The Most Beautiful Equation

[@digitalgenius111]

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[@blockybfdi8876]

yes

[@IPlayMultiCraft]

e^iπ + 1 = 0 so e^iπ = -1

[@TaimTeravel]

Amazing. Too many concepts 😮

[@Youtube_Stole_My_Handle_Too]

I find this more beautiful: e to the power of i tau equals unity.

[@mattgroom1]

It is the most awful equation, e^i.pi =-1. You are idiots, the Tau equation is the most beautiful.

[@gruk3683]

This is absolutely incredible. I just finished Calculus II, and when we talked about Taylor Series they were explained very poorly. This not only made me completely understand how Taylor series are formed, but also what e^ipi really means (something I’ve been wondering for a very long time). People like you make the world of learning a better place. Thank you

[@user-lu6yg3vk9z]

It comes from Euler identity e^xi=cos(x)+isin(x) x=pi e^pii=cos(pi)+isin(pi) e^pii=-1

[@echo4k915]

@@user-lu6yg3vk9zwe watched the video thanks 👍

[@ShubhGG12]

I agree, its a great video... I just finished 8th grade and I'm half lost but interested nonetheless 😅

[@ironmansac]

e^yipee

[@CherryColaCake]

TAYLOR SWIFT

[@mustafayigitkartal4257]

This might be the most concise (and perhaps the prettiest) explanation of euler's identity that I've ever seen. I love how you show each derivation (pun intended) step by step and using first principles, really shows that you're not just listing off an arbitrary set of rules but actually understand what each of them mean.

[@attica7980]

Actually, if you take the definition e^x=lim_{n\to\infty}(1+x/n)^n, a much more satisfactory and intuitively appealing explanation of e^{i\pi}=-1 can be given. The Taylor series explanation has zero intuitive appeal; it works, but it does not show why the identity is really true. Just google for e^i pi youtube , and probably the first thing that comes up is a non-Taylor series explanation. Mathologer gives such an explanation, but there may be also others.

[@victoryfirst06]

If only my math teacher explained this so well.

[@dagan5698]

It was a great explanation, but be honest if this was the first time you saw any of these concepts, you wouldn't understand any of this based on this video alone. It takes time and exposure with these subjects to really grasp what is taught. My calc 2 teacher explained this. My differential equations teacher explained this. And while I was in the class, it didn't make a lot of sense. But trust me they explained it just as well if not far more in depth in class. Again, it's a great video but I wish people wouldn't blame teachers for students not immediately grasping confusing concepts. Now maybe you didn't have the best teacher but in my experience it's not the teacher's fault. (It's not the students either)

[@gokiburi-chan4255]

The problem then is the system. For expecting us to get this shit in in one hour

[@nutsi3]

Ikr when my teacher told me this I only understood 1 word, but when he is telling me the same thing I understand at least 2

[@deserado11]

... aint that the truth ...@@dagan5698

[@Nom8d]

This is your math teacher and I'm failing you in the upcoming exams.

[@swdhags2875]

Derivative, Taylor seires, sin cosine, iota , pie all in one video!! Incredible

[@samuraijosh1595]

yeah like wtf this guy is cray

[@gamer__dud10]

Do you want to know Jesus? Click Read more Truly truly i say to you all Jesus is the only one who can save you from eternal death. If you just put all your trust in Him, you will find eternal life. But, you may be ashamed by the World as He was. But don't worry, because the Kingdom of Heaven is at hand, and it's up to you to choose this world or That / Heaven or Hell. I say these things for it is written: "Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, *teaching them* to observe all that I have commanded you; and behold, I am with you always, even to the end of seasonal". Amen." -Jesus -Matthew 28:19-20 🩶🖤❤🩷❤🧡❣️🧡💟🤍🩵💓🩵🥰💙🖤❤❣️🥰♥️🥰💛🤍🧡💟❤💟❤💓🩵🖤🩵🩶🥰♥️🧡💓🩵💓🤍❣️❤♥️🤎💚💟💓❣️🧡🖤❤🩷❤🧡🩵❣️🩵🖤🥰🤎❤💛🤍❣️💚❣️💓🩶🤍💛🩵💓❤💟💓🩶💚🩷🤎❤💟🩵❣️💜💛🥰💓💜💛💚❣️💓💟🤍💛🩵💚❤🖤🥰❣️💓💟🤍💓🩵💓❤🩷🥰🩶🧡💟🤍🧡🩵💟❤❣️💚🩷💜🧡❤💛🩵❣️🤍🩶❤💛💜💛🩵💟💙❣️🥰♥️💚💛🥰❣️💜🖤🩵🤎🤍💓❤♥️💚❣️💚🩷💜💓♥️💜❣️🧡🖤💚💛🩵💓💙💟🥰❣️💓🖤🥰🤎❤💓🤍♥️🤍❣️🥰💟💚💛🩵💓🩵💟♥️🤍💓🩵💚❤💟🧡❣️💓♥️🤍💛🩵🥰❤💟💓❣️💓🖤💜🩷🩵💓🩵💚💙💛💜❣️💓❣️💓💟💜💓🤍💓🩵❣️💜💟💓💟💚🤎🤍💚❤💛🧡❣️💓🖤🥰🤎❤🧡🩵❣️❤🧡🖤💚🤎🤍💓🩵♥️❤🥰🖤💚💛💙💓🩵

[@ElijahMeadow]

I very much apreciate the way you spelled pi lol, now I'm hungry.

[@CuRiOuS--MEHRAN]

As a 9th class student, understanding Euler's Identity in 13:38 secs is crazy 😭😭☠️

[@akushiplays]

my current class is learning Pythagorean theorem rn, but here I am learning pre calc for the sake of my future😂🙏

[@joemomma1560]

@@akushiplays This is calc not precalc lol u are doing precalc right now!

[@DUGGIRALAVNANILKUMAR]

Me too

[@fun-damentals6354]

so this guy actually explained radians, calculus and other stuff in 13 minute video. he explained them well enough to actually understand the subject matter. you sir are a legend. so damn rare to find content like this. hats off man

[@i_have_no_pronouns7037]

Dude, this is the beauty of math that an engineer like me won’t truly be able to experience. We learn a lot of stuff without proper explanation so it’s nice to see a video like this

[@aaronfidelis3188]

You can always defect to the mathematician's side and take a math major 😂

[@Kaspa969]

You did an amazing job explaining It! I tried many times to understand the Euler's identity, but I couldn't because other people didn't do what you did. You explained everything from the basics, and It really helped a lot.

[@ShivamTiwari-tt2gv]

B complex oh my tree like last leaf

[@kennethbrack4061]

Oh my gosh. That equation was a wonder to me when I was a teenager and very good at math. Now I am a senior citizen and have understood it for the first time. Thank you for your excellent explanation.

[@-_-h1]

as a teenager sad that such resources were not available in your time, None of my teachers explain such stuff, KZbin is a life saver

[@OmarElsayedd]

The animation, the explanation and the way you covered so many topics in one video is just amazing.

[@vampire_catgirl]

e^iπ = -1 is a much more beautiful equation in my opinion. Not only is there no problem with having negative numbers in equations, but it gets the meaning of e^iπ across much better: -1 is the number π radians around the unit circle. Rearranging it not only obscures the entire point of e^iθ, but it also makes light of the significance of negative numbers as a whole.

[@OKchromia]

This channel is too underrated, this was explained flawlessly

[@uchiaru8559]

me who understood nothing,but still found it cool 😂

[@JARG-Random_Guy]

not alone there, bud.

[@sanatkundu2293]

Now there's three of us

[@AvnilSanjeev]

now four brooo

[@endlesswick]

A really good explanation. I have heard of solving Euler's Identity with the Taylor series before, but you really went into detail explaining how the Taylor series works, how to turn sin, cos, and e^x into Taylor series, and finally bringing it all home equating the Taylor series of e^x to that of sin and cos. All in 13 minutes. Impressive.

[@among-us-in-tetris]

this has been my favorite equation since i read it on a math book, but now is the first time i actually understood the process of it. most useful 14 minutes of math in my life

[@notwithouttext]

in my opinion, the general formula e^ix = cos x + i sin x is more beautiful since it directly shows that e^ix makes a circle on the complex plane, and the one with pi just says that halfway around the circle it's -1. but with 2pi (or tau) it's 1, and with pi/2 (or tau/4) it's i, and with 3pi/2 (or 3tau/4) it's -1, which are beautiful in themselves as well, so i think all points should be included.

[@insentia8424]

Euler's identity doesn't only say that the one with pi is halfway around the circle. It ties together 5 of the most important constants in mathematics, e, pi, i, 0 and 1. That's what it focuses on, the connection to a circle... is trivial, since pi is included. And if we have pi, then we have something that could be described as a circle with more or less effort.

[@notwithouttext]

@@insentia8424 it's true that it connects them, but surely the reason _why_ the equation works is more meaningful the equation itself, and personally i'd prioritize meaning over "connection of constants". and really, it only connects _four_ constants. the 0 doesn't really do anything here: the equation could be expressed equivalently, and in my opinion more clearly, as "e^(pi*i) = -1".

[@insentia8424]

It connects the most fundamental constants in mathematics, with the most fundamental operations: addition, multiplication and exponentiation. It connects close to everything together. And the beauty comes from it being the *solution* to using pi as the value for Euler's formula. We set formulas equal to 0 whenever we can in mathematics, because having everything on one side rather than spread around on both, makes it easier to categorize and compare to other known formulas and equations. It's a convention in mathematics. And a natural consequence of always wanting to set any equations to 0 to make solving easier.

[@notwithouttext]

@@insentia8424 ah, i think i see the beauty you describe in the formula. i still think the general formula is more beautiful, but i guess it's a bit subjective. for me, the fact that exponential (and hyperbolic) functions connect to trigonometric ones is more beautiful a fact, but connecting fundamental constants with other operations is similarly beautiful. (i also suspect that addition just tends to be more "beautiful" than subtraction: after all, we don't say euler's formula is "cos x + i sin x - e^ix = 0".)

[@JD-ee4df]

This is insane, there's about 5 different concepts in this video that I understood for the first time despite years of studying Maths and having to take these things for granted. Amazing video, thank you.

[@mario-px8pb]

This is the most beautiful thing i have ever seen. Amazing explanation. Thank you!

[@drasiella]

Step 1: cry

[@Ilikeinsideout]

​@FaizThe-kc6dk because this shit hard as fuck😭😭

[@lyingcat9022]

There’s no crying in Mathematics!!! Wait… no that’s baseball. Carry on :)

[@sk1ller_604]

Step 2: suffer

[@Teleios77]

I thought im the only one who find this hard to understand🥲​@@Ilikeinsideout

[@3amoood]

@@Ilikeinsideoutnah

[@ЛевАронов]

it's like magic... I first saw this equation in the video "Math vs Animation". Since I am just in 11th grade, I know nothing about complex numbers or eulers number e. So I never understood what those complex equations mean. But now when you wrote e^ipi = cosx + isinx I was shocked, because I remember this equation from that video. This is so well done, thank you so much for the explanation!

[@joey5305]

Euler's form is there in complex numbers in class 11th. You will know if you are preparing for JEE.

[@realsstudios8153]

@@joey5305 "i sTuDiEd cALcULuS iN gRaDe 4" -🤓

Fr

[@FundamSrijan]

​@@joey5305yes , exactly, but this video is still god level .

[@justsaadunoyeah1234]

​@@realsstudios8153bruh I literally did I'm now one grade higher and studying vector calc and a tiny bit of number theory and I'm looking to move forward to abstract algebra (this is my mom's acc I use it to watch math and geography vids)

[@michajasinski8457]

I feel scared for understanding everything in this video.

[@Tryh4rd3rr]

Same bro 😢

[@abdheshpratapsinghraghuwan4158]

Coz your basics about maths r week

[@ikennaokoro7894]

🤓☝️

[@ikennaokoro7894]

@@abdheshpratapsinghraghuwan4158ur basics of English are trash

[@anibeto7]

​@@abdheshpratapsinghraghuwan4158 He understands all of it and that is what makes him scared.

[@supremeclamitas5053]

That was the best explanation of the derivative limit I've ever seen!

[@YoutubeBorkedMyOldHandle_why]

Thank you sir. This is the most elegant and understandable explanation I've seen, which ties these important concepts together. It is truly amazing that Euler and others understood these things some 3 centuries ago, yet we still struggle with them today.

[@CrosshairClips]

This identity is fundamental in helping design the very devices you are watching this video on. Euler’s identity is used heavily in circuit analysis to solve first/second/ and even higher power circuits with multiple capacitors and inductors. Very cool stuff!

[@pelasgeuspelasgeus4634]

No it's not. You simply repeat bs you read somewhere.

[@CrosshairClips]

@ Yes it is. The expanded identity is e^ix = cos(x) + i*sin(x) In the electrical world, this is rewritten as e^-jx = cos(x) - jsin(x). As to not confuse it with i being the symbol for current. This is used to solve RLC circuits, where you have some logarithmic decay, following the sin and cos shapes, with a phase change of j.

[@pelasgeuspelasgeus4634]

​@@CrosshairClipsare you an electrical engineer?

[@CrosshairClips]

@@pelasgeuspelasgeus4634 computer engineer.

[@fano72]

You explain so much about complex numbers in this little video, which never been told in any maths class. Thats brilliant!

[@GourawRaj-hj4jy]

First time I m seeing this much effort to explain Euler identity. Well done

[@thomaskember3412]

We can go further by writing the identity as e^ipi = -1 and from that write ipi = ln(-1) then dividing both sides by I we get pi = ln(-1) /i or pi = ln(-1) / square root of-1 which is a new definition of pi. I am sorry my keyboard doesn’t have much in the way of mathematical notation.

[@frimi8593]

Well, yes and no. Tl;dr while π is one solution to the equation x = ln(-1)/i, that does not work as a definition of π. L;r When you’ve got imaginary numbers in the exponent you’ve got to be very careful when manipulating values because you may end up with an equation that has multiple solutions. In fact, logarithms kind of break on the complex plane for this very reason. While Euler’s is true, “iπ” is not the only the only value that gives -1 when you take its power of e. Looking back at the explanation you may notice that e^(i3π) also equals -1, as e^(i3π) = cos(3π)+i*sin(3π) = -1+0i. In fact for any integer n, (2n+1)π is a solution to the equation x=ln(-1). The fact that logarithms are multivalued in the complex plane means that doing algebra on them starts to fall apart, so you can’t totally trust the exponent/logarithm rules that you learned for the real numbers. For instance, you’ll notice that by manipulating your equation a little more, using classic real valued log rules, you may arrive at the conclusion that π=0: Start with π = ln(-1)/i. Now in math we don’t like to have square roots in the denominator, including i, so let’s turn that into -i*ln(-1) by multiplying the fraction by i/i. Next, we can move part of that scalar inside the logarithm like so: π = -i*ln(-1) = i*ln(-1^-1) = i*ln(-1) There is only one number x on the entire complex plane such that x = -x, 0. Thus, given that π = -i*ln(-1) = i*ln(-1) = -π, π must be equal to 0. The reason we can arrive at this false conclusion is because while π IS a solution to x = ln(π)/i, -π is ALSO a solution. So is -3π, -5π, 3π, 856203757π, and every other odd product of pi. You can see this clearly in the fact that -1 is equal to itself raised to any odd power, thus we can pull any odd number we want out of the expression ln(-1).

[@anvisingh2735]

i=sqrt(-1) e=2.71828182845904523536028747135266249775724

[@abdullahbintahir2297]

​@@frimi8593 Thank you! This was an awesome read.

[@gamingbunny3434]

I am literally astonished by how much clear the explanation is, of each and every concept of mathematics expalined in the video. Please never stop making videos.

[@Robin-Dabank696]

Now I understand everything in those math videos that I'm addicted to 😂😂😂(especially the cos(x) + isin(x) part) Thanks!

[@BentleyCreates]

-1

[@tHaTsWhAtI.mSaYiNg]

This was awesome! I’m an electrical engineering major and never really understood how imaginary numbers fit into calculus until this video. The explanation and derivations were very concise and helpful. Thanks!

[@flibby4973]

the way it all pieces together at the end is crazy.

[@The_Mask_Official]

Absolutely beautifully explained

[@nbspWhitespaceJS]

in my opinion, 1 + 1 = 2 is still the most beautiful equation ever because all of math is based off of this seemingly simple equation that cannot be proved.

[@hhhhhh0175]

it can't be proved because that's the definition of 2. 2 is just shorthand for 1 + 1

[@theunstoppable0357]

There is actually a proof for this

[@matesafranka6110]

There's actually a video on Half as Interesting titled "The 360-page proof that 1 + 1 = 2"

[@clickrick]

@@theunstoppable0357 Sure, but the book containing it is a little slow to get started. It only reaches this part of the plot when it's about 2/3 of the way in.

[@TheCyanKiller]

That’s kinda like proving that the colour purple is green and blue. U can’t prove it, it’s just the definition of purple.

[@nohumanisagod]

This is just so lovely. Seeing so many concepts in math explained so quickly, feeling like I could understand all of this without any previous knowledge, because of how well this was explained. If only all of math would be explained to me like this. Really cool to see all these different concepts play together aswell, they don't look like they should make any sense, but math can be just this beautiful

[@IMAHMS]

This is how one should sound when explaining mathematics, it is disturbing that other channels on youtube use too much emotions in their tone.

[@ytsimontng]

I'm a math teacher and i found this video extremely helpful and inspirational, thanks!

[@FundamSrijan]

I salute you 🙏🙏🙏 god of mathematics . You explained me derivatives , pi , i , e e^x = cosx + i sinx and Euler's identity itself in a single video better than any teacher I have seen and far far better than my school teachers . 🙏🙏🙏🙏🙏 Respect

[@Redstoner34526]

Your videos are really great for learning these things even made more sense than the Stewart calculus book.

[@patrax6studios155]

This video is incredible. It is so thought-out and well put-together anyone would be able to understand this. I truly wish one day I can be like you, helping other people learn. Thanks a bunch.

[@alabamacow]

I have watched countless hours in countless genres of videos on KZbin for over 10 years, but this is easily one of the best videos I have ever watched. Brilliant work!

[@rokaq5163]

Genuinely shedding a tear. This is the most concise, comprehensive and ultimately effective explanation I have seen of this wonderful equation. It made me appreciate the efforts of mathematicians in a way I'm not sure I would have achieved by myself had I not encountered this video. Thank you for sharing this and letting everyone know the origin of this breathtaking piece of mathematics.

[@zamnodorszk7898]

The incredible beauty of the equation explained! As a physicist, I only ever considered it through the real-imaginary phase relation, but never considered the derivation! Thank you!

[@manthansingh8036]

One of the best maths video on KZbin I have ever watched Thankyou very much

[@macultic00]

This video was so good and i was so immersed that i forgot it was about e^ipi

[@darryllmaybe3881]

I'm gonna be perfectly honest, I dodn't understand maybe 20% of the things discussed in this video, but I understood it just well enough that it was satisfying to see it come together in the end and know I wasn't completely lost.

[@Okoro-l6k]

4:22 Where did u get h²?

[@owlzyxowl1995]

(A+B)^2=a^2+2ab+b^2

[@AndrasBalintBoroczky]

I have never found anybody explain this thing this well

[@ahmxdhsn]

bro this explained everything so well. I LOVE IT!

[@thecringeyboylol]

This is the easiest video to understand, it truly fragments every piece to fully explain for the main topic. Wow, I'm already getting excited for college. The best explanation I have ever watched in KZbin, gave a like and subscribed for more of these vids

[@jerzyzajaczkowski8537]

Euler's real achievement is a function identity e^(ix)=cos x + i*sin x, not the above-mentioned numerical curiosity (e^(i*pi)+1=0) that stems from the identity.

[@hellothere-cx8dz]

Got to agree, it explains much better the relationship between the argument and exponential form of a complex number 👍👍

[@MadTheDJ]

Okay, I got to ex^iπ = -1 on my own, and I know what pi, exponents and roots are, but man-oh-man was I totally not keeping up with the formulae once you got into complex numbers and derivatives. Like, I was watching you explain, watching you simplify, and was completely trusting your math because I realized quickly that I was truly out of my depth. That's absolutely NOT a knock on you! It's all on me. This is calculus waaay beyond my skill level. But I still find it fascinating and this video makes me want to understand these principles better. I WANT to be able to practically apply them to manipulate equations this artfully. I envy anyone who comes by these skills easier than I do.

[@oru]

the explanation of Taylor Series and how to derive the formula for e^ix was so well done! initially i thought the video would just be stating the formula for e^ix and plugging pi in it to call it a day, but i was really wrong (thankfully)

[@billybobbjo]

0:34 half expected the pi to wave at me , the 3blue1brown brainrot is real

[@nikitaavdeev9681]

I was not expecting much, but honestly, this is the best explaination I've ever heard. The only thing I would add is to make the deffinition of sin more clear.

[@ManiSafarzadeh]

This was the most perfect explaination I seen so far

[@sparx0s]

This is the best video I've ever seen on entry level derivatives, and it's not even the main topic

[@dylangianino7616]

INCREDIBLE explanation 10/10 no notes

[@TheodorRiegger]

So cool how the Maclaurin series of cosine and isine are equal to e^ix!!! Love the video 🧡

[@Death.4225]

Idk if i my sub counts, but this video blew up my mind, and it was the first one i watched of this channel! I HAD to show appreciation and ig the best i could do was subscribe and leave a comment.... Keep up bro! You are doing a great job, i have always connected with maths best, but i never understood Euler's identity much except the formulas related to it, but you have explained it so well including its origin and need! Im just flabbergasted! Thanks again! Love maths! ❤

[@tnnm2022]

UR SUCH A CHAD BROO...SIMPLEST WAY TO UNDERSTAND THIS MAN

[@baykkus]

I'm an engineering dropout now pursuing a degree in the humanities, personally I wouldn't change it for the world but the beauty of mathematics is something I will always appreciate. I am glad I took all those calculus classes just for that fact alone, and this is a wonderful video.

[@frosch_9782]

this is the best explanation of the Euler identity i have ever Seen

[@frozenturtl827]

I don’t know much about Taylor series as I was never formally taught but this made perfect sense. Nice

[@muhammedrayan4048]

You got me hooked from the start itself, your explanation was very interesting! You just earned a new sub from me

[@tea.cup.16]

This was so beautiful it made me cry

[@Quartz512_]

When you blink in math class: 3:30

[@syphon5899]

The effort put into this video is immaculate

[@hardikgarg2021]

brilliant explanation this never felt so easy

[@Roman_CK]

Euler's identity using calculus, trig and Tylor. Impressive. Your video covers that ridiculous expression quite elegantly. Awesome work.

[@gagelucas6036]

This was beautiful. I’m currently in Calculus BC, and the explanation for Taylor Series was a lot more straightforward here than my teacher made it 😂

[@dorukayhanwastaken]

2:04 Making a counterclockwise circle and putting i's powers where they would be on the complex plane was deliberate, wasn't it?

[@maxeverest5564]

Probably the best Maths video I've ever seen!

[@uvspy]

Another thing to note, why it equals 0, is to consider the polar form of the equation e^(ipi) + 1 = 0; 1. In polar form, this would mean (cos pi + isin pi) + 1 = 0., where pi is the argument of the equation. 2. When evaluating this, cos pi = -1, sin pi = 0, this means (-1 + 0) + 1 = 0, which can be simplified into -1 + 1 = 0, where 0=0.

[@TriaMilia]

I'm gonna use this video to introduce calculus to any person beginning their journey with a engineering degree, I think it'll be perfect to show many things to be teached, specially calculus 1 and 4 (idk how it is for you guys, but 4 is ODEs and PDEs)

[@SPV66]

You explained *The Most Beautiful Equation* in *The Most Beautiful Way !!!* 🤗👏👏👏👍

[@monkee3613]

Btw at 9:59, I just realised you can differentiate the Taylor series of sin(x) to instantly find the Taylor series of cos(x) instead of having to do the whole method again

[@swarnendukarfa8480]

This video is a masterpiece in basic calculus

[@muiznik1323]

Your explanation is too clean bro😊😊

[@adrians9367]

The best explanation man I understood everything you really explain all the context and didn't went direct to the taylor series 😅

[@toastdog214]

This is the best video prooving Euler's identity on youtube that I've seen so far. Brilliant video

[@synonymous123]

Truly the one of the few Digital geniuses of youtube

[@MinecraftIsLoveMinecraftIsLife]

This was easy to follow and i actually understand how a taylor series is formed now. This is a great video.

[@androg0000]

Very elegant explanation and the process behind the formula

[@dityaharpatipraja4442]

I wish I had a teacher like you. you have explained it so clearly and beautifully. I wish I could like the video 5-6 times. Respecc +++ 🙏

[@Redstoner34526]

Yo in 8th grade when we learned sin and cos I asked if it was possible to make sin x with an ifinitely long polynomial when I looked at the graph in Desmos and the teacher told me you couldn’t but now we have Taylor series in calculus.

[@Haffi684]

Great work, I really hope your channel blows up

[@warwithworld11]

Algebraic visualization is too cool! But geometric visualization is an awesome! Good work!

[@آسررديني]

How beautiful is this explanation 😍

[@twachl8039]

Great Video! Really enjoyed how you went step by step, but in order the understand everything you need some knowledge of calculus, stillt great and „short“ video

[@rdtyphon6684]

I have a question, since Taylor's series is infinite, even if the values being added are very small for larger powers, shouldn't the sum still equal infinity given that we are adding an infinite no. Of times? Even if Ii were to add 1*10^-100 to itself, it would still be infinity given enough time right? So if we talk about infinite series, how can we approximate the value to anything less than infinity

[@dries2579]

I suggest you google for convergent series and divergent series, which will explain your question

[@Enddeous]

No, because the numbers get smaller and smaller, and so the sum just converges on a specific number. Basically with each term it zooms in on a specific number, and with each passing term it gets more and more accurate.

[@rdtyphon6684]

Thank you

[@darklightmotion5534]

This has been the most comprehensove video on this topic I have ever watched

[@sevi630]

>click video >insanely strong accent >go back

[@Random3.142]

Beautiful explanation, just the right level and speed, thanks!

[@Queso_Burguesa]

as a high school freshmen who doesn't know calculus, this video made sense. I don't know how you did it but damn was that an amazing video! Really though, thank you

[@ΙάκωβοςΠαπαμαγκανάς]

That's an excellent video!!! Congratulations!!! Everything was very clear!!!

[@Action_0051]

Beautifully done my guy👍🏻

[@bruhnish598]

bro taught the whole of calculus in 13 minutes....and it was amazing!

[@HolaSoyElToto]

I dont know how i ended up watching this, but it was crazy, i liked it

[@limpaika]

Wow, I dont even know how to do derivatives yet, but I kinda understood everything, and thats why I love math. Great video❤