I completely agree to your comment!

It's essentially the same formula that we get when generalizing the squares of complex numbers for these triplets. It's incredible how many proofs you can do with complex numbers, even in things you wouldn't normally expect them to appear!

givemetruth when you acquire K N O W L E D G E

Shiladri Chakraborty: Absolutely Correct. These videos are fantastic

Maths as a service

Exactly! Well said!

For sure. Normally I'm there trying to cram my head with as much math as it can fit in for some test I don't give a crap about, and I don't like the math at all. But there is hidden beauty waiting to be discovered, and I am waiting for me to discover that I CAN discover the hidden beauty in mathematics.

I usually feel saddened while watching these videos when I realize just how little I know, and worse yet, how I’ll never be able to know everything there is to know in maths. Not only because we lost a lot of valuable information as time went on, but also because it is such a broad field.

I bet Euler saw this when he became blind

엌

닦을려다 휴지없는 기분

닦는데 휴지 뚫린기분

yes

Yes

A side note: The creation of the parabola equation started by trying to determine the trajectory/path of a cannonball. The framework takes the parameters of gravitation and the earth below but the earth must be flat. Yes, the earth is flat (and stationary), while thinking of the ball earth as "Close enough for govt work" is just that.

THE GOATTTTTT

FACTS

DAMN IM BOUTA DO THIS

holy fuck if Bob Ross blows my mind I can only imagine what this will do

username checks out

ᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟ v

Mithra and now you studied programming for nothing jk programming = low effort, high reward

he is better at math then grammar

than*

than*

I was wondering if anyone else noticed that lmfao

I love the one sentence proof for the laplacian operator in polar coordinates. "trivial and left for the reader as an exercise."

창의융합형인재 양성중

ㅋㅋㅋㅋㅋ실전! 영어 듣기 평가

+Milo Jacquet Oh I remember. Hope all is well!

Yep! Recently I've been learning about a continuous function that is nowhere monotonic. It's quite strange!

Milo Jacquet the weierstrass function? 3b1b could make a cool video on that I bet. It has a pretty badass look to it.

SpaghettiToaster that's the one that's like an infinite sum of cosines right? It's all jaggedy when you zoom in. It's also continuous everywhere but differentiable nowhere, right?

-_-

◕_◕

つ ◕_◕ ༽つ

_-_

that mascot is really nice pi

all i know is that it has something to do with modular forms which is connected to algebraic geometry. in any case, thats a lot of deep background material and thats why i think it would be impossible to understand in even an hour long video

Clingfilm Productions There's a reason why it took the worlds greatest mathematicians over 350 years to solve it.

Dude Man Nah, its solved by Fermat himself. It's just that the proof is too large for the margin to contain. :')

Angel33Demon666 Oh not again! You sneaky fermat

Apparently his proof is too long to contain in a video.

아니 페이지 번역으로 댓글 읽고 있는데 국수잔치 있어서 개 놀랬잖앜ㅋㅋㅋ

엘프어인듯

ㅋㅋㅋㅋㅋㅋㅋㅋㅋ

뭐야시발 왜 한국어써요

Ah so basically if for some j != 1 we have that 2j+1 + 2j+3 + 2j+5 ... = m^2 then obviously 1+3+5... 2j-1 = n^2 and 1 + 3 +5 + ... 2j-1 + 2j+1 + 2j+3 ... a square number as well. That's a nice observation!

@�̴̀͌̕ The Euler Identity happens from realising that, if you interpret the concepts of an angle and of an exponent in a weird way : r*e^(i*x) = r*cos(x) + r*i*sin(x) Where x is an angle *MEASURED IN RADIANS, NOT DEGREES; VERY IMPORTANT* Essentially, you just plug in the value of the angle (IN DEGREES) for the x power of e, then you discard the "rad" unit And r is the *square root* of _the addition of the squares of the real number and the multiplier of i_ So we now know that you can rewrite additions of real numbers with a multiple of the imaginary number _i_ with a single term, that is use without having to add 2 or more things together So, since 2 + 1*i is such an addition, we can convert this into a single number, "r*e^(i*x)", where, again, r is a square root involved with the real number (2) and the multiplier of i (1); but when we square this "r*e^(i*x)", then we square "r", therefore we square a square root, tus we get the number that's inside, which is, again, _the addition of the squares of the real number and the multiplier of i_ , which is "2^2 + 1^2", or "5"

And x is the angle between the line connecting to the origin of the Real-Imaginary graph and the complex number and the x-axis; if the complex number's above the negative values of the x axis, then the angle's between 90 degrees and 180 degrees; and if the complex number's under the x axis, then the angle's negative

+

Some times, taking the route that looks harder or more complicated is the best, simplest, easiest way.

Jordan Ellenberg in his book How not to be wrong, the power of Mathematical Thinking: Outsiders sometimes have an impression that mathematics consists of applying more and more powerful tools to dig deeper and deeper into the unknown, like tunnelers blasting through the rock with ever more powerful explosives. And that's one way to do it. But Grothendieck, who remade much of pure mathematics in his own image in the 1960's and 70's, had a different view: "The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration...the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it...yet it finally surrounds the resistant substance." The unknown is a stone in the sea, which obstructs our progress. We can try to pack dynamite in the crevices of rock, detonate it, and repeat until the rock breaks apart, as Buffon did with his complicated computations in calculus. Or you can take a more contemplative approach, allowing your level of understanding gradually and gently to rise, until after a time what appeared as an obstacle is overtopped by the calm water, and is gone. Mathematics as currently practiced is a delicate interplay between monastic contemplation and blowing stuff up with dynamite.

You made the complex plane become plain!

pLaNe

It is the complex _plane_ that is valid, not the complex plain, you moron

@@vari1535 Besides, "complex plain" is an _oxy_moron.

that ¹+²=³ 😂

huh cool

Interesting, but why does u^2 - v^2 has to be greater than 0 ?

@@forrest3797 Yeah why?

@@darshdodeja I'm not entirely sure, but I think its because it represents a length/distance, which can't be negative

But neither 9 + 12i nor 12 + 9i are hit

​@@smiley_1000 But 4i + 3 is

ㅆㅇㅈ

+Maik Klein Just wait...

3Blue1Brown Woaahahahahaha I am excited

@@3blue1brown and wait and wait ......

Maik Klein 2018, 10 September, that quaternions vid already exists

??? 길이가 정수가 아닌 유리수인 건 단위원으로 푼 부분에서 감탄이...

@@user-wn1nl1uw3y 피타고라스 요점을 보니까 꼭 어떤수를 더하면 갇은값이 나온다는것과 피타고라스를 이용한 로또 번호를 활용하면 되겠네요 25를 기점으로 잡고 나온숫자를 중심선에 위치해서 피타고라스 정의를 내려서 하면 해답이 나오겠네요....

Hello hello!