This man is a proof of how unfair life is ..He is the cleverest man ever lived and still some idiots in Big Brother with IQ less than 90 are more popular
If we redefined pi as the ratio of the circumference to the radius of the circle, wouldn't e^i pi be equal to 1 instead of -1? In my opninion this would be an even nicer equation.
the formula is not paradoxical, if you understand it it accords perfectly with your intuition. i think the reason it amazes people is because 1) pi is considered to be something to do with circles, whilst more fundamentally its a special distance for a function satisfying f''=-f, and 2) exp(z) is often written e^z since exp(z) still satisfies the laws of indices, whilst e^z hasn’t any meaning apart from plugging z into the Taylor expansion for e^x, x real
Higher mathematics is REQUIRED for most modern forms of engineering. There are certain things you can build without higher mathematics and there are certain things that absolutely require it.
Most modern electrical technology relies upon higher mathematics. All electromagnetic wave connected technology rely upon Maxwell's equations. GPS relies upon mathematics, cell phones, computer science algorithms, TVs, and most modern technology
Without higher mathematics we'd be living in the stone age
what a load of rubbish. what possible use could this have anyway? maths is horsecrap. all you need is centimetres and millimetres to build stuff. ,maths is just make a hoo hoo out of nothing. so what is 10 boxes fit in a box x 10? its obvious.
@itsnobody hey internet tough guy, you still havent expalined what use this dumbass equation has. i can tell you .. nothing. thats right. I can build a radio without any stupid ass equations.
eletromagnetics was around along time before maths. highter maths is just used to check stuff. we build something and use the maths to check it it functioning as in the design. you ass!
Hans Christian Oersted first demonstrated that electromagnets could be made in 1820. Math didn't exist before 1820. I don't want to live on this planet anymore
Are you serious? Math is the foundation of physics; without math physics would just be trial and error. Building satelites through trial and error would not have been accomplished. Nor would building computers or the internet or most other modern technologies have been through trial and error.
Also, as someone else said, electromagnetism is a fairly recent invention compared to math (which is >2500 years old).
@JohnnyRedzin computers are just 1's and 0's so there goes your math theory about that. maths is just used to create hogwash and "jobs for the boys" any fool with a calculator can work out the length of a piece to cut or just with a ruler. certainly dumbass equations are never needed in real world physics. it is just an excuse for hippies to ponce off the state fro 10 years after leaving school and not to get a proper job.
@plasticspastic201 Trust me, without Mathematics, there would be no modern Engineering, Computer Science or Physics. Your comments clearly indicate youve clearly never seen anything beyond middle school Physics. "Dumbass equations" like differential equations for example are pretty much ubiquitous in nearly every single branch of Physics and actually those are only basics, the more advanced the Physics gets, the more so does the Mathematics used in it too.
First of all, all of the modern computer use higher arithmetic (a.k.a. the least useful branch of mathematics) to encode informations. This includes your social security ID, credit card info, et cedera.
Second of all- let us put aside the equations first- you cannot make it through kinematics without basic derivatives and integrals. If you can't even predict the motion of something, how are you suppose to do physics?
Euler's Identity can be use to solve oscillating motion.
@plasticspastic201 Ever heard about Boolean algebra? Thank the mathematician George Boole for being able to write comments on youtube. Ironically, his book is called "An Investigation of the Laws of Thought". I really, really recommend it.
@plasticspastic201 actually... computer science and software/program engineering requires a lot of mathematics, at least a good background with it. Maybe it's not the math you're used to, but much of how it works breaks down into complex but pure mathematics.
As a double major in Computer Science and Mathematics, I can only agree with you, I love the math in both fields, very interesting. I should however point out that most "programmers" by trade are closer to computer engineers, engineering=/= science. Computer Science involves abstractions, formal logic, physics, mathematics and more. Engeneering is less theoretical, more practical. An engainer might work for google, a true scientist ponders P=NP, Quantum computing, AI et cetera.
I'd also like to apologise off the bat, English is not my first language, I'm hoping I spelt everything above correctly because I don't have an English spellcheck to help me otherwise. Stupid phone only let's me have one language active, and I'm not changing langages just to write this.
If you think you don't need math to be a computer scientist trust me you won't go far in this industry. You might as well go work as a PHP programmer, or get you LINUX + now because without math you're pretty much useless to anyone who needs real programmes written. Let's say you're modeling a system. This system is best approximated with a set of shapes & vectors, to define those shapes you need to know the math to produce them, then execute such math as a line of code.
@cynicalbluewhale How many formulas were used to create Windows? How about MS office or my email client?
High level math is most certainly not a requirement to build 'real' software products. Take a look through the iphone app store and count how many would've needed high level math. Go ahead and call them 'useless' applications but they're what real people use.
Don't get me wrong I love math and it can be very useful in software. Just not as important as you say it is.
@plasticspastic201 You're all wrong without Maxwell's equations it's simply IMPOSSIBLE to invent a radio
You can't guess and experiment your way into inventing a working radio without Maxwell's equations. You can build a radio after someone has given you the instructions, but you can't invent it.
Without Maxwell's equations all radio and electromagnetic wave connected technology is quite impossible!
You would have a near 0% of success of inventing a working radio without Maxwell's equations
@plasticspastic201 Nah dickhead you can build a radio without Maxwell's equations once given detailed instructions but you can't INVENT a radio without it fool
Obviously once given detailed instructions on how to build a radio you can do it, but you can't INVENT the design of a radio without Maxwell's equations
Maxwell's equations form the basis of all radio design shithead
With cm and mm alone the only thing you can do is measure the length of your dick
@itsnobody of course you can invent a radio without math you turgid tosspiece. i suggest you go and find the math book that is currently nearest to you and you procede you shove it up your ass sideways, like i do to your prostitue mother. she likes to measure my dick in CMs she uses the 30 cm ruler to do it because she likes a foot up her ass.
@ElectroMagneticWeak what beauty? it misses by 1. if the equation rounded up nicely then fair enough but it has to add 1 to make sense. oh thats right.. we will just add this little 1 here i will grab it from thin air and the equation all makes sense now. pffft maths is phoooey
Thumbs up if you're watching this in the year X , for arbitrarely large values of X.
Euler is definitely my favorite matematician,the graph theory,the modern function notation....this identity....he could have done more,but one lifetime just wasn't enough.
@Cyphlix first class mathematicians is different from first class student. That kind of mathematicians are rare and have an incredible talent to see patterns, hence I think there is a lot truth in his words. Admittedly I myself didn't see proof with taylor series(nobody teaches them in 10th grade). Only hypocrite would compare himself with Tao Willes Poincare Cantor or any other prodigious mathematician. They are first-class for a reason don't you think so? :)
About Gauss saying that if this were not immedietly apparent to a student they would never be a first rate mathematician - can any mathematician actually "comprehend" this with intuition ?
@ILiveForScience It feels like it should not be the case. Imagine 2*2, 3*3. Some can stretch themselves to 3.4*3,4. But what does it mean to raise a number to the power of SQRT(-1)? No human on Earth can visualize it. You cannot hold it, or touch it. Yet, it exists in atoms, at the heart of quantum mechanics. How the heck does pi have anything to do with it - it shouldn't be there!
And all that somehow equals a negative REAL positive number? My God.. it's beautiful!
In this equation, Pi is not the ratio of Circumference to Diameter. Rather it is the angle in radians of a semicircle. So, I am sorry, the video is misleading. This is truly a beautiful equation, but it is also a very misunderstood equation.
@salilgaonkar You have to re grasp basic geometry and arithmetic. Radian measure comes from varying values of pi which is defined as the ration of c to d.
@floopsie666 Well, if Pi in this case is a number (approximately equal to 3.1415...., which is the ratio of c to d as you state), then here is a fallacy that follows:
e^(I*pi) = -1 . Therefore squaring both sides, e^ (2i*pi) = 1. Taking log to the base e of both sides, we get
2i*pi = ln(1). But ln(1) = 0. Therefore, 2*i*pi = 0, which is absurd. Therefore pi in this case is not a number it is an angle.
Numbers are just symbols humans tried to use in order to find "order" or to "understand" "reality". Ancient guys chose the system of ""10" integers" and tried to use it as the language of the universe. But you could have systems of ""5","15","20" or even "50"" and then you would have other "paradoxes" in which humans would still try to find meaning. Euler's identity is just an example of humans being trapped in the web that they created.Maths is intelligent, but it is philosophically immature.
@AbsurdityofExistence Euler's identity does not arise because of our system of numbering. Sine cosine, pi, i, 1, or taylor expansions would all arise regardless of the base you choose to represent your numbers in. Anyone who truly understands mathematics should know its much more than numbering. Its the patterns and symmetries we see when we represent and manipulate things in their exact magnitudes and orientations.
@dheeraj54 ah right. currently i'm in year 12, and i do higher level physics. and i still don't see how one can use complex numbers/euler's identity in physics :(
@illumined1 feynman uses it to prove things like the lower of wavelength through transparent surfaces of higher refreactive index and uses it to explain refractive idex
@Austin101123 One use I can think of is in the study of Hilbert Spaces in QM regarding wave functions for infinite square wells. Euler's identity presents itself as highly useful when representing a separable wave function as a sum of functions defined over a Hilbert function space.
@Austin101123 Actually it's kind of a normal thing to say after the first glance. But believe it or not, we have the ease of analyzing sinusoidal signals and the steady-state sinusoidal responses of linear RLC circuits thanks to the Euler's identity. I'm sure it has lots of other uses in applied sciences but since i'm an electronics engineering student, i use it that way all the time.
@Austin101123 I'm guessing you're not familiar with the terminology i used. Sinusoidal signals are the signals that vary with time, like a sinus curve. We use electricity in this form, for example. The voltage at the input, (i.e. mains voltage) changes with time, often expressed mathematically with trig functions. And it actually takes both positive and and negative values. To find out (easily) about currents and voltages on the components of a circuit, we need this identity.
@Austin101123 I'm actually beginning to think that you've got some mental disabilities. Didn't you ask, "But of what use is this for?"? Well, I'm trying to answer that question of yours. And you're telling me what does this have to do with the video? :D
"if this formula was not immediately apparent to a student..." - did he mean, if the student didn't know what the formula means, or if the student didn't know how to prove it?
This proof is really fucking amazing. It shows how those three constants, so exquisitely converge with integer numbers. I’m sure there are many things else that converge nicely, but that is the one in particular that popped out at me. Also, I think that equation demonstrates quite convincingly that the imaginary number “i” does indeed grapple firmly with our commonplace reality. If you don’t understand what I’m saying, then try graphing that equation – you’ll see what I’m talking about.
@poopinitup Yeah, the part where he does e^(x) = 1 + x^2/2! + ... (similar with sinx and cosx) is called Taylor series, something you learn in second semester calculus :)
NERDS! somebody says to me "Euler's identity is the most beautiful theorem in mathematics." So I come here expecting to see fractals and awesome sweet math shit and what do I get? nothing. Fucking nerds, masturbating over nothing.
@supadox you mean the type of nerds that allow for youtube to work, and for your favorite porn site to work, and the nerds that design computers and run the infrastructure of the country? those nerds? yea, go f yourself you worthless piece of shit
@supadox Ask any electrical or computer engineering undergrad if this is "nothing." This identity has countless practical applications. Modern technology would not be where it is without Euler's identity.
Think about it. Without it, you couldn't post such a stupid comment, displaying to the rest of the world that you are, in fact, an idiot.
@E90PAT Many! Used in electrical engineering to model impedence (amplifyers, etc). Used in differential equations to model motions of springs and dashpots (used in trains, engines, etc) and is at the heart of quantum mechanics!
@dangflo it's so beautiful because it has a power, a multiplication and an addition in it, as well as the two most important numbers (0 and 1) and the two most important irrational numbers. So That's why it is Beautiful!
@nxvznx I do not quite agree. First of all, we can invent things in mate\hematics. Definitions are often inventions, and the number i is an invention. Second of all. A galaxy is discovered, not invented, and oh my can they be beautiful.
@VeritySeeker There are several approaches. I guess the question in the heart of it all, in this context, is "is the number i an invention, or is it just a name we made up for something which already exists?".
While I'm not arrogant enough to claim I know the answer, I'm leaning towards the latter (out of purely emotional considerations, though).
When I think of eulor's identity I don't really see beauty. I feel more fear than I do beauty. It scares the shit out of me. Because it's like it's telling me that we are just scratching the surface of what's really out there. That there is something out there much greater than us. I don't believe in god but man, eulor's identity could make one hell of an argument for one.
While i may not be able to understand why, i'm definately able to understand what it means. And some of all the cool awesome things it can be used for, like the fourier transform for instance. or the representation of any complex number as simply A*e^(ix), where 0<x<2*Pi.
X is the angle in radians that the complex vector makes with the real-axis and A is some magnitude of or length of this vector. e^(ix) is simply a unit vector and its really just an equation for a unit circle in the complex plane (Re-axis and Imaxis). If you plot it 3-dimensionally with x as the third axis (x, Re(e^(ix), Ime^(ix)) The you'll see that it makes a spiral, spiralling round once ever 2*Pi.
My teacher showed us this today, she went into a bit more detail. I understand how you come up with this equation, I just don't understand what it means. :(
How does e^(i*pi)=-1? And what can this be used for?
@osbiath Nice to hear that the video has been used in class. What it can be used for? Well, when e^(i*pi) ever pops up, we can substitute it with -1. How's that for simplifying? :) Thanks for commenting...
@osbiath Well if e^(ix)=cos(x)-isin(x), then e^(iπ)=cos(π)-isin(π). Cos(π)=-1, and Sin(π)=0, and ix0=0 obviously. Therefore, -1+0=-1. And thus, e^(iπ)=-1.
I jizzed.
MathPhysChemSkyNerd 2 days ago
sexist quote at the start. why cant women be successful mathematicians. go suck ur dick u bastard
MsFootballunited 4 days ago
Comment removed
Secretology 4 days ago
i dont see the beauty ...
klegend0 5 days ago
what's the name of the music piece at the beginning of the video?
womanwithmanydoubts 2 weeks ago
@womanwithmanydoubts A Beautiful Mind - 01 A Kaleidoscope of Mathematics
skuller1225 1 week ago
@womanwithmanydoubts Kaleidoscope of mathematics, its a great soundtrack
JSasRays 4 days ago
Cool vid though.
SkymanBrother 2 weeks ago
Facking math, never understood shit, never really bothered.
SkymanBrother 2 weeks ago
This has been flagged as spam show
This man is a proof of how unfair life is ..He is the cleverest man ever lived and still some idiots in Big Brother with IQ less than 90 are more popular
CFVEful 1 month ago
no u dont but is it just a coencidence that all programmers just happen to be good at math ?
7orqu3 2 months ago
jus a loada dumb numbas.
Only kidding. Anyone with grammar like this should be withdrawn from society.
Keith Devlin's quote is very touching.
mrbinary1001 2 months ago
If we redefined pi as the ratio of the circumference to the radius of the circle, wouldn't e^i pi be equal to 1 instead of -1? In my opninion this would be an even nicer equation.
Jordy41 2 months ago
@Jordy41 That number is τ(tau). You can read more about it at tauday(dot)com
TheCobraagent 2 months ago
the formula is not paradoxical, if you understand it it accords perfectly with your intuition. i think the reason it amazes people is because 1) pi is considered to be something to do with circles, whilst more fundamentally its a special distance for a function satisfying f''=-f, and 2) exp(z) is often written e^z since exp(z) still satisfies the laws of indices, whilst e^z hasn’t any meaning apart from plugging z into the Taylor expansion for e^x, x real
abrelosojo 3 months ago
i was just trying to learn about imaginary numbers and i stumbled upon this....im scared
hanzcurrie 3 months ago
i find this theorem beautiful and I am half way through my mathematics degree.
xTheBulletSaintx 4 months ago
Higher mathematics is REQUIRED for most modern forms of engineering. There are certain things you can build without higher mathematics and there are certain things that absolutely require it.
Most modern electrical technology relies upon higher mathematics. All electromagnetic wave connected technology rely upon Maxwell's equations. GPS relies upon mathematics, cell phones, computer science algorithms, TVs, and most modern technology
Without higher mathematics we'd be living in the stone age
itsnobody 4 months ago
"QED mother fuckers!" - Euler
Raselix 4 months ago
very interesting video.....only pornographers will dislike this vidoe .....lmao :)
rishin458 4 months ago
Mathematics is to Physics as Masturbation is to Sex.
foroparapente 4 months ago
Nice synching with the music.
whateverni 4 months ago
what a load of rubbish. what possible use could this have anyway? maths is horsecrap. all you need is centimetres and millimetres to build stuff. ,maths is just make a hoo hoo out of nothing. so what is 10 boxes fit in a box x 10? its obvious.
plasticspastic201 4 months ago
@plasticspastic201 what a fuckin idiot,,,just cm and mm needed to build stuff?
Try inventing a radio without Maxwell's equations.....oh wait you can't invent a radio without Maxwell's equations, it's virtually impossible to do so
Higher mathematics is what made most electrical technology possible! Not simple arithmetic.
Without higher mathematics all technology relying on electromagnetic waves and communication wouldn't be possible!
itsnobody 4 months ago
@itsnobody hey internet tough guy, you still havent expalined what use this dumbass equation has. i can tell you .. nothing. thats right. I can build a radio without any stupid ass equations.
eletromagnetics was around along time before maths. highter maths is just used to check stuff. we build something and use the maths to check it it functioning as in the design. you ass!
plasticspastic201 4 months ago
@plasticspastic201 "electromagnets was around a long time before maths"
Hans Christian Oersted first demonstrated that electromagnets could be made in 1820. Math didn't exist before 1820. I don't want to live on this planet anymore
jonny34351 4 months ago 13
@jonny34351 lol @ not wanting to live here anymore... i feel the same too many time... neo, i believe!
okara83 3 months ago
@plasticspastic201
Are you serious? Math is the foundation of physics; without math physics would just be trial and error. Building satelites through trial and error would not have been accomplished. Nor would building computers or the internet or most other modern technologies have been through trial and error.
Also, as someone else said, electromagnetism is a fairly recent invention compared to math (which is >2500 years old).
JohnnyRedzin 4 months ago
@JohnnyRedzin computers are just 1's and 0's so there goes your math theory about that. maths is just used to create hogwash and "jobs for the boys" any fool with a calculator can work out the length of a piece to cut or just with a ruler. certainly dumbass equations are never needed in real world physics. it is just an excuse for hippies to ponce off the state fro 10 years after leaving school and not to get a proper job.
plasticspastic201 4 months ago
@plasticspastic201 Trust me, without Mathematics, there would be no modern Engineering, Computer Science or Physics. Your comments clearly indicate youve clearly never seen anything beyond middle school Physics. "Dumbass equations" like differential equations for example are pretty much ubiquitous in nearly every single branch of Physics and actually those are only basics, the more advanced the Physics gets, the more so does the Mathematics used in it too.
EngineerAfghan 4 months ago
@plasticspastic201
6/10 troll, fooled me the first time.
If not troll then I fear for humanity...
JohnnyRedzin 4 months ago
@JohnnyRedzin come come.... that's an easy 10 which ever way you add it up... LOL
plasticspastic201 4 months ago
@plasticspastic201
First of all, all of the modern computer use higher arithmetic (a.k.a. the least useful branch of mathematics) to encode informations. This includes your social security ID, credit card info, et cedera.
Second of all- let us put aside the equations first- you cannot make it through kinematics without basic derivatives and integrals. If you can't even predict the motion of something, how are you suppose to do physics?
Euler's Identity can be use to solve oscillating motion.
ElectroMagneticWeak 4 months ago
@ElectroMagneticWeak thank christ you came along to explain it so well. all these other douchebags pale in comparison to you! thankyou~! thankyou!
plasticspastic201 4 months ago
@plasticspastic201 Ever heard about Boolean algebra? Thank the mathematician George Boole for being able to write comments on youtube. Ironically, his book is called "An Investigation of the Laws of Thought". I really, really recommend it.
VeritySeeker 2 months ago
@VeritySeeker you thick fuck. you dont need maths to write programs you numbskull
plasticspastic201 2 months ago
@plasticspastic201 actually... computer science and software/program engineering requires a lot of mathematics, at least a good background with it. Maybe it's not the math you're used to, but much of how it works breaks down into complex but pure mathematics.
KevZyro 1 month ago
@KevZyro
As a double major in Computer Science and Mathematics, I can only agree with you, I love the math in both fields, very interesting. I should however point out that most "programmers" by trade are closer to computer engineers, engineering=/= science. Computer Science involves abstractions, formal logic, physics, mathematics and more. Engeneering is less theoretical, more practical. An engainer might work for google, a true scientist ponders P=NP, Quantum computing, AI et cetera.
cynicalbluewhale 1 month ago
@cynicalbluewhale
I'd also like to apologise off the bat, English is not my first language, I'm hoping I spelt everything above correctly because I don't have an English spellcheck to help me otherwise. Stupid phone only let's me have one language active, and I'm not changing langages just to write this.
cynicalbluewhale 1 month ago
@plasticspastic201
If you think you don't need math to be a computer scientist trust me you won't go far in this industry. You might as well go work as a PHP programmer, or get you LINUX + now because without math you're pretty much useless to anyone who needs real programmes written. Let's say you're modeling a system. This system is best approximated with a set of shapes & vectors, to define those shapes you need to know the math to produce them, then execute such math as a line of code.
cynicalbluewhale 1 month ago
@cynicalbluewhale How many formulas were used to create Windows? How about MS office or my email client?
High level math is most certainly not a requirement to build 'real' software products. Take a look through the iphone app store and count how many would've needed high level math. Go ahead and call them 'useless' applications but they're what real people use.
Don't get me wrong I love math and it can be very useful in software. Just not as important as you say it is.
LegendLength 6 days ago
Comment removed
itsnobody 4 months ago
@plasticspastic201 You're all wrong without Maxwell's equations it's simply IMPOSSIBLE to invent a radio
You can't guess and experiment your way into inventing a working radio without Maxwell's equations. You can build a radio after someone has given you the instructions, but you can't invent it.
Without Maxwell's equations all radio and electromagnetic wave connected technology is quite impossible!
You would have a near 0% of success of inventing a working radio without Maxwell's equations
itsnobody 4 months ago
@plasticspastic201 Nah dickhead you can build a radio without Maxwell's equations once given detailed instructions but you can't INVENT a radio without it fool
Obviously once given detailed instructions on how to build a radio you can do it, but you can't INVENT the design of a radio without Maxwell's equations
Maxwell's equations form the basis of all radio design shithead
With cm and mm alone the only thing you can do is measure the length of your dick
itsnobody 4 months ago
@itsnobody of course you can invent a radio without math you turgid tosspiece. i suggest you go and find the math book that is currently nearest to you and you procede you shove it up your ass sideways, like i do to your prostitue mother. she likes to measure my dick in CMs she uses the 30 cm ruler to do it because she likes a foot up her ass.
plasticspastic201 4 months ago
Why cant the politicians just stop quarreling and appreciate this beauty...
ElectroMagneticWeak 4 months ago
@ElectroMagneticWeak what beauty? it misses by 1. if the equation rounded up nicely then fair enough but it has to add 1 to make sense. oh thats right.. we will just add this little 1 here i will grab it from thin air and the equation all makes sense now. pffft maths is phoooey
plasticspastic201 4 months ago
@plasticspastic201
Just FYI:
if you raise it to Tau (a.k.a. 2 pi) power then you'll get one...
ElectroMagneticWeak 4 months ago
THAT'S HOW HE PROVED IT!
I've been looking at this equation for the past month or so. And I've been trying to understand some sort of proof.
THIS HELPS! Thank you. Thank you. Thank you for posting.
8644371 4 months ago
Thumbs up if you're watching this in the year X , for arbitrarely large values of X.
Euler is definitely my favorite matematician,the graph theory,the modern function notation....this identity....he could have done more,but one lifetime just wasn't enough.
dxfede 5 months ago
Comment removed
dxfede 5 months ago
I disliked the quote by Gauss essentially saying "if you didn't get this at first, you can never be the best" - but the rest was wonderful.
In my view a first-class student will vigorously pursue what they don't understand - regardless of their initial intuition.
Cyphlix 5 months ago 21
@Cyphlix first class mathematicians is different from first class student. That kind of mathematicians are rare and have an incredible talent to see patterns, hence I think there is a lot truth in his words. Admittedly I myself didn't see proof with taylor series(nobody teaches them in 10th grade). Only hypocrite would compare himself with Tao Willes Poincare Cantor or any other prodigious mathematician. They are first-class for a reason don't you think so? :)
Shefleris 2 weeks ago
@Shefleris Nevertheless a passionate student will achieve a lot in his carrier.
Shefleris 2 weeks ago
About Gauss saying that if this were not immedietly apparent to a student they would never be a first rate mathematician - can any mathematician actually "comprehend" this with intuition ?
dickie4thepeople 6 months ago
Beautiful
3200manpro 6 months ago
I'm sure it's a problem with me and not the maths, but I just can't see it.
ILiveForScience 7 months ago
@ILiveForScience It feels like it should not be the case. Imagine 2*2, 3*3. Some can stretch themselves to 3.4*3,4. But what does it mean to raise a number to the power of SQRT(-1)? No human on Earth can visualize it. You cannot hold it, or touch it. Yet, it exists in atoms, at the heart of quantum mechanics. How the heck does pi have anything to do with it - it shouldn't be there!
And all that somehow equals a negative REAL positive number? My God.. it's beautiful!
adoado16 7 months ago 2
I'll never get tired of seeing Euler's Identity proved. Never.
MonicaKn17 7 months ago
loved it
illumined1 7 months ago
2.17^sqrt-3.14 = -1
wat?
Zander101084 7 months ago
@Zander101084 its sqrt(-1)*3.14
and it comes from the expression e^ix =cos x +isin x which was shown in this video
substituting x= pi in this equation we get e^i(pi)=-1
p.s. please done equate pi to 3.14 and e to 2.17 the point of calling them irrational numbers is lost
dheeraj54 7 months ago
pi in this equation means the angle and not as a constant as shown in the description.
iluvpatecita 7 months ago
In this equation, Pi is not the ratio of Circumference to Diameter. Rather it is the angle in radians of a semicircle. So, I am sorry, the video is misleading. This is truly a beautiful equation, but it is also a very misunderstood equation.
salilgaonkar 7 months ago
@salilgaonkar You have to re grasp basic geometry and arithmetic. Radian measure comes from varying values of pi which is defined as the ration of c to d.
floopsie666 7 months ago
@floopsie666 Well, if Pi in this case is a number (approximately equal to 3.1415...., which is the ratio of c to d as you state), then here is a fallacy that follows:
e^(I*pi) = -1 . Therefore squaring both sides, e^ (2i*pi) = 1. Taking log to the base e of both sides, we get
2i*pi = ln(1). But ln(1) = 0. Therefore, 2*i*pi = 0, which is absurd. Therefore pi in this case is not a number it is an angle.
salilgaonkar 7 months ago
Numbers are just symbols humans tried to use in order to find "order" or to "understand" "reality". Ancient guys chose the system of ""10" integers" and tried to use it as the language of the universe. But you could have systems of ""5","15","20" or even "50"" and then you would have other "paradoxes" in which humans would still try to find meaning. Euler's identity is just an example of humans being trapped in the web that they created.Maths is intelligent, but it is philosophically immature.
AbsurdityofExistence 7 months ago
@AbsurdityofExistence Euler's identity does not arise because of our system of numbering. Sine cosine, pi, i, 1, or taylor expansions would all arise regardless of the base you choose to represent your numbers in. Anyone who truly understands mathematics should know its much more than numbering. Its the patterns and symmetries we see when we represent and manipulate things in their exact magnitudes and orientations.
ForgedInASupernova 3 months ago
Mathgasm !
abhimanyu95 7 months ago
This has been flagged as spam show
"Repent&Believe only in Jesus before too late" or "Burn in hell for eternity"
"Repent&Believe only in Jesus before too late" or "Burn in hell for eternity"
"Repent&Believe only in Jesus before too late" or "Burn in hell for eternity"
The end is coming soon. Hell is real&forever for sinners.
fuckmania07 7 months ago
whoa awesome! but what is it used for? haha.
DJDavverMusic 8 months ago
@DJDavverMusic e^ix=cos x+isinx is used extensively in physics and engineering
and also in maths
this result itself is only an outcome of it
dheeraj54 7 months ago
@dheeraj54 ah right. currently i'm in year 12, and i do higher level physics. and i still don't see how one can use complex numbers/euler's identity in physics :(
DJDavverMusic 7 months ago
@DJDavverMusic Have you considered analysis and derivations? It may very well be used in deriving many of the formulas physics uses today.
illumined1 7 months ago
@illumined1 i am about half way through the course, so probably not yet. that probably explains why i didn't use it yet haha.
DJDavverMusic 7 months ago
@illumined1 also i just finished standard 12
dheeraj54 7 months ago
@dheeraj54 srry wrong person
dheeraj54 7 months ago
@illumined1 feynman uses it to prove things like the lower of wavelength through transparent surfaces of higher refreactive index and uses it to explain refractive idex
dheeraj54 7 months ago
@DJDavverMusic have u heard of the feynman lecture series?
if so ull c that he denotes complex numbers to two dimensional vectors
he uses it extensively in the chapters on light
the complex numbers using euler's form are a huge help in coordinate geometry also as far as i can c
dheeraj54 7 months ago
@DJDavverMusic wait til you see circuit theory!
metro2089 7 months ago
isnt it the soundtrack of the beautiful mind? i've just seen it
DayStyle92 8 months ago
isnt it the soundtrack of the beautiful mind?
DayStyle92 8 months ago
ZOMG the music is so stimulating!
ryanrenesis 8 months ago
What music did you use?
joshuawbunce 8 months ago
they should make a movie about Leonard Euler
Iluminista991 9 months ago
nice vid
utubeshighlites 9 months ago
so euler used taylor's work to get to his identity?
mehdiuk 9 months ago
But of what use is this for?
Austin101123 9 months ago
@Austin101123 One use I can think of is in the study of Hilbert Spaces in QM regarding wave functions for infinite square wells. Euler's identity presents itself as highly useful when representing a separable wave function as a sum of functions defined over a Hilbert function space.
floopsie666 9 months ago
@floopsie666 welp im 7th grade so I only know what a wave function is and what an infinite sqaure well is
can you dumb it down for me?
Austin101123 9 months ago
@Austin101123
kinda hard to dumb it down without using taylor polynomial. just keep studying and you'll understand it soon enough
JoceyXcore 8 months ago
@JoceyXcore you could also explain taylor polynomial to me
do you mean like this?
3x^2+7x+4
(x+3)(x-4)?
Austin101123 8 months ago
@Austin101123 Actually it's kind of a normal thing to say after the first glance. But believe it or not, we have the ease of analyzing sinusoidal signals and the steady-state sinusoidal responses of linear RLC circuits thanks to the Euler's identity. I'm sure it has lots of other uses in applied sciences but since i'm an electronics engineering student, i use it that way all the time.
Erk7RK 8 months ago
@Erk7RK Sentences I understood: 0%
Austin101123 8 months ago
@Austin101123 I'm guessing you're not familiar with the terminology i used. Sinusoidal signals are the signals that vary with time, like a sinus curve. We use electricity in this form, for example. The voltage at the input, (i.e. mains voltage) changes with time, often expressed mathematically with trig functions. And it actually takes both positive and and negative values. To find out (easily) about currents and voltages on the components of a circuit, we need this identity.
Erk7RK 8 months ago
@Erk7RK Sentences Understood: 50%
Paragraph understanding: 5%
What does this have to do with the video?: 0%?
Austin101123 8 months ago
This has been flagged as spam show
@Austin101123 I'm actually beginning to think that you've got some mental disabilities. Didn't you ask, "But of what use is this for?"? Well, I'm trying to answer that question of yours. And you're telling me what does this have to do with the video? :D
Erk7RK 8 months ago
Astounding resounding profounding theorem which make us want to seek more grounding in it. EEK!
lexinaut 9 months ago
"if this formula was not immediately apparent to a student..." - did he mean, if the student didn't know what the formula means, or if the student didn't know how to prove it?
Gytax0 9 months ago
i like that you added the "a beautiful mind" soundtrack,
:)
AnnTheDirector 9 months ago
0:43 - Incorrect. Pi can be written as a fraction.
What you meant so say was, pi cannot be expressed as a fraction, x/y, such that both x and y are integers.
JesusHatesChristians 9 months ago
@JesusHatesChristians yup.
c/d
or
A/r^2
or
well other formulas that involve pi
or
pi/pi^2
Austin101123 9 months ago
I know the movie, A Beautiful Mind. Yes?:)
egi152003 9 months ago
i got a tattoo of this identity on my upper back last week. I love it! =D
bobbyfearfactor 9 months ago
Really beautiful video, with beautiful music too.
Thank you!
OldSchoolSkill 10 months ago
I swear I get chills looking at stuff like this sometimes.
hedonism13 10 months ago
This proof is really fucking amazing. It shows how those three constants, so exquisitely converge with integer numbers. I’m sure there are many things else that converge nicely, but that is the one in particular that popped out at me. Also, I think that equation demonstrates quite convincingly that the imaginary number “i” does indeed grapple firmly with our commonplace reality. If you don’t understand what I’m saying, then try graphing that equation – you’ll see what I’m talking about.
MarvelsofaLifetime 10 months ago
@MarvelsofaLifetime actually i only use complex numbers when i study electromag
masochistnteam 9 months ago
@nxvznx So you don't think fractals are beautiful? At all?
Mephisarisa 10 months ago
man FUCK THIS, why can't it be as easy as 1+1=2
holy crap I have to head to the retard department in campus to have all these nerds teach me this crap like 30 times for me to get even the basics
two plus two equals five SEE 1984
tHeWasTeDYouTh 10 months ago
I'm about to take calculus. I guess I have to learn calculus before I understand anything :( right...?
poopinitup 11 months ago
@poopinitup Yeah, the part where he does e^(x) = 1 + x^2/2! + ... (similar with sinx and cosx) is called Taylor series, something you learn in second semester calculus :)
whitesketchbook 11 months ago
@poopinitup you don't, I'm still in high school and i can understand that
qcpatente 10 months ago
@nxvznx thats gotta be one of the stupidest things i ever heard man
BlackMonkey24 11 months ago
This proof brings tears to my eyes. It is unequivocally beautiful.
Gearhe1d 1 year ago
NERDS! somebody says to me "Euler's identity is the most beautiful theorem in mathematics." So I come here expecting to see fractals and awesome sweet math shit and what do I get? nothing. Fucking nerds, masturbating over nothing.
supadox 1 year ago
@supadox you mean the type of nerds that allow for youtube to work, and for your favorite porn site to work, and the nerds that design computers and run the infrastructure of the country? those nerds? yea, go f yourself you worthless piece of shit
MrGreenknight11 11 months ago 7
@supadox Ask any electrical or computer engineering undergrad if this is "nothing." This identity has countless practical applications. Modern technology would not be where it is without Euler's identity.
Think about it. Without it, you couldn't post such a stupid comment, displaying to the rest of the world that you are, in fact, an idiot.
Good day.
JesusHatesChristians 9 months ago
@nxvznx so you find no beauty in nature, at all?
PCGamerPortal 1 year ago
This comment has received too many negative votes show
whats so beautiful? it's just something that mathematics has no answer for, or that mathematics has some limitations.
dangflo 1 year ago
@dangflo Has no answer for? What are you saying? They have the answer. They proved it.
VeritySeeker 1 year ago 27
@VeritySeeker any known applications to this?
E90PAT 5 months ago
@E90PAT one is: simplify the study of oscillatory phenomena
arenics 5 months ago
@E90PAT To stare at in awe ;).
VeritySeeker 4 months ago 2
@E90PAT Many! Used in electrical engineering to model impedence (amplifyers, etc). Used in differential equations to model motions of springs and dashpots (used in trains, engines, etc) and is at the heart of quantum mechanics!
adoado16 4 months ago
@E90PAT ..it has applications in complex number theory,trigonometry and numerous other fields....
refer... wiki
sreekanthhere 4 months ago
@E90PAT yea....complex number theory and trigonometry and other numerous applications... :)
sreekanthhere 4 months ago
@E90PAT It is used in engineering a lot. You can represent sinusoidal functions as exponents and it makes them a lot easier to deal with.
codenamecody 4 months ago
@codenamecody quite interesting, im an engineering student myself but have yet to learn this. I will research, thank you for informing me!
E90PAT 4 months ago
@E90PAT no
plasticspastic201 4 months ago
@dangflo Having five most significant numbers in a relation to each other in this simple manner isn't beautiful to you at all?
markomaric2 11 months ago
Comment removed
rockaholic7777 11 months ago
@dangflo it's so beautiful because it has a power, a multiplication and an addition in it, as well as the two most important numbers (0 and 1) and the two most important irrational numbers. So That's why it is Beautiful!
rockaholic7777 11 months ago
@dangflo WTF?
MultiBrados 8 months ago
This has been flagged as spam show
@dangflo what the fuck are you talking about. are you really that stupid?
Zander101084 7 months ago
@dangflo I really pity you.. You have no idea of the world you are missing out on, and may never see.
adoado16 7 months ago
@dangflo lmao stick to literature, a subject for dumbasses like yourself.
JSasRays 4 months ago
i feel very discouraged, i dont understand this theorem i think i should just give up on math,
Holyfrik1 1 year ago
@nxvznx I do not quite agree. First of all, we can invent things in mate\hematics. Definitions are often inventions, and the number i is an invention. Second of all. A galaxy is discovered, not invented, and oh my can they be beautiful.
VeritySeeker 1 year ago 5
@VeritySeeker There are several approaches. I guess the question in the heart of it all, in this context, is "is the number i an invention, or is it just a name we made up for something which already exists?".
While I'm not arrogant enough to claim I know the answer, I'm leaning towards the latter (out of purely emotional considerations, though).
Tikeslar 6 months ago
Absolutely gorgeous. Thank you for creating and sharing this.
cluebcke 1 year ago
what's really scary is that cos(π)+i*sin(π)=-1
When I think of eulor's identity I don't really see beauty. I feel more fear than I do beauty. It scares the shit out of me. Because it's like it's telling me that we are just scratching the surface of what's really out there. That there is something out there much greater than us. I don't believe in god but man, eulor's identity could make one hell of an argument for one.
toxzen 1 year ago
@nxvznx Beauty this, beauty that...these guys are far from George Clooney's!
foundede 1 year ago
While i may not be able to understand why, i'm definately able to understand what it means. And some of all the cool awesome things it can be used for, like the fourier transform for instance. or the representation of any complex number as simply A*e^(ix), where 0<x<2*Pi.
mortenrobinson 1 year ago
X is the angle in radians that the complex vector makes with the real-axis and A is some magnitude of or length of this vector. e^(ix) is simply a unit vector and its really just an equation for a unit circle in the complex plane (Re-axis and Imaxis). If you plot it 3-dimensionally with x as the third axis (x, Re(e^(ix), Ime^(ix)) The you'll see that it makes a spiral, spiralling round once ever 2*Pi.
mortenrobinson 1 year ago
@mortenrobinson EE students love this stuff ;)
foundede 1 year ago
@foundede EE students are what? Electrical Engineers? Yes? :)
VeritySeeker 1 year ago
...what's the big deal? >_<
Illyria23alyssa 1 year ago
@Illyria23alyssa Is there a big deal? Where?
VeritySeeker 1 year ago
@VeritySeeker I don't know, I can't find it :*(
Illyria23alyssa 1 year ago
@Illyria23alyssa
Ah... :(
But let me know when you do.
VeritySeeker 1 year ago
My teacher showed us this today, she went into a bit more detail. I understand how you come up with this equation, I just don't understand what it means. :(
How does e^(i*pi)=-1? And what can this be used for?
osbiath 1 year ago
@osbiath Nice to hear that the video has been used in class. What it can be used for? Well, when e^(i*pi) ever pops up, we can substitute it with -1. How's that for simplifying? :) Thanks for commenting...
VeritySeeker 1 year ago
@osbiath Well if e^(ix)=cos(x)-isin(x), then e^(iπ)=cos(π)-isin(π). Cos(π)=-1, and Sin(π)=0, and ix0=0 obviously. Therefore, -1+0=-1. And thus, e^(iπ)=-1.
DevoutSkeptic 1 year ago
1+1=2
TheDEATHMYSTERY 1 year ago
@TheDEATHMYSTERY Yep!
VeritySeeker 1 year ago
It also shows that e=cos(i)-i*sin(i)
TheMikeSideGallery 1 year ago
There is another identity that comes from his equation cos(i)+i*sin(i)=1/e I think thats even crazier than the more famous one
TheMikeSideGallery 1 year ago
Beautiful!
...but wouldn't it be easier and more clear just to prove e^(i*x)=cos(x)+i*sin(x) first? :p
Thymonico 1 year ago
@Thymonico Sure, it is the same proof. But I wanted, in this video, just to arrive at the identity.
VeritySeeker 1 year ago
@Thymonico To get there you'd need this first.
raydredX 8 months ago
@VeritySeeker your videos changed my young life forever haha
i love mathematics
seniorbooboojuice1 1 year ago
It's so amazing that the complex power of an irrational number with another irrational number is a rational number. It's just beautiful
muzammilali007 1 year ago
James Horner — "A Kaleidoscope of Mathematics". This piece was the opening to "A Beautiful Mind"
MuleXC09 1 year ago
Thanks! This is a nice exposition. The mystery behind all of this is
extraordinary. The video kindles mathematical motivation, and LORD KNOWS, it TAKES lots of motivation to push forward many times in math!
lexinaut 1 year ago
What I want to know: what is:
(exp + delta)^(i*x) = ?
where "delta" is small. How does "delta" upset the ordinary "cosine(x) + i*sin(x)" we ordinarily expect?
bjnartowt 1 year ago
its not really a theorm, its a collolary, ie. it follows directly from eulers theorm
mpdp85 1 year ago
I still can't accept it as a student of electrical engineering, but I use it even don't accepting it, damn ignorance... :( (taylor's series right ?)
arenics 1 year ago
@arenics yesh
Cammie010 1 year ago
@arenics nevermind. MacLaurin's.
Cammie010 1 year ago
why do people cream their pants over this? all it means is that cos pi = -1 , which any dumbass knows, fucking hell
TheZanipolo 1 year ago
@TheZanipolo It means a lot more than that.
VeritySeeker 1 year ago 17
@VeritySeeker well I prefer Jordan's Lemma anyway
TheZanipolo 1 year ago
@TheZanipolo Yeah, a nifty lemma it is.
VeritySeeker 1 year ago
@TheZanipolo It can be applied in many more ways. As I've learned in Diff. Equations.
saionjik 1 year ago
@TheZanipolo It.s because people like magic
the12thfloor 1 year ago