(this is following the timestamps in the original video btw) 0:07 Numbers 0:11 Equations 0:20 Simple Addition 1:24 Simple Subtraction 1:34 Negative Numbers 1:40 e^i(x)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 introduced. 3:43 Irrational Numbers 3:50 Imaginary numbers 3:59 i^2 = -1 4:01 1^3 = -i = i (x) -1 = ie^-i(x)pi 4:02 One of Euler's formulas. It equals -1. 5:18 Introduction to the Complex Plane (This sucked to learn) 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 Euler's Formula 7:35 Another Euler Identity 8:25 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" Theorem 13:04 Gamma(x) = (x-1)! 13:36 Zeta, Delta and Phi 13:46 Aleph
Here’s my explanation of the math stuff throughout the video: 0:22 - equals sign. It means both sides are the same 0:28 - the + means addition 1:32 - the - means subtraction 1:48 e^i*pi is known as Euler’s identity, and it does equal -1. This is because if you bring anything to e^ix, it creates a unit circle on the complex plane (explained later), and the x is the angle on the unit circle in radians (also explained later). for Euler’s number, x is pi, which means you create a 180° angle on the unit circle (because pi radians is equal to 180°) which lands at the point -1. Therefore, e^i*pi is -1 1:57 - when the e guy multiplied himself by i, I guess it sent him to the “imaginary world”, which is a pretty cool concept in this story 2:32 - this a cool representation of multiplication 2:45 - cool representation of division 2:57 - this is a good visual to why you can’t divide by zero, because you’ll never be able to subtract anything from 6 4:01 - exponents is to multiplication in the way that multiplication is to addition, in that you multiply the big number for the amount of times the small number says 4:27 - negative exponents give a fraction because subtracting the exponent by 1 basically divides the number by 4. 4^0 is 1 because that’s 4/4, and 4^-1 is 1/4 because you divide 1 by 4 4:47 - this is the introduction to imaginary numbers. The letter i is equal to the square root of -1 because you can’t normally square root negative numbers. To counteract this, mathematicians created i as a way to represent the square root of -1 to not end up in a dead end while doing math 4:58 - as I previously said, i is equal to the square root of -1. This means i x i = -1 = e ^ i x pi 5:09 - the e guy didn’t travel through the door because the i he pulled out multiplied with the one the Second Coming threw to make -1, which is a real number, causing the e guy to stay in the real world 5:13 - this expansion is known as Euler’s formula. It’s created because of the unit circle e ^ i*pi creates in the complex plane, and it uses the sine and cosine functions to separate the real and imaginary values of the number in the unit circle 5:16 - the Second Coming was multiplied by the negative sign, causing him to flip aroundirm that 5:20 this goes with the unit circle thing. the e guy changed his exponent to 0, which is the same as 0i. because it changed from i*pi to 0i, he went from pi radians (180°) to 0 radians (0°) on the complex plane unit circle, causing a 180° arc to the right 5:34 similar to what happened earlier with the Second Coming 5:53 the e guy put the 4 into his exponent, causing him to move to pi/4 radians (45°) on the unit circle 6:04 - when he multiplied himself by i here, he rotated 90° on the unit circle because when you multiply a number by i on the complex plane, the number is rotated 90° on the plane 6:15 - here, the Second Coming learns about the complex plane. It’s like a number line with a horizontal axis containing the real numbers, but it has a vertical axis too that contains the imaginary numbers, forming the two dimensional complex plane 6:33 - the Second Coming creates the complex plane unit circle that that e^i*pi is based from 6:38 - these are radians. A radian is the angle at which its arc length is equal to the radius, which ends up being 180/pi degrees. The little gap shoes that in a full circle, there are 2pi, or about 6.283 radians 6:58 - I’m not sure why these appear to be multiplied, but the r means the radius and the weird 0 with a line is theta, which is the angle (typically in radians) 7:35 - because theta (the angle) is pi radians and the radius is 1, theta/the radius is pi 7:47 - this shows how sine and cosine can be used to separate the horizontal and vertical aspects of a circle 8:07 - here, he multiplied sine by i, which caused the sine wave to rotate 90 degrees 8:15 - he added them together to create Euler’s formula, which as previously stated is equal to e^i*x , and x is pi because the trig functions contain pi. Therefore. Combining them created the e guy 8:26 - more of the unit circle stuff 8:32 - the e guy expanded into his Taylor expansion form. Thee giant E thing is sigma notation, and it basically adds the part after it, replacing it with integers consecutively going up. You can see this with the the bullets it fires 8:46 - volume of a cylinder 9:02 - he pulled the negative trick again 9:22 - the e guy used the formula for himself and the formula for the trig functions to split himself up a lot 9:29 - here, he made a function, which is basically a placeholder for an expression. Unfortunately, I don’t understand the arrow above it is 9:59 - he changed the angle to pi radians (180°) 10:26 - I’m guessing here, but I think when the Second Coming replaced the dot with the infinity symbol, it caused the function to expand to every point on a graph, which also created the tangent lines (since the Second Coming put the tangent function into that function) 10:55 - the blast became an integral symbol with a limit, because the tangent graph was kind of infinitely long, so the limit allowed the tangent graph to converge I guess. The integral symbol means nothing, it just looks like a cool staff 11:14 - he added an imaginary number, which causes things to move vertically in the complex plane 12:23 - now you see the imaginary world 14:01 - I didn’t entirely understand what this is, but looking at other comments, it seems like the e guy expanded into an equation that can find the volume of spheres beyond the third dimension, but i can’t confirm that, though 14:29 - these symbols are zeta, phi, delta, and aleph
Yes, the last one calculates the sum of the volumes of a sphere in each (even numbered) dimension. It turns out that this sum is precisely e^π. Φ(Phi) is the golden ratio. ζ (Zeta) is usually referring to the zeta-function, an important and very famous function in number theory. It sort of holds the key to understanding how prime numbers are distributed. δ(Delta) is more of a technical thing, but delta (and ε (epsilon)) are kind of the mascots of real analysis so it makes sense. Aleph usually refers to the "smallest kind of infinity"
5:29 I only got through third year of college calculus so bear with me. TSC is playing around with Euler formula aka the “e” which is like one of the most important numbers in math cause it’s the base for ALL natural logarithms which in short meats it kinda shows up everywhere. Hence why it’s so powerful here. Plus a cool thing about the “i” is that it represents imaginary numbers. a general rule is i x i = -1 and e^(ipi) is also equal to -1 it’s just another way of writing it. What’s cool about e^(x) is that it’s the only number that’s the derivative of itself so when you find the derivative of e^(8x) for example you get 8e^(8x). i and e together have this power that when it’s multiplied to stuff it kinda “switch dimensions” so when TSC threw an i at ie^(i pi) it was forced back here as iei^(ipi) or -e^(ipi) pretty cool way to show that imo. Also while sin(a) = y coordinate and cos(b) = x coordinate. The two waves when forces next to each other due to i “switching dimensions” don’t exactly line up. The fact that they can look like a helix when applied in a 3d scope surprised even me. I love how Alan’s team displayed that! And they essentially turned it into a rail gun.😂
Yeah.. So true.. Maybe I can learn math if it was interesting and adventurous and not just sitting at a desk thinking maths is gonna be useful in the future..
Comments like this make me sad. Mathematics is the most interesting and beautiful thing possible. An enormous, intricate universe that anyone can explore. But almost everybody has the exact wrong idea about what math actually is, because in school they mostly only teach you how to use it as a toolbox.
I have a theory. There is a possibility that this is where every stickman that's created ends up before being converted to a symbol as seen in AvA 1, 2 and 3. TSC woke up literally in pitch black. A void of nothingness. A world of nothing but symbols, letters, and numbers. When you code/make something digitally, you would use symbols, letters, and numbers. And since the stick figure is still in the making, it would make sense for there to be just a void of black. If this is where every stick figure has been before being converted to a symbol, then the evil stick figures such as TCO, (TCO isnt evil anymore though) TDL and Victim most likely caused terror. This explains why Euler's identity (e^ipi) is afraid of TSC when they encounter one another. And it also explains why all the other symbols that appear at the end come out of nowhere. They were probably hiding. They were aware that some of these figures were dangerous, moreso the ones with empty circle heads. It all adds up. Here's something that can also be connected to this: TSC came alive during his process of creation. He was not converted into a symbol yet, TSC found a way out of the void, which was not supposed to happen. This could lead to why TSC cannot control his power the same way TCO and TDL can, he is not working properly due to the fact he was not finished/converted properly.
During the episode it should be noted that The Second Coming is also considered a number by the rules of the dimension, it can be speculated that his number is his "Frames Per Second" which is how fast his animation runs (e.g being around 20 frames a second). This number is probably the only reason any of the mathematical things had any impact on him (such as being effected by the multiplication and subtraction symbols) I don't understand much of the maths stuff itself though so for anyone who wants to learn more about the intricate details, i'd recommend watching "A Complete Over-Analysis of Animation vs Math" made by someone a lot smarter than I am.
TSC is also a symbol himself, in the digital sense: he’s made up of vectors. Not saying you’re wrong about the FPS, I just think it’s neat that there could be multiple reasons the math affects him ^_^
It's interesting how bland and forced education is in school to the point where you don't even want to remember it but I think you just need some amazing visuals and it all comes back like a boomerang that hasn't come back for years.
The prussian model of education is designed not to encourage learning, but to prepare you for being a factory worker; you are meant to get used to sitting in place and doing dull monotonous tasks.
This video is mostly about "Euler's Identity", which is an incredibly elegant formula that unites 5 of the most fundamental numbers in all of mathematics. e^iπ + 1 = 0 where e = Euler's number (2.7812...) i = The square root of negative one (this is referred to as an 'imaginary' number). π = Pi (3.1415...) 1 (one) and 0 (zero). Many mathematicians think this formula contains some incredibly fundamental truths about the universe. It's supposed to be the most beautiful equation in all of mathematics. Both e and π are referred to as 'transcendental' numbers, but my math knowledge isn't good enough to explain why. This video probably does though.
Mathematician here. e and pi are transcendental because they cannot be represented with a finite algebraic equation made of elementary functions. They "transcend" algebra.
Math teacher here. I’d like to explain what i and e^(iπ) mean, but first I need to lay some background. When math gets more complicated, that’s because you *want to do more things.* For example, suppose you’ve been doing subtraction on whole numbers. You know that 2 − 1 = 1 and 7 − 3 = 4. But then you want to calculate 3 − 7. Well, to solve this problem, you must invent negative numbers. Now you can *do more* (you can subtract anything from anything), but you have introduced more numbers - thereby *adding complexity.* You can see The Second Coming grapple with this repeatedly in the video as he encounters negative numbers, irrationals, fractions, and exponents. *The letter i stands for the square root of negative 1.* Multiples of i are called *imaginary numbers,* and numbers of the form x + iy such as 3+2i or 7−12i are called *complex numbers.* Just like negative numbers, i was invented to *do more things.* It turns out that when you introduce a square root of -1, every polynomial equation has a solution. Thus, i is like the ultimate cheat code for a mathematician who wants to *do more things.* Complex numbers can be graphed, as well. The number x + iy corresponds to the point (x, y). So 7−12i corresponds to the point (7, −12). To explain e^(iπ), I need to talk about Euler’s formula. Suppose you have an angle, θ (“theta”). Euler’s formula says that e^(iθ) = cos(θ) + i sin(θ). In English, this means both e^(iθ) and cos(θ) + i sin(θ) are ways of writing *the point on the unit circle with angle θ.* This is why you see so much action with circles in this video. One more thing: θ must be in _radians._ Radians are another way of writing angles. You can even see TSC discover radians at 6:31 in the video! Let’s try putting π in for θ. Well, π radians means 180° - a half-turn around the circle. Conventionally, 0° on the unit circle means (1, 0), so 180° must mean (−1, 0). And remember, we can turn a point into a complex number, so (−1, 0) ↦ -1 + 0i, which is just a fancy way of writing -1. Thus, e^(iπ) = -1. This is called *Euler’s identity.* Sometimes it is written as e^(iπ) + 1 = 0, and it is often praised as one of the most beautiful equations in all of mathematics. I believe that, when e^(iπ) sticks an i on itself in the video, it is multiplying itself by i to enter the imaginary realm. That’s why you see a door open when it does that. You can also see it turn itself into cos(π) + i sin(π) to punch TSC at times 🤭
Thank you, Thank you, Thank you. 🙏 This explanation is just beautiful, I respect anyone who takes the time to learn this subject. For me personally it's frustrating, I can only get the basics of math, and the basics are really all I need to pass a test and get through life. But I do appreciate the deep understanding of what math truly is, math is a beautiful language, even if it can be hard to understand at times.
@@V_ARIETY4145 Math is beautiful since that's literally how video games existed. High school just made its reputation as one of the most hated things on the planet if you're not a nerd.
I remember seeing a lot of math in class but i honnestly gave up trying to understand it all felt like that would be something i'd never understand and leave it to those who actually did.
@@darklegion2268 I'm not sure what you mean by that; all mathematical formulae are facts and they have to be supported with hundreds of proofs before they can be added into the repertoire of Maths. In fact, Euler's identity is considered the most beautiful formula in all of Mathematics; it combines many aspects of the field and combines the 5 core constants (e, i, pi, 1 and 0) into one simple, elegant formula.
theorically, Those symbols are immortal in the number void, since they can multiply and recreate themselves over and over again. btw, did anyone else notice somehing huge at the ending. Its like really faint, but there are huge legs surrounding the symbols at the end
The emotional journey of this animation, from TSC's perspective, is so relatable. Math felt like a mysterious enemy for a very long time, but I slowly came to appreciate it more and more. The power of understanding things that it can bring is really exciting, and now, I feel like math is my best friend. I think TSC is better friends with math, though, by the end of this, than I am, as evidently he made peace with complex numbers. All things considered, I think if you found any parts you may not have understood gratifying to watch, it's with taking some time to understand those topics on your own terms rather than being locked into a particular curriculum. Math is so much more fun that way.
i is Euler’s number. you can add i to anything that can’t be done in one system, but can in another one. example: square root of -25 can’t be done with the system that we grew up with. so, we use another system, i. square root of -25 equals 5i.
e^i•π is called Euler's number. Hope this helps! The • symbol is another way of using the multiplcation sign. Edit: Also, the ^ symbol is called a caret. Example: 10^4=10,000 10⁴=10,000 Heres how it works: 10^4=10×10×10×10 10×10=100 10×10×10=1,000 10×10×10×10=10,000 Edit 2: IM ONLY 10
You all are babys and idont like you motherf##### dont have brains mother died in a car crash little shit 1+1 obsili equals 2 dumbass not 11 cant believe that humanity became this STUPID in 100 years 🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬😡😡😡🤬😡😡🤬😡🤬😡🤬😡🤬😡🤬😡🤬😡🤬😡🤬😡🤬😡🤬🤬🤬🤬🤬🤬🤬😡😡🤬😡😡🤬😡😡😡😡😡😡🤬😡😡😡🤬🤬🤬😡🤬😡🤬😡🤬😡🤬😡🤬😡🤬😡🤬😡🤬😡👿👿👿👿👿👿👿👿👿👿👿👿👿👿👿👿👿👹👹👹👹👹👹👹👹👹👹👹👺👺👺👺👺👺👺👺👺🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🤦🤦🤦🤦🤦🤦🤦🤦🤦🤦🤦
Number Equations Addition Subtraction Negative part 1 Euler's identify Negative part 2 Multiplication The commutative property Multiplication part 2 Division Fraction Irrational number Imaginary number i^2=-1 Euler's formula Complex Complex part 2 Radians Diameter Sin wave Cos wave Sin^2(θ) Infinity Limit if x can find the value Gamma Zeta,delta,phi Aleph Bonus:graphs Decimals
the upside down/white dimension are impossible equations. the 'e' always pulls out an 'i' to open the portal because 'i' times 'e' is impossible. This is proven by how it's full of impossible equations, including square root of negative numbers (it's impossible to find the square root of any negative number)
Those aren't "impossible" expressions and numbers; they're called imaginary numbers. The square-root of (-1) is defined as i, which is the basis of the imaginary numbers.
1:47 This, is Euler's Number. It is the number e, it is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways. It is the base of natural logarithms. It is the limit of (1 + 1/n)n as n approaches infinity, an expression that arises in the study of compound interest. It can also be calculated as the sum of the infinite series
funfact: the symbol e is a mathematical constant approximately equal to 2.71828183.Prism switches to scientific notation when the values are very large or very short, thats all i know- edit: i changed the big into large because it doesnt suit for e
If yall didn't know yet the second coming is inside a scientific calculator the black represents the void where numbers pop up when you type and the white is where the buttons are.This is my theory about the episode since it makes alot of sense I hope this theory will further expand others theories
e^iπ is Euler's identity a useful way to write -1, the symbols at the end Φ,δ,ζ, and א in the background all represent different maths Φ is the golden ratio, δ is used in space and time dilation equations, and א is used to represent infinity set 1
Ah yes!!! 1 + 1…. The hardest question in the universe, no one has ever manage to solve it in a millennium and it will continue forever it seems until neena came by!!! Now we know the answer!!! *Scientists believe it is 3! Lmao* 💀💀💀
Ok, I will be as simple as possible. Basically i is an imaginari number which stands for sqrt(-1). We don't have a solution for this root so we attribute this to the comolex numbers. This numbers are literally another dimension because in there there are all the numbers that cant be explained or solved. Inside this dimension a very important expression is the one with e, which it is obvious by the video that we can do a lot with this expression
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(this is following the timestamps in the original video btw)
0:07 Numbers
0:11 Equations
0:20 Simple Addition
1:24 Simple Subtraction
1:34 Negative Numbers
1:40 e^i(x)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 introduced.
3:43 Irrational Numbers
3:50 Imaginary numbers
3:59 i^2 = -1
4:01 1^3 = -i = i (x) -1 = ie^-i(x)pi
4:02 One of Euler's formulas. It equals -1.
5:18 Introduction to the Complex Plane (This sucked to learn)
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 Euler's Formula
7:35 Another Euler Identity
8:25 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" Theorem
13:04 Gamma(x) = (x-1)!
13:36 Zeta, Delta and Phi
13:46 Aleph
Nice
Thx teacher:D
Can you name one of your monsters Hermie because my pet hermit crab died pls?
I love the help, but a few of the time points are a little off from what they are describing in the video.
holy god.... i need go back to school because GOD
Here’s my explanation of the math stuff throughout the video:
0:22 - equals sign. It means both sides are the same
0:28 - the + means addition
1:32 - the - means subtraction
1:48 e^i*pi is known as Euler’s identity, and it does equal -1. This is because if you bring anything to e^ix, it creates a unit circle on the complex plane (explained later), and the x is the angle on the unit circle in radians (also explained later). for Euler’s number, x is pi, which means you create a 180° angle on the unit circle (because pi radians is equal to 180°) which lands at the point -1. Therefore, e^i*pi is -1
1:57 - when the e guy multiplied himself by i, I guess it sent him to the “imaginary world”, which is a pretty cool concept in this story
2:32 - this a cool representation of multiplication
2:45 - cool representation of division
2:57 - this is a good visual to why you can’t divide by zero, because you’ll never be able to subtract anything from 6
4:01 - exponents is to multiplication in the way that multiplication is to addition, in that you multiply the big number for the amount of times the small number says
4:27 - negative exponents give a fraction because subtracting the exponent by 1 basically divides the number by 4. 4^0 is 1 because that’s 4/4, and 4^-1 is 1/4 because you divide 1 by 4
4:47 - this is the introduction to imaginary numbers. The letter i is equal to the square root of -1 because you can’t normally square root negative numbers. To counteract this, mathematicians created i as a way to represent the square root of -1 to not end up in a dead end while doing math
4:58 - as I previously said, i is equal to the square root of -1. This means i x i = -1 = e ^ i x pi
5:09 - the e guy didn’t travel through the door because the i he pulled out multiplied with the one the Second Coming threw to make -1, which is a real number, causing the e guy to stay in the real world
5:13 - this expansion is known as Euler’s formula. It’s created because of the unit circle e ^ i*pi creates in the complex plane, and it uses the sine and cosine functions to separate the real and imaginary values of the number in the unit circle
5:16 - the Second Coming was multiplied by the negative sign, causing him to flip aroundirm that
5:20 this goes with the unit circle thing. the e guy changed his exponent to 0, which is the same as 0i. because it changed from i*pi to 0i, he went from pi radians (180°) to 0 radians (0°) on the complex plane unit circle, causing a 180° arc to the right
5:34 similar to what happened earlier with the Second Coming
5:53 the e guy put the 4 into his exponent, causing him to move to pi/4 radians (45°) on the unit circle
6:04 - when he multiplied himself by i here, he rotated 90° on the unit circle because when you multiply a number by i on the complex plane, the number is rotated 90° on the plane
6:15 - here, the Second Coming learns about the complex plane. It’s like a number line with a horizontal axis containing the real numbers, but it has a vertical axis too that contains the imaginary numbers, forming the two dimensional complex plane
6:33 - the Second Coming creates the complex plane unit circle that that e^i*pi is based from
6:38 - these are radians. A radian is the angle at which its arc length is equal to the radius, which ends up being 180/pi degrees. The little gap shoes that in a full circle, there are 2pi, or about 6.283 radians
6:58 - I’m not sure why these appear to be multiplied, but the r means the radius and the weird 0 with a line is theta, which is the angle (typically in radians)
7:35 - because theta (the angle) is pi radians and the radius is 1, theta/the radius is pi
7:47 - this shows how sine and cosine can be used to separate the horizontal and vertical aspects of a circle
8:07 - here, he multiplied sine by i, which caused the sine wave to rotate 90 degrees
8:15 - he added them together to create Euler’s formula, which as previously stated is equal to e^i*x , and x is pi because the trig functions contain pi. Therefore. Combining them created the e guy
8:26 - more of the unit circle stuff
8:32 - the e guy expanded into his Taylor expansion form. Thee giant E thing is sigma notation, and it basically adds the part after it, replacing it with integers consecutively going up. You can see this with the the bullets it fires
8:46 - volume of a cylinder
9:02 - he pulled the negative trick again
9:22 - the e guy used the formula for himself and the formula for the trig functions to split himself up a lot
9:29 - here, he made a function, which is basically a placeholder for an expression. Unfortunately, I don’t understand the arrow above it is
9:59 - he changed the angle to pi radians (180°)
10:26 - I’m guessing here, but I think when the Second Coming replaced the dot with the infinity symbol, it caused the function to expand to every point on a graph, which also created the tangent lines (since the Second Coming put the tangent function into that function)
10:55 - the blast became an integral symbol with a limit, because the tangent graph was kind of infinitely long, so the limit allowed the tangent graph to converge I guess. The integral symbol means nothing, it just looks like a cool staff
11:14 - he added an imaginary number, which causes things to move vertically in the complex plane
12:23 - now you see the imaginary world
14:01 - I didn’t entirely understand what this is, but looking at other comments, it seems like the e guy expanded into an equation that can find the volume of spheres beyond the third dimension, but i can’t confirm that, though
14:29 - these symbols are zeta, phi, delta, and aleph
Why this comment doesn't have any replies ?
I can't read that
Yes, the last one calculates the sum of the volumes of a sphere in each (even numbered) dimension. It turns out that this sum is precisely e^π.
Φ(Phi) is the golden ratio. ζ (Zeta) is usually referring to the zeta-function, an important and very famous function in number theory. It sort of holds the key to understanding how prime numbers are distributed. δ(Delta) is more of a technical thing, but delta (and ε (epsilon)) are kind of the mascots of real analysis so it makes sense. Aleph usually refers to the "smallest kind of infinity"
Thx teacher.
mY Bones AAAaaAAAaAAAAaAA
This really shows how smart the second coming is he went from learning basic math to calculous in a matter of minutes
Y eso que es solo el segundo mas inteligente del equipo, amarillo es mucho mas inteligente que el
@@peew1231true I guess
But in different prospective s
you spelt calculus wroung
wrong
@@jomardanvers6563Well you spelt wrong into "wroung".
Hey im just saying, I dont want an argument.
5:29 I only got through third year of college calculus so bear with me. TSC is playing around with Euler formula aka the “e” which is like one of the most important numbers in math cause it’s the base for ALL natural logarithms which in short meats it kinda shows up everywhere. Hence why it’s so powerful here. Plus a cool thing about the “i” is that it represents imaginary numbers. a general rule is i x i = -1 and e^(ipi) is also equal to -1 it’s just another way of writing it. What’s cool about e^(x) is that it’s the only number that’s the derivative of itself so when you find the derivative of e^(8x) for example you get 8e^(8x). i and e together have this power that when it’s multiplied to stuff it kinda “switch dimensions” so when TSC threw an i at ie^(i pi) it was forced back here as iei^(ipi) or -e^(ipi) pretty cool way to show that imo. Also while sin(a) = y coordinate and cos(b) = x coordinate. The two waves when forces next to each other due to i “switching dimensions” don’t exactly line up. The fact that they can look like a helix when applied in a 3d scope surprised even me. I love how Alan’s team displayed that! And they essentially turned it into a rail gun.😂
*ahhh* brain hurtty
Wow
My brain. Aaahhhhhh myyy braaiiiinnnn
Didn't understand a thing but it sounds interesting :S
So many...... X_X
what math teachers expect from us:
Exactly bro
Lol exactly bro
fr
Teacher: do this do you what the video does me: 2+2=fish
💀
honesty, imagination and animation can make anything look interesting
a bot copied your comment
True
Yeah.. So true.. Maybe I can learn math if it was interesting and adventurous and not just sitting at a desk thinking maths is gonna be useful in the future..
Comments like this make me sad. Mathematics is the most interesting and beautiful thing possible. An enormous, intricate universe that anyone can explore. But almost everybody has the exact wrong idea about what math actually is, because in school they mostly only teach you how to use it as a toolbox.
I have a theory. There is a possibility that this is where every stickman that's created ends up before being converted to a symbol as seen in AvA 1, 2 and 3. TSC woke up literally in pitch black. A void of nothingness. A world of nothing but symbols, letters, and numbers. When you code/make something digitally, you would use symbols, letters, and numbers. And since the stick figure is still in the making, it would make sense for there to be just a void of black.
If this is where every stick figure has been before being converted to a symbol, then the evil stick figures such as TCO, (TCO isnt evil anymore though) TDL and Victim most likely caused terror. This explains why Euler's identity (e^ipi) is afraid of TSC when they encounter one another. And it also explains why all the other symbols that appear at the end come out of nowhere. They were probably hiding. They were aware that some of these figures were dangerous, moreso the ones with empty circle heads. It all adds up.
Here's something that can also be connected to this: TSC came alive during his process of creation. He was not converted into a symbol yet, TSC found a way out of the void, which was not supposed to happen. This could lead to why TSC cannot control his power the same way TCO and TDL can, he is not working properly due to the fact he was not finished/converted properly.
Raise r hand if or not reading all of that ✋
This is why tldr exists
With is tldr
Wth
✋️
During the episode it should be noted that The Second Coming is also considered a number by the rules of the dimension, it can be speculated that his number is his "Frames Per Second" which is how fast his animation runs (e.g being around 20 frames a second). This number is probably the only reason any of the mathematical things had any impact on him (such as being effected by the multiplication and subtraction symbols)
I don't understand much of the maths stuff itself though so for anyone who wants to learn more about the intricate details, i'd recommend watching "A Complete Over-Analysis of Animation vs Math" made by someone a lot smarter than I am.
TSC is also a symbol himself, in the digital sense: he’s made up of vectors.
Not saying you’re wrong about the FPS, I just think it’s neat that there could be multiple reasons the math affects him ^_^
that's not quite right but you're on the right track
It's interesting how bland and forced education is in school to the point where you don't even want to remember it but I think you just need some amazing visuals and it all comes back like a boomerang that hasn't come back for years.
I was thinking… this is honestly a really good representation of math, like if they showed things like this it would be monumentally more interesting
The prussian model of education is designed not to encourage learning, but to prepare you for being a factory worker; you are meant to get used to sitting in place and doing dull monotonous tasks.
This video is mostly about "Euler's Identity", which is an incredibly elegant formula that unites 5 of the most fundamental numbers in all of mathematics. e^iπ + 1 = 0
where e = Euler's number (2.7812...)
i = The square root of negative one (this is referred to as an 'imaginary' number).
π = Pi (3.1415...)
1 (one)
and
0 (zero).
Many mathematicians think this formula contains some incredibly fundamental truths about the universe. It's supposed to be the most beautiful equation in all of mathematics. Both e and π are referred to as 'transcendental' numbers, but my math knowledge isn't good enough to explain why. This video probably does though.
Ah yes, fancy -1, the most important part of all math
Mathematician here. e and pi are transcendental because they cannot be represented with a finite algebraic equation made of elementary functions. They "transcend" algebra.
What do "i" meaning?
@@羅文又 "i" is the imaginary unit.
i^2 = -1
the square root of -1 is i
Math teacher here. I’d like to explain what i and e^(iπ) mean, but first I need to lay some background.
When math gets more complicated, that’s because you *want to do more things.* For example, suppose you’ve been doing subtraction on whole numbers. You know that 2 − 1 = 1 and 7 − 3 = 4. But then you want to calculate 3 − 7. Well, to solve this problem, you must invent negative numbers. Now you can *do more* (you can subtract anything from anything), but you have introduced more numbers - thereby *adding complexity.*
You can see The Second Coming grapple with this repeatedly in the video as he encounters negative numbers, irrationals, fractions, and exponents.
*The letter i stands for the square root of negative 1.* Multiples of i are called *imaginary numbers,* and numbers of the form x + iy such as 3+2i or 7−12i are called *complex numbers.* Just like negative numbers, i was invented to *do more things.* It turns out that when you introduce a square root of -1, every polynomial equation has a solution. Thus, i is like the ultimate cheat code for a mathematician who wants to *do more things.*
Complex numbers can be graphed, as well. The number x + iy corresponds to the point (x, y). So 7−12i corresponds to the point (7, −12).
To explain e^(iπ), I need to talk about Euler’s formula. Suppose you have an angle, θ (“theta”). Euler’s formula says that e^(iθ) = cos(θ) + i sin(θ). In English, this means both e^(iθ) and cos(θ) + i sin(θ) are ways of writing *the point on the unit circle with angle θ.* This is why you see so much action with circles in this video.
One more thing: θ must be in _radians._ Radians are another way of writing angles. You can even see TSC discover radians at 6:31 in the video!
Let’s try putting π in for θ. Well, π radians means 180° - a half-turn around the circle. Conventionally, 0° on the unit circle means (1, 0), so 180° must mean (−1, 0). And remember, we can turn a point into a complex number, so (−1, 0) ↦ -1 + 0i, which is just a fancy way of writing -1.
Thus, e^(iπ) = -1. This is called *Euler’s identity.* Sometimes it is written as e^(iπ) + 1 = 0, and it is often praised as one of the most beautiful equations in all of mathematics.
I believe that, when e^(iπ) sticks an i on itself in the video, it is multiplying itself by i to enter the imaginary realm. That’s why you see a door open when it does that. You can also see it turn itself into cos(π) + i sin(π) to punch TSC at times 🤭
Thank you, Thank you, Thank you. 🙏
This explanation is just beautiful, I respect anyone who takes the time to learn this subject. For me personally it's frustrating, I can only get the basics of math, and the basics are really all I need to pass a test and get through life.
But I do appreciate the deep understanding of what math truly is,
math is a beautiful language, even if it can be hard to understand at times.
You are amazing, holy crap.
the fuck did you even say i just got brainwashed
@@V_ARIETY4145 Math is beautiful since that's literally how video games existed. High school just made its reputation as one of the most hated things on the planet if you're not a nerd.
I cant wait for some random commenter to join and type in that emoji
its funny seeing how different the reactions from mathematicians to normal reaction youtubers are
Ikr my reaction going from 😆 to 😐
When you don’t know your math, Alen Becker can help😎
With his animation😎
True😎
TSC could help too😎
The math teacher nobody expect.. But we all need..
true 😎
When orange becomes a hacker:
I love this animation so much.
Also nice reaction!
My singing monsters has the yoll now
THE POWER OF MATH IS UNSTOPPABLE
I remember seeing a lot of math in class but i honnestly gave up trying to understand it all
felt like that would be something i'd never understand and leave it to those who actually did.
TSC is like a little kid who is fantasised by Math until he discovers harder sums 😂
hudfuirsdjkhfjkdh
This taught me more math than school
@@darklegion2268 wat
@@darklegion2268 e^i(pi) = -1; that's Euler's identity.
@@darklegion2268 I'm not sure what you mean by that; all mathematical formulae are facts and they have to be supported with hundreds of proofs before they can be added into the repertoire of Maths. In fact, Euler's identity is considered the most beautiful formula in all of Mathematics; it combines many aspects of the field and combines the 5 core constants (e, i, pi, 1 and 0) into one simple, elegant formula.
Be honest. This didn't teach you anything, it just kept you entertained.
😇@@lexmachina8961
Fun fact!In 5:39,SC hold the "+" sign like the cross,It is mentioned in AvG reacts
The mechanics here would make an awesome and educational puzzle game.
Honestly watching you nerd out was so adorable
This is so good even tho ive saw it like 5 times already BUT I LOVE IT
Best way to learn math:
Step 1: get stuck in a blackroom which only math exists and get out using the power of math
Me with math: math is really complicated
Alan Becker makes this animation
Me: YAY MATH IS FUN TO WATCH
I nearly had an aneurysm when I saw the sigma symbol and the factorials. Thank you, Calculus II, for making me afraid of those.
And what have we learned today?
Math is to powerful 😊
"MaTh Is TwO pOwErFuL : an awkward guy who became nothing.
Yeah
I learned that tetration exists and my brain blew apart
10:58 "WAAAAAAAAEEEEHHH!!!!!"
Im 11 and i know most of these equations easily it's probably because of the hard teaching my teachers used on me back in Africa
Bro I live in Africa
equation shows the square root of negative 1 = i
2 seconds later: i WoNdEr WhAt ThAt StAnDs FoR
the second coming went from adding, subtraction to pi, circles = radius, cos and sin, square roots, square, cubes
theorically, Those symbols are immortal in the number void, since they can multiply and recreate themselves over and over again. btw, did anyone else notice somehing huge at the ending. Its like really faint, but there are huge legs surrounding the symbols at the end
why is this more simple than what my school teaches me?
It's just a small summary of what school teaches them. You aren't expected to learn here.
It's not simpler. You just don"t need to understand here to appreciate the animation.
You are entertained, not taught.
@@lexmachina8961 well you see I'm just stupid kk?
@@blueisthenumberonecolor Actually no. If you find this simpler, you are a genius.
If teacher's taught math like this math would be everyone's favorite subject.
The emotional journey of this animation, from TSC's perspective, is so relatable. Math felt like a mysterious enemy for a very long time, but I slowly came to appreciate it more and more. The power of understanding things that it can bring is really exciting, and now, I feel like math is my best friend. I think TSC is better friends with math, though, by the end of this, than I am, as evidently he made peace with complex numbers. All things considered, I think if you found any parts you may not have understood gratifying to watch, it's with taking some time to understand those topics on your own terms rather than being locked into a particular curriculum. Math is so much more fun that way.
for me rn math just feels like walking on lava barefoot
i is Euler’s number. you can add i to anything that can’t be done in one system, but can in another one.
example: square root of -25 can’t be done with the system that we grew up with. so, we use another system, i.
square root of -25 equals 5i.
e^i•π is called Euler's number. Hope this helps!
The • symbol is another way of using the multiplcation sign.
Edit: Also, the ^ symbol is called a caret. Example:
10^4=10,000
10⁴=10,000
Heres how it works:
10^4=10×10×10×10
10×10=100
10×10×10=1,000
10×10×10×10=10,000
Edit 2: IM ONLY 10
God i hope this was right...
i have just one thing to say bro
🤓
This is correct
@@darklegion2268 it does it's caled euler's identity. 3blue1brown has a few vids on the topic if youre interested
@@PumpkinatorZ leave me alone. im only 10.
Math:
π=3.8 9.9 combination
Grafs are double-digit
If you ± in negative then you get positive and you know the rest
1 + 1 is obviously 11 what was Alan Becker thinking!
Yeah
Yup
You all are babys and idont like you motherf##### dont have brains mother died in a car crash little shit 1+1 obsili equals 2 dumbass not 11 cant believe that humanity became this STUPID in 100 years 🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬😡😡😡🤬😡😡🤬😡🤬😡🤬😡🤬😡🤬😡🤬😡🤬😡🤬😡🤬😡🤬🤬🤬🤬🤬🤬🤬😡😡🤬😡😡🤬😡😡😡😡😡😡🤬😡😡😡🤬🤬🤬😡🤬😡🤬😡🤬😡🤬😡🤬😡🤬😡🤬😡🤬😡👿👿👿👿👿👿👿👿👿👿👿👿👿👿👿👿👿👹👹👹👹👹👹👹👹👹👹👹👺👺👺👺👺👺👺👺👺🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🖕🤦🤦🤦🤦🤦🤦🤦🤦🤦🤦🤦
HOW DO U NOT KNOW!? its actually 1+1=2!
@@Jupiter5-q5n its actually 1+1=21
This was actually so cool
1:52 tpot
Number
Equations
Addition
Subtraction
Negative part 1
Euler's identify
Negative part 2
Multiplication
The commutative property
Multiplication part 2
Division
Fraction
Irrational number
Imaginary number
i^2=-1
Euler's formula
Complex
Complex part 2
Radians
Diameter
Sin wave
Cos wave
Sin^2(θ)
Infinity
Limit if x can find the value
Gamma
Zeta,delta,phi
Aleph
Bonus:graphs
Decimals
Bonus ideas!
I is a letter
the upside down/white dimension are impossible equations. the 'e' always pulls out an 'i' to open the portal because 'i' times 'e' is impossible.
This is proven by how it's full of impossible equations, including square root of negative numbers (it's impossible to find the square root of any negative number)
Those aren't "impossible" expressions and numbers; they're called imaginary numbers. The square-root of (-1) is defined as i, which is the basis of the imaginary numbers.
I am just surprised that Alan Becker can do this whole mini fight scene in my brain its liquidity and anime fight scene
Animation vs Math shows how Orange successfully made the death star out of math
The teacher: What! You learned this in Kindegarten..
1:47 This, is Euler's Number.
It is the number e, it is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways. It is the base of natural logarithms. It is the limit of (1 + 1/n)n as n approaches infinity, an expression that arises in the study of compound interest. It can also be calculated as the sum of the infinite series
it also, happens to = -1!
@@minicrewmate7865 No, e^i(pi) = -1.
I have waited for this and I am amazed that your watching stickmam you are a legendary
funfact:
the symbol e is a mathematical constant approximately equal to 2.71828183.Prism switches to scientific notation when the values are very large or very short, thats all i know-
edit: i changed the big into large because it doesnt suit for e
11:28 my man is about to take math to a whole new level
Very true. Math hurts... MY BRAIN!
The math teachers teaching us:
now the second coming is big brain
Hey forever nenaa I started watching you 3 days ago and I've been on the grind since I'm proud to declare you one of the best RUclipsrs❤
If yall didn't know yet the second coming is inside a scientific calculator the black represents the void where numbers pop up when you type and the white is where the buttons are.This is my theory about the episode since it makes alot of sense I hope this theory will further expand others theories
What teachers expect you to answer in math problems
His Bow is made out of: 2 2 X = Which is 2X2= The answer is 4 which is why he shot 4s
e^iπ is Euler's identity a useful way to write -1, the symbols at the end Φ,δ,ζ, and א in the background all represent different maths Φ is the golden ratio, δ is used in space and time dilation equations, and א is used to represent infinity set 1
If math was like this,math would be everyone's favorite subject.
11:00 math be like when I'm in 9th grade:
My teacher asks me a math problem me thinking:
I get it😂😂
10:45 Me just realizing Nenaa has been standing the whole time 💀
It’s raining or windy hard here…… but I do reallylike these animations and your videos A LOT!!!!!
New math lore
I love Alan and it is great to see that you are enjoying his work also!!
Very smart animation, read about quantum, complex rulers...
Are in heart
Forever Nenaa + Alan Becker + Reaction = My Favourite!
What I like about your reactions is that YOU DONT PAUSE EVERY 0.3 SECONDS
It's Marta being that whole going through that void
"Good morning everybody,"
*Me watching this at 7pm: 🗿*
NENNA BECAMING SMART!
Me with my friends in math class be like:
Day six of asking nenaa to continue PvZ2
Ah yes!!! 1 + 1…. The hardest question in the universe, no one has ever manage to solve it in a millennium and it will continue forever it seems until neena came by!!! Now we know the answer!!! *Scientists believe it is 3! Lmao* 💀💀💀
Beyond infinity! 10:23
10:16 It's that serious. They're the series. Heh
The fact that TSC broke oblivion where all complex numbers comes to broke it with imaginary numbers
I haven't see you for like a day
Ok, I will be as simple as possible. Basically i is an imaginari number which stands for sqrt(-1). We don't have a solution for this root so we attribute this to the comolex numbers. This numbers are literally another dimension because in there there are all the numbers that cant be explained or solved. Inside this dimension a very important expression is the one with e, which it is obvious by the video that we can do a lot with this expression
The Second Coming is a frikin genius
Nena is like very smart 😅
Second: *”I knew this day would come. Time to not remember everything yellow taught me and just mess around.”*
P.O.V: Easy math for teachers:
Students: AAAAAAUUUUUJGGGGGGHHHH
Alan Becker is definitely running out of ideas💀 Animation vs Alphabet is coming in quicker than I thought💀
My guy learned this in minutes while I struggle doing basic math
At this time it’s actually eight million, just a solid:YAY!🎉
9:00 my man just did the pac-man strat
Can we talk about THAT PERFECT COR LE THE SECOND COMING DID WITH THE GRAPH LIKE DAMN BRO
I know I said “COR LE” I ment Circle, I’m to lazy to change it
4:02 THE POWER OF TWOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO!!!
*TPOT intro*
Everyone gangsta until the Euler identity appears 🤣
Ain’t no way bro learned the whole math before me
Nenaa‼️‼️ Alan Becker just made an Animation vs Geomatry😁😁😁
Imagine every single equation that alan becker showed answered 69
We all call Orange "Second Coming" now. It's weird how reputation can change your known name like that.
Can We Appriciate That We Got Nenna To 1.30M?
Second Coming: does math with complete ease
Me: struggling to understand any type of math :/
What the fun teacher shows
The power of two 😂 object show likers be hearing that
My math teacher expecting me to do this.
Me: Brain , go!
My Brain: Hellow your computer has virus
Teacher: Okay… and show us your work on how you got your answer?
TSC: