Animation vs. Math
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- čas přidán 23. 06. 2023
- How much of this math do you know?
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🔹🔶 WRITTEN BY 🔶🔹
Terkoiz
🔹🔶 ANIMATION🔶🔹
Terkoiz
n8ster @n8sterAnimates
Ellis02 @Ellis02Media
Hexal @Hexalhaxel
Oxob @oxob3000
ARC @ARCpersona
SmoilySheep @smoilysheep4670
CoreAdro @CoreAdro
SimpleFox @SimpleFox1
ExcelD
eds! @eds7236
ajanim@ajanimm
Fordz @Fordz
🔹🔶 SOUND DESIGN🔶🔹
Egor / e_soundwork
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Pepper @dan_loeb
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Scott Buckley @ScottBuckley
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Hatena360 @hatena360 - Krátké a kreslené filmy
To be clear, my lead animator is the math nerd behind all this. And as always, watch DJ and I talk about it: czcams.com/video/dRj3X7IFCjY/video.html
Woah
Edit: i was about to say first but i remember i have a brain.
Edit 2: Wow many likes anyway here is a recipe for brownies and uh idk just make a brownie here it is: 10 tablespoons (142 grams) unsalted butter
1 cup (200 grams) granulated sugar
1/3 cup (67 grams) packed light brown sugar
3/4 cup plus 2 tablespoons (88 grams) unsweetened cocoa powder, sifted
1/2 teaspoon vanilla extract
2 large eggs plus 1 egg yolk
1 tablespoon corn syrup
2/3 cup (85 grams) all-purpose flour
1 tablespoon cornstarch
1/4 teaspoon salt
For the frosting:
1/2 cup heavy cream
1 1/2 cups (255 grams) semisweet chocolate chips
Wilton Rainbow Chip Crunch or mini M&M’s, sprinkles, or other candy
Yoo pogchamp
@@Emirhanoleo78hi
hi alan
1 minute lol
If you could turn this format into a video game, you'd have an incredibly powerful tool to teach kids math.
imagine
Just to add to this I went and learned eulers identity is after wondering why E to pi I was so crazy
@@jesseweber5318me too, i had no idea
Like minecraft?
@@rickt.3663 you mean, Minecraft Education edition?
*THE MATH LORE*
0:07 The simplest way to start -- 1 is given axiomatically as the first *natural number* (though in some Analysis texts, they state first that 0 is a natural number)
0:13 *Equality* -- First relationship between two objects you learn in a math class.
0:19 *Addition* -- First of the four fundamental arithmetic operations.
0:27 Repeated addition of 1s, which is how we define the rest of the naturals in set theory; also a foreshadowing for multiplication.
0:49 Addition with numbers other than 1, which can be defined using what we know with adding 1s. (proof omitted)
1:23 *Subtraction* -- Second of the four arithmetic operations.
1:34 Our first *negative number!* Which can also be expressed as *e^(i*pi),* a result of extending the domain of the *Taylor series* for e^x (\sum x^n/n!) to the *complex numbers.*
1:49 e^(i*pi) multiplying itself by i, which opens a door to the... imaginary realm? Also alludes to the fact that Orange is actually in the real realm. How can TSC get to the quantity again now?
2:12 Repeated subtraction of 1s, similar to what was done with the naturals.
2:16 Negative times a negative gives positive.
2:24 *Multiplication,* and an interpretation of it by repeated addition or any operation.
2:27 Commutative property of multiplication, and the factors of 12.
2:35 *Division,* the final arithmetic operation; also very nice to show that - and / are as related to each other as + and x!
2:37 Division as counting the number of repeated subtractions to zero.
2:49 Division by zero and why it doesn't make sense. Surprised that TSC didn't create a black hole out of that.
3:04 *Exponentiation* as repeated multiplication.
3:15 How higher exponents corresponds to geometric dimension.
3:29 Anything non-zero to the zeroth power is 1.
3:31 Negative exponents! And how it relates to fractions and division.
3:37 Fractional exponents and *square roots!* We're getting closer now...
3:43 Decimal expansion of *irrational numbers* (like sqrt(2)) is irregular. (I avoid saying "infinite" since technically every real number has an infinite decimal expansion...)
3:49 sqrt(-1) gives the *imaginary number i,* which is first defined by the property i^2 = -1.
3:57 Adding and multiplying complex numbers works according to what we know.
4:00 i^3 is -i, which of course gives us i*e^(i*pi)!
4:14 Refer to 3:49
4:16 *Euler's formula* with x = pi! The formula can be shown by rearranging the Taylor series for e^x.
4:20 Small detail: Getting hit by the negative sign changes TSC's direction, another allusion to the complex plane!
4:22 e^(i*pi) to e^0 corresponds to the motion along the unit circle on the complex plane.
4:44 The +1/-1 "saber" hit each other to give out "0" sparks.
4:49 -4 saber hits +1 saber to change to -3, etc.
4:53 2+2 crossbow fires out 4 arrows.
4:55 4 arrow hits the division sign, aligning with pi to give e^(i*pi/4), propelling it pi/4 radians round the unit circle.
5:06 TSC propelling himself by multiplying i, rotating pi radians around the unit circle.
5:18 TSC's discovery of the *complex plane* (finally!) 5:21 The imaginary axis; 5:28 the real axis.
5:33 The unit circle in its barest form.
5:38 2*pi radians in a circle.
5:46 How the *radian* is defined -- the angle in a unit circle spanning an arc of length 1.
5:58 r*theta -- the formula for the length of an arc with angle theta in a circle with radius r.
6:34 For a unit circle, theta / r is simply the angle.
6:38 Halfway around the circle is exactly pi radians.
6:49 How the *sine and cosine functions* relate to the anticlockwise rotation around the unit circle -- sin(x) equals the y-coordinate, cos(x) equals to the x-coordinate.
7:09 Rotation of sin(x) allows for visualization of the displacement between sin(x) and cos(x).
7:18 Refer to 4:16
7:28 Changing the exponent by multiples of pi to propel itself in various directions.
7:34 A new form!? The Taylor series of e^x with x=i*pi. Now it's got infinite ammo!? Also like that the ammo leaves the decimal expansion of each of the terms as its ballistic markings.
7:49 The volume of a cylinder with area pi r^2 and height 8.
7:53 An exercise for the reader (haha)
8:03 Refer to 4:20
8:25 cos(x) and sin(x) in terms of e^(ix)
8:33 -This part I do not understand, unfortunately...- TSC creating a "function" gun f(x) = 9tan(pi*x), so that shooting at e^(i*pi) results in f(e^(i*pi))= f(-1) = 0. (Thanks to @anerdwithaswitch9686 for the explanation -- it was the only interpretation that made sense to me; still cannot explain the arrow though, but this is probably sufficient enough for this haha)
9:03 Refer to 5:06
9:38 The "function" gun, now "evaluating" at infinity, expands the real space (which is a vector space) by increasing one dimension each time, i.e. the span of the real space expands to R^2, R^3, etc.
9:48 log((1-i)/(1+i)) = -i*pi/2, and multiplying by 2i^2 = -2 gives i*pi again.
9:58 Blocking the "infinity" beam by shortening the intervals and taking the limit, not quite the exact definition of the Riemann integral but close enough for this lol
10:17 Translating the circle by 9i, moving it up the imaginary axis
10:36 The "displacement" beam strikes again! Refer to 7:09
11:26 Now you're in the imaginary realm.
12:16 "How do I get out of here?"
12:28 -Don't quite get this one...- Says "exit" with 't' being just a half-hidden pi (thanks @user-or5yo4gz9r for that)
13:03 n! in the denominator expands to the *gamma function,* a common extension of the factorial function to non-integers.
13:05 Substitution of the iterator from n to 2n, changing the expression of the summands. The summand is the formula for the volume of the *n-dimensional hypersphere* with radius 1. (Thanks @brycethurston3569 for the heads-up; you were close in your description!)
13:32 Zeta (most known as part of the *Zeta function* in Analysis) joins in, along with Phi (the *golden ratio)* and Delta (commonly used to represent a small quantity in Analysis)
13:46 Love it -- Aleph (most known as part of *Aleph-null,* representing the smallest infinity) looming in the background.
Welp that's it! In my eyes anyway. Anything I missed?
The nth Edit: Thanks to the comment section for your support! It definitely helps being a math major to be able to write this out of passion. Do keep the suggestions coming as I refine the descriptions!
hey, are you my teacher?
Nice lore.
I will be waiting for your part 2!
Please continue dude, till end. I confused about the end of the video.
Do everything pls.
never in my life would I have ever thought I would see something tactically reload a math formula...
10:45 orange you've been here for 11 minutes and you've already made a all destroying death laser out of math how
Because Math, that's how!
@@month32 ....
Just imagine Yellow
0:07 introduction to numbers
0:11 equations
0:20 addition
1:24 subtraction
1:34 negative numbers
1:40 e^i*pi = -1, euler's identity
2:16 two negatives cancellation
2:24 multiplication
2:29 the commutative property
2:29 equivalent multiplications
2:35 division
2:37 second division symbol
2:49 division by zero is indeterminate
3:05 Indices/Powers
3:39 One of the laws of indices. Radicals introcuced.
3:43 Irrational Number
3:50 Imaginary numbers
3:59 i^2 = -1
4:01 1^3 = -i = i * -1 = ie^-i*pi
4:02 one of euler's formulas, it equals -1
5:18 Introduction to the complex plane
5:36 Every point with a distance of one from the origin on the complex plane
5:40 radians, a unit of measurement for angles in the complex plane
6:39 circumference / diameter = pi
6:49 sine wave
6:56 cosine wave
7:02 sin^2(θ) + cos^2(θ) = 1
7:19 again, euler's formula
7:35 another one of euler's identities
8:25 it just simplifies to 1 + 1/i
8:32 sin (θ) / cos (θ) = tan (θ)
9:29 infinity.
9:59 limit as x goes to infinity
10:00 reduced to an integral
11:27 the imaginary world
13:04 Gamma(x) = (x-1)!
13:36 zeta, delta and phi
13:46 aleph
30 likes and no replies let me fixed that😊
Yep the pretty much it
Man this makes me wanna learn math more
alan should put this in the video.
I need to know what types TSC is using
@@xvie_z2900fax I wanna understand everything in this video
Utterly delightful!
yo legit thought you collabed on this or smthn haha
Hi there Mr. Pi
Yoooo it's the math guy
i KNEW 3b1b would comment
Hello
Masterpiece
What 1:33 1:34 1:34
Yoo these emojis are so cool
@@BIackhole i know the code
Cool
@@BIackhole i know the code
I love the surprise Euler identity early on when just playing with simple addition and subtraction, because it’s just like when your playing with a simple concept in math and stumble across something bizzare/that you have no clue how to understand yet.
as an nerd myself, here's the actual math:
0:06 1 as the unit
0:13 equations
0:18 addition, positive integers
0:34 base ten, 0 as a place holder
0:44 substitution
1:09 simplifying equations, combining terms
1:20 subtraction
1:30 0 as the additive identity
1:34 -1, preview of e^(iπ) = -1
2:10 negative integers
2:16 changing signs
2:20 multiplication
2:28 factors
2:33 division
2:48 division by 0 error
3:03 powers
3:23 x^1 = x , x^0 = 1, x^(-1) = 1/x
3:35 fractional exponents = roots
3:42 √2 is irrational
3:48 √(-1) = i
3:54 complex numbers
4:00 e^(iπ) returns, i*i*i = i*(-1) = i*e^(iπ)
4:15 Euler's formula: e^(iθ) = cosθ + i*sinθ
4:54 e^(iθ) rotates an angle of θ
5:12 complex plane
5:33 unit circle
5:38 full circle = 2π radians
5:55 circle radii
6:36 π
6:41 trigonometry
7:17 Euler's formula again
7:33 Taylor series of e^(iπ)
7:44 circle + cylinder
7:51 (-θ) * e^(iπ) = (-θ) * (-1) = θ
8:22 Euler's formula + complex trigonometry
8:29 sinθ/cosθ = tanθ, function f(x) = 9*tan(πx)
9:01 π radians = half turn
9:57 limits, integrals to handle infinity
10:15 translation
13:01 factorial --> gamma function, n-dimensional spheres
13:31 zeta, phi, delta, aleph
(comment by MarcusScience23)
Someone already did it
Sorry bro
@@Lebanoncontryball at least I got likes + replies
@@marcusscience23 yeah gg
@@marcusscience23 but he did too
I love how he goes from learning basic operations to university level maths
Evening at home myc myself
We are learning most of this in 9th grade
@@ferferarry5242 key phrase: “most of”
bruh, you guys think this is uni-level math... damn
@idk-lz4nl Most of this is high school level, though the stuff in the last quarter is more common in universities.
09:58 I love seeing my logo so powerful!
Medematiques sous une vidéo d'Alan Becker qui parle de Maths, le monde est petit 🤣🤣
11:06 D O A B A R R E L R O L L
11:17 fast
And then get yourself obliterated roughly 30 seconds later
symbol v greek alphabet symbol SIGMA (rotated at a axis of 90°)
why is it that e^i*pi is genuinely adorable lmaooo
The reason why I love this series so much isn't just because of the animation and choreography, but because rules of how the world works are established and are never broken. Regardless of how absurd fight scenes play out there's a careful balance to ensure that not a single rule is broken.
Absolutely. The limitations create room for playing around within them. Combat feels just as much of a battle of wits, finding the right application for a tool, as a contest of strength.
I know! It’s incredible how he can just add world building in and make it so believable
You clearly haven't seen the Minecraft series yet have you? "Fall damage goes brrrrr"
@@captainsprinkles6557 Fall damage is present, and it’s relatively consistent. It’s just less severe for rule of cool.
@@dragoknight589 Less severe? Man they jump off multiple cliffs
It speaks to Alan and his team’s talent on a number of levels that they can even make me feel sympathy for Euler’s number.
Now all we need is natural logs in minecraft vs animation 😅
He is on another dimension, not on another level anymore
Finally, somebody said what it’s called so I can look up what the antagonist actually is.
Ironically enough, this is the first time I’ve utilized my calculus knowledge outside of school hahaha
@@FletchableEven though I use lot’s of this stuff daily (I’m a programmer) I’d literally never heard it called Euler’s number before this animation lol.
Mathematics smells genocide in any era. This is why the Ego always stuck periodically.
I love how people dont even know what is the imaginary number and still watch this
Imaginary Number (written as 'i') is equal to the square root of -1 which we considered the second dimension in our Real Number Line, the Real Number line with the Imaginary Number line is known as Cartesian Plane, which is basically a place used to graph equations.
Part 2 - 25 likes:
Fun Fact is that |i| is not equal to i, but 1, beacuse if you look at the Cartesian Plane, you see that the distance from 0 to i is 1 unit, so |i|=1, and so |-i| is also equal to 1.
The reason of i being 2root(-1) comes with some other weird facts, such as e^(pi×i)=-1, i^5=i^2, etc...
About the Cartesian Plane being used to graph equations, the x-axis is the Real Number Line which is the number we insert in an equation, and the y-axis being the Imaginary Number Line where it's the result of the equation respect to the number inserted.
You know the Reals and the Imaginaries, but there are also Complexs, writen in form a+b×i where a and b are real numbers, ex: 5+2i, this equation can't be compressed more than it is beacuse of mathematical number relation reasons.
I is the second, j is the third and k is the fourth dimension in graphing equations. (More nerdy stuff at 75 likes)
Just one more like...
Already reached 25 likes
i thought everyone knew what imaginary numbers are
since this guy didnt update it at 25 likes ill explain quaternions
quaternions are basically complex numbers in 4 dimensions
i^2=-1
j^2=-1
k^2=-1
ijk=-1
"quaternions provide the definition of the quotient of 2 vectors" and is written in the form of a+bi+cj+dk∈H where a,b,c,d∈R
note that quaternion multiplication is not necessarily commentative (meaning that p*q is not always the same as q*p)
You have more than twice of 25 likes, where's the additional nerdy stuff?!
Oh tysm everyone
Done
If math lessons were like this, math would for sure be everyone’s favorite subject
Edit: well, this blew up fast. Thanks!
Math is beauty, if not you just not understand it very well
@@naufaljb8204 People have opinions, not saying you're wrong but, People have opinions.
@@naufaljb8204 maybe you're good at math, but you suck at english
@@aliaakari601yeah
@@aliaakari601pople
Only Alan Becker can make a video about maths and we’ll all genuinely be invested in it.
Edit: GUYS PLEASE STOP COMMENTING ON HOW THERE’S OTHER CHANNELS THAT CAN MAKE MATHS-BASED VIDEOS THIS WAS COMMENTED TWO MONTHS AGO AND I WAS JUST IMPRESSED AT HOW ALAN AND HIS TEAM WERE ABLE TO EXECUTE IT I DON’T WATCH VSAUCE
Facts
Fr fr
true
Disagreed.
Fr
Wow. This animation is as cool as reality if I had to rate it it will be 10/10👍
10:02 WAAAAAAAH!
To the math nerd that did the equation and to the animator, heavily respected
especially in that mech section
pp entry looks pretty accurate lmao
bro both are the same person
There is literally a pinned comment saying the lead animator did the math-
DJ did it all.
edit: woah woah woah woah too fast y'all too fast y'all this is gaining too much traction p.s. i'm only thirteen!
edit two: too much. WAY TOO MUCH. TOO MUCH ATTENTION, THANK YOU ALL SO SO MUCH, and for those who were kind enough to write out things i missed out, i credited them!
0:07 introduction to numbers
0:11 equations
0:20 addition
1:24 subtraction
1:34 negative numbers
1:40 e^i*pi = -1, euler's identity
2:16 two negatives cancellation
2:24 multiplication
2:29 the commutative property
2:29 equivalent multiplications
2:35 division
2:37 second division symbol
2:49 division by zero is indeterminate
3:05 Indices/Powers
3:39 One of the laws of indices. Radicals introcuced.
3:43 Irrational Number
3:50 Imaginary numbers
3:59 i^2 = -1
4:01 1^3 = -i = i * -1 = ie^-i*pi
4:02 one of euler's formulas, it equals -1
4:55 pi/2 is 45 degrees in radians, also 1/8th of the unit circle. (etxrnaleclipse)
5:18 Introduction to the complex plane
5:36 Every point with a distance of one from the origin on the complex plane + also the cartesian plane (kinda) (etxrnaleclipse)
5:40 radians, a unit of measurement for angles in the complex plane
6:22 Ellipse (Conic sections in pre-calculus) (etxrnaleclipse)
6:39 circumference / diameter = pi
6:49 sine wave
6:56 cosine wave
7:02 sin^2(θ) + cos^2(θ) = 1
7:19 again, euler's formula
7:35 Taylor's expansion of E, when n = i*pi
7:45 Area of a Circle = πr^2 (JiReyAnimation)
7:47 The sigma function (or summation) (etxrnaleclipse)
7:50 The formula for the volume of a circular prism, (L)pir^2 (etxrnaleclipse)
8:25 it just simplifies to 1 + 1/i
8:32 sin (θ) / cos (θ) = tan (θ)
9:29 Infinity.
9:39 Infinity represents an idea for the biggest number, and the fancy R represents all the Real numbers (therefore from -infinity to infinity). The span is another way of saying vector. As TSC shoots, he adds another dimension to the vector.
9:49 e^i pi expands into a more complex form, as e^2i^2 log((1-i)(1+i)), and 1-i/1+i multiplied by it’s conjugate and simplified gets us i, which means it simplified to -2log i, which is beyond my comprehension.
9:58 Logarithms (etxrnaleclipse)
9:59 limit as x goes to infinity
10:00 reduced to an integral
10:07 Area under a curve or bounded by two or more curves (etxrnaleclipse)
11:27 the imaginary world
13:04 Gamma(x) = (x-1)!
13:36 zeta, delta and phi
13:46 aleph
and that is all the references in the video to the best of my ability!
Bro you to smart!!
Waaah best comment! Thank you so much for taking the time
i have no word to say, :OOOOOOOOOOOOOOOOOOOOO
Bro, Your math knowledge is incredible
Bro understand the math lore
7:53 Euler's Identity really released their Domain Expansion
This was brilliant. I think some short stories for individual mathematical concepts would be highly educational. I thought the battle was a bit prolonged without much new discernable math was presented, but I take this video to depict the authors struggle with natural logarithms and the concept of "e". Everything was clear and intuitive to that point.
The fact that Alan and his team are the first to make math look insane in animation speaks cm3 volumes....
@@kingsrevenge9234Your message is undermined when you post it to literally everyone without changing a single thing
True
@catassistant3365 it's just a bot, best thing to do is just ignore and report it for spam
This is the greatest video ever made
0:00 introducing numbers in addition
1:21 equality
1:28 subtraction
1:41 Introducing eiπ
2:37 multiplying and dividing
2:52 falling numbers
3:08 something weird (6+2)²=1
3:25 small numbers
3:40 introducing new symbol √
3:53 weird I (is this a number?
4:02 meeting eiπ again
4:16 insane fight
5:22 some other symbols and lining
5:39 Meeting θ
6:51lining and new symbol π
7:20 meeting eiπ again
7:36 new symbols Σ 𝑛 ! ∞ _ () ⁿ
8:34 new symbols 𝑓 • ()
8:51 insane fight again
9:55 transform (the boss)
13:11 last goodby (portal)
13:36 Weird symbols (friend of eiπ) ζφδא
13:52 Outro (The + End)
Btw I liked my own comment :3
10:00 was most epic scene
This is actually insane. Having just graduated as a math major and honestly being burnt out by math in general, being able to follow everything going on in this video and seeing how you turn all the visualizations into something epic really made my day. Can’t help but pause every few minutes. GET THIS MAN A WHOLE ASS STUDIO.
He has an entire crew working with him
He does have a WHOLE ASS BUILDING
Yeah😂
I can only understand a bit.
...and at the end, in comes the zeta function
An animation masterpiece ✅
A cinematic masterpiece ✅
A mathematical masterpiece ✅
A physics masterpiece ✅
Cinematography ✅
Sound design ✅
Everything is so perfect
@@ultraactiveGDust another bot, ignore him
how is this physics
Fr
Worm
12th standard nostalgia in the most epic cinematic way possible!
Thank you so much for this experience.
Here's my interpretation of each scene as a second-year undergrad:
0:00 Addition
1:23 Subtraction
1:40 Euler's identity (first sighting)
2:25 Multiplication
2:36 Division
2:48 Division by zero
3:05 Positive exponents
3:29 Zero and negative exponents
3:40 Fractional exponents and square roots
3:50 Imaginary unit, square root of negative one
4:00 Euler's identity (second sighting)
4:44 a + -a = 0
5:18 The complex plane
5:34 The unit circle
5:38 Definition of a radian
5:59 Polar coordinates
6:39 Definition of pi
6:51 Trigonometry and relationship with the unit circle
7:12 Phase shift
7:19 Euler's identity (third sighting)
7:35 Taylor series expansion for e^x, x=iπ
7:50 Volume of a cylinder (h = 8)
8:25 Hyperbolic expansion for sine and cosine
8:30 f(x) = tan(x)
9:28 Infinite domain
10:00 Calculus boss fight
11:00 Amplitude = 100
11:30 Imaginary realm?
12:10 TSC befriends Euler's identity (wholesome)
12:38 i^4 = 1
13:05 Taylor series expansion for e^x, x=π
13:06 Gamma function, x! = Γ(x+1)
13:25 Reunion with Zeta function, delta, phi and Aleph Null
Definitely my favourite Animator vs. Animation video yet, and I'm not just saying that because I'm a math student. It really says something about Alan's creativity when he can make something like mathematics thrilling and action-packed. Top notch!
Needs a pin!
you forgot aleph at the end, it’s really big but sort of hidden in the background for being transparent
@@existing24As it’s the biggest infinity!
@@bananaeclipse3324 aleph is not the biggest infinity. its a set of cardinal numbers that represent the different types of infinities. Aleph_0 is the number of whole numbers, aleph_1 is the number of real numbers and so on.
I dont see the a + -a one
I'm studying at the Faculty of Math in university right now and every month i come back to this masterpiece to see what new did i learn. When this animation came out i didnt understand anything besides the begining, now i almost got everything, and everytime it gets more and more interesting to analyse every small detail i notice
Thanks for it, it helps he understand that im getting better, smarter, and my efforts arent worthless
I showed this to my Precal teacher and she really enjoyed pointing out all the references to stuff like the unit circle and Sin waves. I think she also had that kind of moment!
Man 5 months of progress huh
what were the functions towars the end ?
@@whimsy_vision phi is probably just generic function, at least I don't remember specific functions that use the name, then there's Riemann zeta function, delta I'm not sure about, might be the delta function, and I don't know which function is in background.
Looking at other comments, it's aleph in background. Aleph is "size" of infinite sets. And phi is fibonacchi sequence
Delta function is not strictly a function, but physicists like it. What's so weird about it, it has a non-zero integral despite being different from zero in only a single point. It's a part of generalized functions (distributions), which are absolutely amazing, but rarely taught. Then there's weaker version, Sobolev functional spaces, which is used more often, but is less amazing. Imagine, being able to integrate and differentiate (integrate by parts) everything. Delta function appears there as differential of heaviside step (or half of second derivative of modulus). Of course there's a corresponding price to pay
Why are you studying math?
As a general nerd myself, and especially a math nerd: This video was awesome 🤓😄
-Simple addition
-Counting to ten
-Adding 2's
-Adding 20's
-Reaching 100
-Simplifying addiion
-Subtracion
-Negatives
-Euler's identity
-Imaginary number usage
-Subtracting negatives
-2 - make a +
-Multiplication
-Some numbers have more factors than others
-Division
-Division by 0 is not possible
-Exponents (squared)
-Higher exponents
-4 to the -x = 1/4 to the x
-Square roots (square numbers)
-Square roots (non-squares)
-Imaginary number (i)
-Euler returns
-Euler's formula: cos(π)+isin(π)
-Euler and TSC fight
-Graphs (x axis and y axis)
-Circles and the concept of π
-Radius, angles, how to calculate π
-Cosines and sines come from π
-Euler and TSC fight club 2.0
-Concept of sums (Σ)
-Functions
-Concept of Infinity ♾️
-Spans
-Integrals
-The imaginary realm
-Imaginary numbers
-Euler and TSC make a truce
The end... of animation vs math.
Some of my favourite things from this masterpiece I noticed:
1:39 e^iπ = -1
1:49 Multiplying by i probably can be represented here as moving to another dimention (of complex numbers) as they're located in a real one
2:37 The division here for a÷b=c is interpreted as "c is how many times you must subtract b from a to get 0" which easily explains later why you can't divide by 0
3:08 The squared number is literally interpreted as a square-shaped sum of single units
4:12 The e^iπ tries to run away to another dimention again by multiplying itself by i but TSC hits it with another i so i×i=-1 returns it back to real numbers
4:16 The e^iπ extends itself according to Euler's formula
4:19 TSC gets hit with minus so he flips
4:22 The reason why e^iπ rides a semicircle comes from visual explaining of e^iπ=-1. e^ix means that you return the value of a particular point in complex plane which you get to through a path of x radians counterclockwise from 1. Therefore e^iπ equals to -1 because π radians is exactly a semicircle. When the e^iπ sets itself to 0 power (e^i0) it returns back to 1 through a semicircle because well 1 is zero radians apart from 1.
4:46 When "+1" and "-1" swords cross they make a "0" effect
4:48 The e^iπ makes a "-4" sword which destroys TSC's "+1" sword making it zero, and as a result e^iπ is now holding "-3". Then the same thing repeats with "-3" and "-2".
4:53 The "2×2=" bow shoots fours
4:55 As I explained above, e^(iπ/4) means you move exaclty π/4 radians (quarter semicircle) counterclockwise
5:06 When you multiply a number by i in complex plane you just actually rotate the position vector of this number 90° counterclockwise, that's where a quarter circle came from
5:39 Each segment here is a radian, a special part of a circle in which the length of the arc coincides with the length of the radius (it's also shown at 5:46); the circle has exactly 2π radians which you can visually see is about 6.283
6:38 Visual explanation of π radians being a semicircle
6:48 Geometric interpretation of sinusoid
7:08 TSC once again multiplies the sine function by i which rotates its graph 90°
7:36 The sum literally shoots its addends so the value of n increases as the lower ones have just been used; you may also notice that every next addend gets the value of n higher and higher as well as extends to its actual full value when explodes
7:45 TSC multiplies the circle by π so he gets the area and can use it as shield
8:04 TSC uses minus on himself so he comes out from another side
8:17 The sinusoid as a laser beam is just priceless
9:02 Multiplying the radius by π here is interpreted as rotating it 180°
9:23 +7i literally means 7 units up in complex plane
9:38 Here is some kind of math pun. TSC shoots with infinity which creates the set of all real numbers (ℝ). With every other shot he creates another set which represents as ℝ², ℝ³ etc. It also means span (vector) in linear algebra and with every other ℝ this vector receives another dimention (x₁, x₂, x₃ etc.).
9:58 The sum monster absorbs infinity (shown as limit) and receives an integral from 0 to ∞
13:34 The golden ratio (φ) when approaching e^iπ takes smaller and smaller steps which shorten according to the golden ratio (each step is about 1.618 shorter than the previous one)
13:46 Aleph (ℵ) represents the size of an infinite set so is presented here as enormously sized number
now i respect u too
same, he probably took a long time to write this since it has 26 lines in it, huge respect
@@Exxtream and i am doing math homewwork rn , related to circles and R
:D
Amazing
@@plyrocea You know that he copy pasted it right?
the actual math:
0:06 1
0:13 equations
0:18 addition, positive integers
0:34 base ten, 0 as a place holder
0:44 substitution
1:20 subtraction
1:31 0
1:34 -1, preview of e^(iπ) = -1
2:10 negative integers
2:16 double negative makes a positive
2:20 multiplication
2:28 factors
2:33 division
2:48 division by 0 error
3:03 powers
3:23 x^1 = x , x^0 = 1
3:30 x^(-1) = 1/x
3:35 fractional exponents = roots
3:42 √2 is irrational
3:48 √(-1) = i
3:54 complex numbers
4:00 e^(iπ) returns, i*i*i = i*(-1) = i*e^(iπ)
4:15 Euler's formula: e^(iθ) = cosθ + i*sinθ
4:54 e^(iθ) rotates an angle of θ
5:12 complex plane
5:33 unit circle
5:38 full circle = 2π radians
5:55 circle radii
6:36 π
6:41 trigonometry
7:17 Euler's formula again
7:33 Taylor series of e^(iπ)
7:44 circle + cylinder
8:22 Euler's formula + complex trigonometry
8:29 sinθ/cosθ = tanθ, function f(x) = 9*tan(πx)
9:57 limits, integrals to handle infinity
13:01 factorial --> gamma function
13:04 n-dimensional spheres
13:31 zeta, phi, delta, aleph
That guy really took the time to write all of that a round of applause
copied from me
First day
If may not be provided
cool
This taught me math better and faster than 12 years of school ever did
1:02 TSC is just like "Yay!!... What did I accomplish?"
TRIPLE DIGITS!!!!! PARTY!!!
This man just gave the sentence “imagine maths are a videogame” a whole new meaning
There is a math game called Baldi’s basics
And the sentence of "imagine math is weaponized"
...You could pick up the sword, the bow, or the arrow...
Obscure reference :)
@@autumn_sunday Gumball reference moment
Video games are made through math.
Some of my favourite things from this masterpiece which I understood:
1:39 e^iπ = -1
1:49 Multiplying by i probably can be represented here as moving to another dimention (of complex numbers) as they're located in a real one
2:37 The division here for a÷b=c is interpreted as "c is how many times you must subtract b from a to get 0" which easily explains later why you can't divide by 0
3:08 The squared number is literally interpreted as a square-shaped sum of single units
4:12 The e^iπ tries to run away to another dimention again by multiplying itself by i but TSC hits it with another i so i×i=-1 returns it back to real numbers
4:16 The e^iπ extends itself according to Euler's formula
4:19 TSC gets hit with minus so he flips
4:22 The reason why e^iπ rides a semicircle comes from visual explaining of e^iπ=-1. e^ix means that you return the value of a particular point in complex plane which you get to through a path of x radians counterclockwise from 1. Therefore e^iπ equals to -1 because π radians is exactly a semicircle. When the e^iπ sets itself to 0 power (e^i0) it returns back to 1 through a semicircle because well 1 is zero radians apart from 1.
4:53 The "2×2=" bow shoots fours
4:55 As I explained above, e^(iπ/4) means you move exaclty π/4 radians (quarter semicircle) counterclockwise
5:06 When you multiply a number by i in complex plane you just actually rotate the position vector of this number 90° counterclockwise, that's where a quarter circle came from
5:39 Each segment here is a radian, a special part of a circle in which the length of the arc coincides with the length of the radius (it's also shown at 5:46); the circle has exactly 2π radians which you can visually see is about 6.283
6:38 Visual explanation of π radians being a semicircle
6:48 Geometric interpretation of sinusoid
7:08 TSC once again multiplies the sine function by i which rotates its graph 90°
7:36 The sum literally shoots its addends so the value of n increases as the lower ones have just been used; you may also notice that every next addend gets the value of n higher and higher as well as extends to its actual full value when explodes
7:45 TSC multiplies the circle by π so he gets the area and can use it as shield
8:04 TSC uses minus on himself so he comes out from another side
8:17 The sinusoid as a laser beam is just priceless
9:02 Multiplying the radius by π here is interpreted as rotating it 180°
9:23 +7i literally means 7 units up in complex plane
9:38 Here is some kind of math pun. TSC shoots with infinity which creates the set of all real numbers (ℝ). With every other shot he creates another set which represents as ℝ², ℝ³ etc. It also means span (vector) in linear algebra and with every other ℝ this vector receives another dimention (x₁, x₂, x₃ etc.).
9:58 The sum monster absorbs infinity (shown as limit) and receives an integral from 0 to ∞
13:46 Aleph (ℵ) represents the size of an infinite set so is presented here as enormously sized number
P.S. Thanks to the people in replies who taught me the name of the orange character (The Second Coming), before that I just called him "the guy" here.
P.P.S. Also thank you all for the feedback, I'm glad you appreciated my half hour work.
Finally someone notices aleph.
Where is the aleph
@@bicillenium4019it’s colored black with a faint graph texture moving at the end. Might wanna turn up ur brightness 2 see it
Is the size of an infinite set not just… infinity? This is so typical of math lol
Hmmmm,interesting,but why the circle is going diagonally at 10:29 (Sorry,i'm still in 9th grade)
i learned everything until 3:55
Cancelling Infinity using Limits.
That is beyond genius!
The sound design is a masterclass on its own
Legitimately, everything has such a nice clack to it, it's half the reason for why it's so satisfying to watch
@@FotoStudios418 Facts
All of the clicks and clacks make the video infinitely better
This needs like 10 games, 3 books, a Netflix series, a movie on Disney+ and Dreamworks, and way more
YES!
IDK half of the things that you need to understand this 😕 🤔
This is already that but better ngl
Why is it always like this? 4:04
I would literally go insane if that happened.
Being an engineer and a math enthusiast I love this❤
A meganalysis of this:
1: a number representing a single entity
Equal: a sign representing the sum of a equation
Plus: a positive function symbol representing addition 1+1=2
Double equation: this is when you put two plus or minus.
10: a even number
Parentheses: 2=(1+1) 3=(1+2)
Minus: a negative function symbol representing a take away in math
Negative: a negative function symbol representing the negativity or the lowest of a number
e i pi: a mathematical equation equaling 0
Multiplication: 3x3=9 (1+1+1+1+1+1+1+1) 3×(4) = (1+1+1..)
Division: 6/2=3 12/6=2 81/9=9
Exponent: 6+2²=64 4+4²=16
Fraction: ½=20%
Square root: sqrt(4)=2 sqrt(16)=4
i.: -1=n i=1.
Radian: also known as rad rad=4.8 maximal rad = 6.2
Pi: symbol representing 3.41
tau: symbol representing t below pi
Summation: a symbol representing Σ a calculus sum.
Function: symbol representing f f(x) f(sin)
Integral: the symbol representing the integral of a number so far good
Ratio: r=100
Idk i quit😊
So far, this is the best action movie in 2023!
Adu anh vfact học toán
Video mới là gì thế anh zai
I can’t believe Alan is making his own Number lore now… ✊
Hey, không nghĩ tôi sẽ gặp kênh yêu thích của mình ở đây. Giữ gìn sức khoẻ và nếu có thể thì có thể làm về vũ trụ được không, video này làm tôi có hứng về vũ trụ học.
Yes
This feels like it should win some kind of award. Not even joking this is gonna blow up in the academic sphere. People are gonna show this to their classes from Elementary all the way through college. I don't know if people realize just how powerful of a video you've created. This is incredible. You've literally collected the infinity stones. This is Art at its absolute peak. Bravo.
This reminds me that in Geography Class, the teacher showed us Yakko's World Country Song from _Animaniacs._
I guarantee Maths teachers will be showing this to their students for decades to come.
❤
I agree!
That’s exactly what I was thinking
That’s actually true
I love how the Internet is being used this way. not abused♥️
it brought me to tears. Especially the f(x)=9tg and my favorite Euler identity
I like how Alan didn’t go for a “Brains vs. Brawn” approach, and instead just made a fight to the death with math terms
Hrklo
Hrklo
Hrklo
Hrklo
Hrklo
As a mathematics teacher, I always dream of explaining math concepts in an interesting and amazing way. Let me say, you have done wonderful work in this regard, even though words are not enough to express my feelings. In my review/reaction video (animation vs math in Urdu Hindi), I tried to explain this masterpiece in Urdu/Hindi for roughly 1 billion people in Pakistan and India!
That's amazing, I struggled to learn math the way my teachers taught in school. I have hyperphantasia, so I struggle to understand things that aren't explained visually, but this video encapsulates exactly how I wish math could be taught to me because it explains mathematical concepts in a way that is intuitive, interesting, and very aesthetically pleasing.
nobody cares bro
@minervatolentino8481
Maybe because they might not speak english???
@@minervatolentino8481 because there are already uploaded some reviews in English I just added subtitles in English and explain in Urdu
@@zylerrogers69 i struggle too! Not to self diagnose but,maybe i have hyperphantsia too
This was incredible. Such an amazing visual of math that makes it understandable. And a better story plot than most Hollywood movies nowadays. Lol
After watching this, now i just want to learn everything and everything about math...this is just mind-blowing ❤
The sound design here is simply masterful, and makes the whole thing feel physical and *very* satisfying.
It shows how the stick figure adapt and try to minimize at 1:15
True
I don’t understand the last part
It sounds like a movie, its awesome
I’m 699 like
As a math nerd, this is like my new favorite thing. I love how you started out with the fundamentals of math, the 1=1 to 1+1=2, and then steadily progressed through different areas until you're dealing with complex functions. There's so much I can say about this, it's so creative. Good job, Alan and the team.
What is e 😂 seriously I want to know
@@stefanoslouk4183e means exponent
i means imaginary
@@stefanoslouk4183its a
The fifth letter of the alphabet
@@stefanoslouk4183 e is Euler's number, it's an irrational number and it's value is approximately equal to 2.7. It's useful in many different equations and can express some very complicated logarithms or series.
@@stefanoslouk4183Euler's number.
2.718...
Perfect, perfect absolutely perfect
Brilliantly creative and boy was it fantastic,a fun creatively made math adventure
Jackson game yesterday was amazing. His hold up ball control and link up play is just amazing
The graphic design in this episode was nothing short of phenomenal. The way e^iπ and TSC interact with numbers is so smooth and natural, and they use complicated formulas so creatively, too... Too bad it didn't fit in the narrative of AvA's grand story because this was one of the most beautifully animated episodes I've ever seen from your team
I suppose it could, since TSC was last seen in a jail cell, and they could have knocked him out during transfer somewhere else, possibly.
Ikr
Are we sure it doesn't fit? I need to rewatch the last chapter, but TSC was captured and in some kind of facility, with the way he woke up in this place he could be in some kind of experiment or simulation
@@Braga_Rcb or mabye this is how TSC learns how to use his power. Math is also a form of code. But thats just a Guess
Incredible truly fantastic the way that you can innovatively come up with this😅
Can we just appreciate how TSC went from basic addition to the far end of Calculus in under twenty minutes. That is a hell of a learning curve.
15+6=21
@@user-eb5bn9xh9w 9 + 10 = 21
@@anicepixelatedbread 2+1 = 21
@@anicepixelatedbread cos(x) = (e^ix + e^-ix)/2
0=ax²+bx+c
Какой раз я уже это пересматриваю..шедевр!
I don’t understand mathematics at all, but it’s so nice and interesting to watch everything that happens! Especially the sound is very cool, the sound of interaction with objects. And although I understand almost nothing from these formulas, I can confidently say that mathematics (geometry or algebra) is an art!)
If you like graphical mathematics that doubles as art, look at the concept called roses. These parametric equations construct beautiful multi "leaved" curves on the Cartesian plane, all from only two interrelated formulas.
TSC discovered the entire realm of calculus in under 15 minutes, seriously one of the coolest parts was when the Euler monster derived from e caught the shot infinity in a limit, and using the 0-∞ integral, that seriously was like a woah moment
Another thing i dont see anyone pointing out is aleph null as a behemoth due to it being the smallest infinity, i loved every bit of this, its my third time rewatching
It’s a behemoth because even if it’s the smallest infinity, it’s still infinity. Not finite. And that means…. IMPOSSIBLY big. So yeah. Behemoth.
i like your funny words magic man
I thought I was wrong when I thought aleph-null for sec there, thanks for confirmation
I didn't understand a good portion of the math, but this is the exact chaotic feeling I get when confronted by math. Only difference is that this animation outs me in awe of math rather than in fear of it. Truly a masterful piece
Mathterful*
Same I wish I understood all math
I plan to study hard wish me luck guys!
bro you just show the beauty of mathematics.
I really love this video and physics video was also the most amazing animation video I ever watched.
I am actually speechless. This was way more mind blowing than i expected it to be.
As a physicist I got to say, this was incredible. I was literally smiling all the way through because of how amazing this was. It captures the math so good and the animations representing the individual math operations, simply astonishing.
almost makes me want to do math
yeah same
Math is like drugs u can be very happy when your right but deppresed when your wrong
I think this just proves TSC is smarter than anyone alive. He just absorbed, learned, and utilized in combat 14 years worth of math learning in just 14 minutes.
Bro became Einstein by examining with numbers and stuff
Several hundred years if we're being real here. Math is a culmination of Humanity's Effort.
@@Aku_Cyclone ???????
@@PurpleHeartE54:/
@@Redanimations424 It's facts though.
Your animation is so well made and nice, I showed it to my math teacher and he basically used it to make his lesson. Wish there will be more of Animation vs Math !
When I watch it, it gives me a relief.
I really like it❤
The start was intriguing, the middle was intense, and the end was heartwarming. This isn't just an animation, it's a masterpiece and will be remembered for generations to come.
Lol yet another youtube "masterpiece" comment 😂
@@Carroty_ I learned imaginary numbers because of this
@@Sebdet9 you didn't know imaginary numbers before??
@@aic8326atleast they spent some effort on the comment instead of the jellybean comment (i actually forgot about that)
Yes kids boss fighting with e
I can see math teachers showing us this video in the future. It's entirely possible. For Grapic Design, our teacher showed us the very first Animator vs. Animation video. And wanted us to see if we could make something similar. That was basically our biggest semester project.
I was always curious about that. My sister did creative tech at uni, and I keep thinking these videos would be brilliant to showcase as examples.
Can I be in your class bro
@themisleadingpath4692 I graduated already, lol. But I can head to my school and put in a good name for you /j
My math teacher teaches with fun students just don't understand themselves and blame her that her teaching is very poor they always talks (I understand math very well by her)
I thought yellow would be in it cause he is a red stone scientist so he would know the simple math😊
Insane video...
Describes what maths is doing under the hood.... DESTRUCTION!!!
The Second Coming is now canonically friends with the letter e.
The ending really conveys that maths does not have limits.
But it does in calculus :)
@@h20dynamoisdawae37 well, the continuum hypothesis really supports your opinion and also rejects it.
6
@@sameelshamnad6142I think they’re talking about literal limits, e.g the one found in the definition of derivative
@@user-lx1yg6ey6h This Is Delta δ Okay?
When I mentioned Alan Becker at the height as an artist I respect, their response was ... "Who?" .... This guy started with a simple animation animator vs animation .. now he makes great crossover stories with his characters and now released , a perfect mathematical spectacle connected to a simple story but so brilliantly done that hats off. I don't care what happened to them, but I will continue to follow his stories, which he permeated in such a way that he creates his own category that he undoubtedly rules. Keep it up.
s
wat
I agree!
Love how it starts with basic additions and ends with traveling to a new dimension in just 13 minutes
Me encantan tus animaciones, sigue asi, eres el mejor.
Can't wait for all the math channels to do breakdowns of this video. It's incredible how much is packed in here.
My school teacher would be good at this until the like, last 25% of the video, then he probably would have gotten nightmares, same as me, can't wait too
Even in a slowmode /100 i'm not sure you would have time to explain everything 😄
@@etakiwarp I wanted to check the math in the video and I had to use frame advance in some scenes.
i came here from a breakdown of the video
this sound design was top notch. The music felt so appropriate for this weird dimension, and the sfx for all the math clinking and plopping felt like it was exactly how math should sound. absolutely stunning.
Damn yes
So nice... I can't admire you because the words of English language is not enough for it ❤
I never was one to like math, now i adore it
Some Small Details
5:29 this shows The Second Coming is approximately 1.65 units tall. An average adult male is 1.6~1.8 meters tall. It appears the math space is in SI units, m being the SI unit of length. This also shows TSC is about 165cm tall, or 5' 5".
7:45 a circle is represented as x^2 + y^2 = r^2. Inserting a pi turns it into the area of a circle, pi*r^2. Inserting 8 turns it into the volume of a cylinder, 8*pi*r^2.
9:01 since f(x) is 9*tan(x) and tangent turns angle into the steepness of a line, it can latch onto the unit circle.
9:40 f(dot) represents the tangent function at a given point (throughout this video, we can see a dot used as an arbitary number on the number line), and f(inf) represents the tangent function over the entire number line [0, +inf). An entire number line can be seen as a span of an unit vector, thus each shot increases the dimension of the span. This also implies that TSC is a being that is four-dimensional.
9:57 Sigma + limit = integral. If you try to derive the definite integral using the sum of rectangles method, you will eventually transform lim(sigma(f(...)) into integral(g(...)).
10:04 Calculating an integral of a function can be seen as getting the total (polar) area between the function and the number line. Thus the Integral Sword attacks with R2.
11:31 welcome to the imaginary realm. Hope you like it here.
Main character in this is TSC (the second coming) but neat analasis
TSC is 5’ 5 hmmmmm may be useful information not gonna lie
@@Foxella2010Big brain 200 iq much?
when a stick man is taller than you
TSC is measured in pixels, not meters
This is literally 100/10. The sounds, the effects, the animation, the accurate equations and the story, they all were hella awesome. Thanks Alan.
100/10 is 10, so it's quite literally 100/10 out of 100/10 :)
The comment sections are so dumb comments💀
When a 14 minute CZcams video teaches math better than a year of school
Like
Now that’s a boss battle if I’ve ever seen
Can you please do Animation vs Science next? 😊
As a mathematician AND a fan of Alan's works, I can't describe how happy I am.
Same here bro
Too bad that i understood no shit related to maths after 3:52
The addition of enjoyment was worth the subtraction of time from my day. I have shown It to multiple people and none are divided on how good this is.
@@grandevirtude9830same
@@grandevirtude9830imagine
Let’s see:
0:14 the number 1, also equalities
0:27 addition
1:32 subtraction
1:42 negative numbers
1:48 Euler’s identity, in trig, a number in the form e^ix can be represented as a point on the unit circle (circle with radius one whose center is the origin on the complex plane), the x is the angle in radiants at which the point is located, since pi radiants is 180 degrees, the identity equals -1.
2:25 double negative makes positive
2:32 multiplication
2:43 division
2:57 dont divide by 0, please
3:14 positive exponents
3:38 negative exponents
3:44 rational exponents/ radicals
3:59 Imaginary numbers, normally you can’t take the principal square root of a negative number, so some old smart guy made imaginary numbers (i) where I squared is -1.
4:22 the euler identity tried to escape by multiplying itself by i, but the i that was thrown made the i into a -1, which is why when the eulers identity went through the wall, it didnt dissaper
4:25 trigonometry representation on eulers identity, sometimes written as cis (cos + isin) for anyone studying trigonometry, you know the beauty of working with complex numbers in trig form
4:31 pi radiants is 180 degrees thus the half circle
4:28 the - flipped orange guy (TSC)
5:01 the bow is made up of two twos and a multiplication sign, so it shoots out 4s
5:04 pi/4 rad is 45 degrees so the circle isn’t complete
5:26 complex plane( reals on x axis imaginary on y)
5:43 unit circle
5:50 2pi rad in circle
5:57 definition of radiant
6:12 r is radius, theta is angle
6:46 pi :)
6:52 cos and sin, and how their graphs are drawn using the unit circle. You can see on the graph that the graph cycle every 2pi, this is the period of the graph.
7:17 i rotates the sin wave 90 degrees
7:28 same eulers identity
7:43 Taylor series (complicated stuff) if im wrong plz correct me, also shoots out the answer.
7:53 circle and cylinder
8:11 TSC uses the - to go to the opposite side
8:33 complex definitions of sin and cos (rest in reply’s cause it’s getting too long)
8:39 sin/cos = tan
8:51 tan waves on the balls
9:12 pi radiants so rotated 180 degrees
9:37 infinity, also the attack is now infinite many periods of tan than just one
9:47 real thing (idk formal name) the exponent next to the real is the amount of reals, so when the exponent is 4, all four variables all belong to the reals
9:54 sick animation, also all the expressions are equivalent
10:07 integrals can Handle infinity, thanks to limits
10:28 +9i moves up 9
10:58 one integral can’t handle multi variable stuff
11:08 big radius
11:15 death laser of trig
11:34 they get rotated 90 degrees because of i, as stated in the video
12:46 ixixixi is 1
13:14 I have no idea what that is, I think something about n dimensional unit spheres or something. But idk 😂 someone smart plz let me know
13:44 zeta, phi, and delta
13:54 aleph null (smallest infinity) *could just be aleph, but judging by context I’m assuming that it’s aleph null.
IF I MISSED ANYTHING OR GOT ANYTHING WRONG PLZ TELL ME :)
-nerdy highschool freshmen
@@MathOverChemistry the 'equal sign' on the bow is just the bottoms of the 2s
@@freerobux49 oh yeah I’ll fix it thanks :)
I think when the big super Euler's thing is shooting out those blasts the explosion is the answer to the equation
When the two one swords are colliding one of them is a negative one sword and the other one is a positive one sword and the resulting clash creates a zero. At one point Euler's increases the value of his blade and orange guy can't deflect the attack and the Sparks is a higher value
i understand nothing but the animation is brilliant.
He literally had the power to distroy the world by doing 0 devided by 0
I've never seen anything so mathematically accurate while also entertaining.
now it is explained how the "chosen one" went to this reality
No appreciation for proofs?
E
3b1b
@@sehr.geheimhe's basically a vector figure, a being made of numbers, to put it in short, he's basically math itself so to speak.
pixar has no right to call itself an animation studio after releasing this masterpiece
they removed the dragon in the mulan remake just so they could save money on by not animating it and not hiring eddie murphy
it’s a whole team behind this not just one man
@@Philgob doesnt make it any less impressive
@@wolfytronic true
YESSS, I love this 5:30 I love the way it works looks, also as a true math expert (not) I can confirm in 0:18 that it is correct.
bro made math epic
I think the sound design is quite an underrated highlight of this animation. The bleeping and clicking as everything falls into place is so satisfying to listen to.
I completely agree
+
Yes, I agree too.
Egor is too good in sound design and animation
Barely anyone talks about sound design in general. Whenever people release an animation or something with great sound design they just take it for granted and continue to laud the animators
It's cool and very interesting. I a little learn math with this video.
It's amazing
This Video Is Really Amazing, I'm A Maths Lover🤩 & I Never Seen Such An Amazing Mathematical Animated Fighting Scene With Perfect Mathematical Logics😲❤
As a person who has taken calculus, I can confirm we fight bosses every day in math class.
😂
OMG 🤣
Too true
i can agree with this ap calculus was scary
as a person just started took it and failed and going to take next year nothings changed
2:48 NEVER divide ANY number by zero.