*WOAHHHH! Who knew Math could get so intense and aggressive! Apart from me being an absolute dumb dumb, I enjoyed the awesomeness behind this animation!* *Ok that division one was a mistake! I'm not that much of a dumb dumb!!!!* Book Me! www.cameo.com/eckosoldier Creator: www.youtube.com/@alanbecker Video: th-cam.com/video/B1J6Ou4q8vE/w-d-xo.html more AB reacts - th-cam.com/video/-0KuBPR3OuI/w-d-xo.html
1:07 law of equality 1:26 discovery of the digit "0" 2:23 every number is unique 2:36 discovery of subtraction 2:46 discovery of negative numbers 2:51 -1=e^iπ (i=imaginary, which unlocks graphs) 3:03 (based on math graphs) a line (x) multiplied by i, the line (x) will be rotated 90 degrees or π÷2 radians, which in this video, it just teleports you in another dimension 3:36 discovery of multiplication 3:47 discovery of division 3:48 representation of the easiest way to divide natural numbers (1, 2, 3 etc.) 4:01 division by zero is invalid 4:17 6^2=6*6=6+6+6+6+6+6 (the sign "^" represents the power of n, and if you didn't know, n is short for number) 4:27 our 3D cube but made out of the digit "1" 4:29 4D hypercube made out of the digit "1" 4:33 5D hypercube made out of the digit "1" 4:35 n^0=1 4:43 n^-1=1÷n 4:50 n÷(1÷2)=√n (√n means square root of n) 4:55 discovery of irrational numbers (and that huge number isn't simplified) 5:45 discovery of complex numbers 5:56 remember e^iπ? i said that e^iπ=-1, and it was shown 2 seconds ago that i*i=-1, so i*i=e^iπ. so basically, i*i*i=i*-1=ie^iπ. 6:07 (based on math graphs) if a line (x) is multiplied by 2i, the line (x) just gets reversed. 6:11 e^iπ=cos(π)+isin(π) (formula for e^iπ) 7:13 discovery of graphs 7:31 representation of a circle in mathematical graphs 7:36 2π radians can actually fully complete the circle 7:46 1 radian arc is enough to calculate the radius of the circle 7:53 θ appeared for no reason, it's like going to a party without even being invited (from 8:17 to 8:23) for people that are still at school, DO NOT DO THIS IN EXAMS 8:43 sine and cosine waves discovered 9:05 the i*sine wave makes a type of a 3D tube with a bunch of gaps 9:13 the combination of cosine and i*sine leads to the formula that made e^iπ 9:30 expansion of e^iπ 10:10 he multiplied a unit length by 4 to get to the white line and throw himself up, then he got the dot from the white line and hit the expansion of e^iπ with an infinite sine wave 10:18 e^iπ=cos(π)+isin(π)=e^iπ+e^-iπ÷2+e^iπ+e^-iπ÷2i 10:28 he just made a mathematical gun, nothing to explain here 11:25 Today, we're sponsoring... THE INFINITY GUN!!! Unlimited bullets, unlimited range! Buy now! 🤣🤣🤣 11:55 the E-MECH 11:57 YAEEEEH! (starts the battle) 12:30 mathematical laser :) 12:45 the mech can't handle multivariable things so it got destroyed 13:01 radius 100 laser 13:19 e^iπ goes into the 90 degree rotated dimension but the stickman also known as TSC follows e^iπ into the dimension 14:09 TSC begs for e^iπ to show him the exit 14:20 TSC spells "exit" with e^iπ's symbols 15:20 TSC banishes out of existence if this helped you (except 11:25, 11:55, 11:57 and 12:30), give this a like!
I am no math person but when TSC confronted the giant "mech" equation, he tried to shoot it with his function of the tangent infinity gun, only to be stopped by it with the integral limit. Limits are self explanatory as it only allows equations to be done at a certain "limit". However, later on, TSC modified his gun to use the cosine and i sine as the trigger, making the function of tangent infinity gun a multi-variable shot, which yields the values of cosine, i sine, and tangent, which the "mech's" integral limit shield cannot handle as it can only do single variables.
Let me explain all the things you were confused about in the video. I'm doing this from memory so I hope I won't make any stupid mistakes. I'll be using programming math notation, so here's what it is: = is the equal sign + is addition - is substraction * is multiplication / is division ^ is power (2^4 is two to the power of four, so 2^4 = 16) 2:50 - Euler's formula. e^(i*pi) = -1. In a more general sense, e^(i*x) = cos(x) + i*sin(x) (in the case of x = pi by definition cos(pi) = -1 and sin(pi) = 0, so e^(i*pi) = -1 + 0*i = -1 + 0 = -1). The constant e is what's called Euler's number, one of the most important mathematical constants. It is equal to 1 + 1/1 + 1/(1*2) + 1/(1*2*3) + 1/(1*2*3*4) + 1/(1*2*3*4*5)... which equals around 2.718. The constant i is what's called an imaginary number. i^2 = -1, which seems impossible as two negative numbers multiplied by each other always equal a positive number. Pi is also a very important constant in math, equal to around 3.142. It is the number you get if you divide the circumference of any circle by its diameter. For now however you only need to know that e^(i*pi) = -1. 3:00 - Euler's number multiplies itself by i, making it an imaginary number and transporting it to the imaginary number space. 3:46 - This is a method of of quickly dividing large numbers. You substract the divisor from the divided number multiple times until you are left with a number smaller than the divisor. The solution is the number of times you substracted plus the number you are left with divided by the same divisor. This breaks with dividing by 0 (which is left undefined because everything suggests that the solution is infinity, but that would make all numbers equal to each other; I won't explain it here, just google why you cannot divide by 0). 4:34 - You seem to be confused about taking something to a power higher than 2. This is actually quite simple. x^5 for example is x*x*x*x*x, so 4^5 = 4*4*4*4*4 = 16*4*4*4 = 64*4*4 = 256*4 = 1024. Taking something to the power of 0 is shown later. Every number except 0 that is taken to the power of 0 equals 1 for reasons I won't get into here. Negative powers are later shown, which are also very simple. x^-y = 1/(x^y). So 4^-2 = 1/(4^2) = 1/16. 4:50 - Square root. A sqaure root is synonymous with taking a number to the power of 1/2. In programming you usually write the square root as sqrt(), but in math it's written like in the video. It's sort of like a reverse to squaring a number. The sqrt(4), the one shown first in the video, is equal to 2 because 2^2 = 4. The sqrt(9) = 3 because 3^2 = 9. The sqrt(1) = 1 because 1^2 = 1. Sqaure roots of numbers that are not perfect squares (0, 1, 4, 9, 16, 25, 36...) will be hard to write with an unending sequence of numbers after the decimal separator (the little period signifying a non-whole number). The sqrt(2) shown in the video is equal to around 1.414, but the actual number is infinitely long if you want to write it. It is however very useful in math. For example the diagonal of a square is always sqrt(2) times the edge of the square. 5:44 - As I previously stated, this is the constant i. i^2 = -1, so sqrt(-1) = i. 6:08 - Orange throws an i at the Euler's number, which is trying to multiply itself by another i to escape to the world of imaginary numbers. This causes them to combine into i*i, which are equal to -1 by definition. This makes the Euler's number equal to -1*-1 = 1, which is not an imaginary number. This is why it gets thrown out back into the world of real numbers. 6:10 - Here Euler's number uses Euler's formula to become cos(pi) + i*sin(pi), which I explained earlier. 6:18 - Euler's number takes out its own pi, which is equal to 180 degrees in a unit of angle called radians (a radian is a unit of angle in which 1 is equal to the legth of the radius of the circle that the angle creates; this means that by definition pi is half of the circle). More of this will be seen later. 6:50 - Here Euler's number has its pi divided by 4, which makes it move by 45 degrees, which is in radians equal to pi/4. Again, more on this later. 7:02 - Orange uses i to rotate him 90 degrees. This is not because of some radian calculation (i cannot even exist as a value in geometry), but because the imaginary and real axis of number are usually shown together on a plain of so-called complex numbers. The axis of the imaginary numbers is vertical and the axis of the real numbers is horizontal, so by multiplying any complex number by i you "turn" it by 90 degrees anticlockwise. This will be shown more clearly in a second. 7:13 - This is when the plain of complex numbers is shown. The first axis drawn by Orange is the imaginary vertical one. The second is the real horizontal one. 7:34 - These are the radians I talked about earlier. The circle can be divided into six segments the size of one radian (one length of the radius) and a small part that makes the total circle slightly larger. This is because the total angle inside the circle, or 360 degrees, is by definition equal to 2*pi, or around 6.283. 7:39 - Orange takes out a single radian, which, as I said, is the size of the radius of the circle. 8:00 - Here the r is the radius of the circle and the weird 0 with a line through it, which is a Greek letter called theta, is the most common symbol used for an angle, especially in physics, but also in math. Orange uses them to get the angle at which the radius is orientated, which is pi at 180 degrees (facing left). 8:38 - I'm not really sure how exactly Orange got the trigonometric functions here, but the sine and cosine functions are highly connected with pi, as the waves of both create sort of "circles" and go through the x axis in intervals of pi. 9:04 - Again we see the sine function multiplied by i to turn it 90 degrees 9:29 - This symbol that Euler's number turns into here is called sigma, and it is again a Greek letter. It is used to not do what I've done while explaining what e is at the beginning and write out a sum with an ellipsis at the end. It is used to write a sum of any large amount (potentially infinite) of numbers if there is a rule that connects them all. For example to get the sum of all the natural numbers up to ten with each number divided by 2 you start with the big E-like thing (sigma), you write the number you start with below the sigma, starting with n= (in this case n=0, which means you start with 0), then you write the number you end at above the sigma (in this case 10). Finally you write the formula to get the specific numbers to the right of the sigma (in this case we want each number to be divided by 2, so we write n/2). I will from now write it as sigma(below: n=0; above: 10; function: n/2). In the case of the video we use the sum from the definition of e, which is e = sigma(below: n=0; above: infinity; function: 1/n!). The ! sign in math is called the factorial and is the multiplication of all numbers up to that number starting from one. So 3! = 1*2*3 = 6, 5! = 1*2*3*4*5 = 120, 1! = 1 and 0! = 1. In the video we see a different sum because the number that is equal to the sum is e^(i*pi), not e. This is why we get sigma(below: n=0; above: infinity; function: (i*pi)^n/n!) in the video. You can also see that the missiles shot by the sigma sum are actually the elements of the sum one after another ((i*pi)^0/0!, (i*pi)^1/1!, (i*pi)^2/2!...). 9:58 - This is actually a thing in math. A negative vector is its positive version rotated in a vector space. The video later confirms that this is a vector space, which I will point out. 10:25 - Orange divided the sine by the cosine of the same angle (pi or 180 degrees), which equals the tangent of the same angle. In mathematical notation: sin(pi)/cos(pi) = tg(pi). I think this is all combined into a tangent function times 9i, but even if it's not, it's definitely some kind of function even though it doesn't have an x parameter. You can actually see the bullets of the weapon leave a trait of tangent functions if you look closely. 10:57 - Here pi is used to rotate the radius by 180 degrees. 11:34 - This confirms that the circle is indeed a vector space. 12:12 - 9i is used to move the circle up by nine (remember the imaginary axis?). 13:21 - Orange and Euler's number end up in the world of imaginary numbers as they have been multiplied by i. They also end up rotated 90 degrees counterclockwise, which is again the result of them being multiplied by i. 14:22 - Orange spells exit here using the Euler's number as e, a multiplication sign as x, the i constant as, well, i, and a half-covered pi as a t. 14:58 - n! is turned into the gamma function, which I will describe as gamma(n - 1). By definition of the gamma function gamma(n) = (n - 1)!. It is not really that important, just explaining what the weird letter in the equasion is. 15:08 - Euler's number adds more and more "volume" to the circle with each use of the function. It's too complicated to explain in a TH-cam comment. 15:28 - The different letters here are different constants in math. I am not really sure what the tall bouncing one is, it is the Greek letter zeta but there is only a zeta function, not a zeta constant. The weird o with a line through it one the left is phi, the famous and very useful golden ratio. Phi = a/b = (a+b)/a = around 1.618. The flying letter is delta, the first Feigenbaum constant, which is too complicated to explain here, but it equals around 4.669. The giant letter at the end is aleph, a type of infinity (yes, there are different types and sizes of infinity in math). There is an infinite amount of alephs, the most commonly used one is aleph-zero, the sum of any infinite set of whole numbers I know this is all very simplified for the math nerds reading this, but this is a very long comment and I just want to finally finish writing this.
@@nothpx It's a function, which takes the variable in brackets, plugs it into a formula and equals the solution of that formula. For example: f(x) = x^2 + 2x + 3. That means that f(2) = 2^2 + 2*2 + 3 = 11. And that f(3) = 3^2 + 2*3 + 3 = 18. You can use a plain to visualize a function, so that the horizontal axis are all the possible x's and the vertical one are the f(x)'s that are given out for each x. This particular function will create a curve known as a parabola (google it if you want to see one. But for example f(x) = 2x + 3 will simply create a diagonal line, f(x) = 2^x will create an exponentially growing function, f(x) = log(x) will be the opposite, creating logarithmically smaller and smaller numbers getting closer to 0 (which is in this case what's known as a limit - a maximal value the function will reach at a certain point, in this case at x = positive infiniry). f(x) = sin(x) will create a sine wave and f(x) = tg(x) will create a weird rotated S-like pattern. Functions are what's covered in the branch of maths called the mathematical analysis.
@@gustavofabiani5153Not quite. The mathematics exists on a range of dimensions. But he is not in the correct one. The gamma function used to send him away accounted for infinite dimensions and then flipped it over to the imaginary.
The symbol at 5:02 is the square root. It's kinda the opposite of squared. (Remember that a number squared means a number multiplied by itself once) For example, 2 squared is 4 so the square root of 4 would be 2. The square root of two would be a decimal since no whole number multiplied by itself is 2. Hopefully that makes sense; I'm not great at explaining.
14:24 that ain't an equation. A lot of people mistake this, but Alan himself stated that the consecutive characters spell out 'exit' as TSC (Orange) wanted a wait out of this "math dimension"
Math is surely complex and interesting at the same time, just lacks fun to be fully understood and this is what I call Math being fun. And now I saw or just had a witness or preview of whatever else Math has prepared ahead for me and for everyone else like me.
Did you know what those things in the end? It was the Greek math symbols. for example: the long thing was 7 the s combine with the o was 4 o with a line was 21 and the big thing was infinity
u mean zeta and delta and stuff? those have other uses other then being normal number (they can be used for stating numbers beyond infinity like omega (w)
Summery :) 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 the orange guy 5:01 the bow is made up of two twos, a multiplication sign, and an equal, 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. 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 7:53 circle and cylinder 8:11 orange guy 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 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 Handel 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 nole (smallest infinity) IF I MISSED ANYTHING OR GOT ANYTHING WRONG PLZ TELL ME :) -nerdy highschool freshmen
@@MathOverChemistry I think its basically the Series of e^x because e^x = x^n/n!, Gamma (n+1) Equals to n! Because Gamma(z) = the integral from 0 to infinity from t^(z-1) *e^-t dt. Then you can say that gamma (z+1) = t(z-1+1)*e^(-t). Now do partial Integration. U= t^z, v‘= e^(-t) v= -e^(-t), u’ = z*t^(z-1)Then do u(x)*v(x) - the integral from u‘(x)*v(x). So that we have -t^z*e^(-t) from 0 to infinty + z*the integral from 0 to infinity from z*t*e^-t dt. -t^z*e^-t goes to 0 if t=infinty. At the end we have Gamma (z+1) = z* the integral from 0 to infinity from t^z-1*e^-t dt. So basically z*Gamma(z). Now we calculate Gamma (1) which equals to the integral from infinty to 0 from t^1-1*e^-t dt. Which is the integral from 0 to infinity from e^-t dt. The integral from 0 to infinity from e^-t = 1. Now we say that Gamma (n) = (n-1)! Because Gamma (1)=1 which is as you probably know 0!. In total we have now Gamma (n+1) = n*Gamma(n). n*Gamma(n) = n*(n-1)! Which is n!. When 2n= Infinity then is n = infinity/2 as well so gamma ((infinity/2)+1) is the same as gamma (n+1). If i*pi is x Then we have (i*pi)^n/n! = e^i*pi. I hope you already did partial integrations. Anyways there is a Formular that can be used to calculate the volume of a n-dimensional sphere which is quite similar. (Pi)^n/2/gamma(n/2+1). I Hope I was able to help you. I know its probably difficult to read that over the screen. (And please dont take it too seriously, if I have made a mistake. Even for me it was hard to write everything down)
e to the i*pi is kinda easy to look at if you are kinda nerdy (its still hard to see how and why it works like that) e to i*n is equal to cos(n) + i*sin(n) and because n is pi, it makes the cos equal to -1 and the isin to i * 0 so its just -1 + 0 and thats why e to the i*pi is -1
Secret ending: it turns out the black void, was Alan’s calculator, and he’s like: Guys, what happened to my calculator? And TSC is just:……..*silently walks away*
Wheather you love math or not, the fact is you still use it almost everyday mainly without knowing e.g. Did you get the right change after purchasing a burger at McDonald's. In the mean time here is a simple question for you! 2 × 2 ÷ 2
TSC was fighting something called the Euler's Identity, which is SUPER important in the whole of MATH (just like how Pi is important), and that's probably why TSC keeps getting it by mixing random operations and numbers. The Euler's Identity consists of 3 important variables. e = 2.71 and e is raised to ( i multiplied by Pi ) i = A special symbol for Imaginary; Hence it is the answer to the square root of -1. It's imaginary but it is still represented by something Pi = 3.141592 obviously
The symbol you see at 5:00 is called Square root. Correct me if I am wrong, but it opposes the concept of how exponents work. At 14:21 you can see it says “exit” not really a math equation, but I can see why people may think it was a math equation lol.
e^i(pi) is equal to the huge floating Taylor series seen shooting out numbers as they are equal to -1 so that is basically a Taylor expansion of e^i(pi) In the end where tsc is teleported each new circle represents a new dimension (0d for a point, 1d for a circle which is a line, 2d another circle and so on) and when e^i(pi) adds an i the whole equation is simplified into -1 equals to -1 in the end the huge grey thing is called Aleph null (0) which is basically all natural numbers (normal numbers) in 1 so from 0 to the end of the number, it is a inaccessible number as you cannot get it by any means it is also the smallest infinity there is. edit: omg im kinda famous
and i is a short form for imaginary number which is equal to squareroot of -1 so 4i would be 1 as 2i cancel the square root and 2i x 2i would be 1 so 2i would be equal to e^i(pi) so when ie^i(pi) goes through a portal tsc throws another i into it turning back into -1 making it impossible to go through the portal
@@noatouwthe algebra you stated is just an expression, not an equation. To “do” 2a + 7b is a meaningless request, therefore you must be jokin’ m8!
Things you didn't know: 1. It was square roots 2. Yes, √-1 = i 3. cos(pi) + isin(pi) = e^i (pi) 4. The dot makes a circle 5. R = radius 6. T in PI means 0 7. E ^i (pi) can turned into Tylor series (hope i type it right) 8. E^i (pi) can multipled himself 9. This part i can't help, for some reason e^i(pi) turned into 0 after being shotted 10. E^i(pi) made a giant robot which even infinity can't handle back 11. 9i with move the circle 12. Cos with isin on tan will destoyed everything on it's sight 13. Imaginary numbers falls down 14. Multyplying will i will go back to the real dimension 15. It spells Exit 16. i × 4 = 1 17. Yes, e^i(pi) 18. Zeta, phi, delta and aleph arrive 19. Don't tell everyone why aleph is huge Final (20). You're clueless 😂😂😂😂😂
when you start dealing with i, your 1-dimensional number line becomes a 2-dimensional number plane. adding i to something is basically just moving it upwards, and multiplying by i is basically rotating it 90 degrees counterclockwise. rotate 1, and you get i. rotate i, and you get -1. (anything more complicated than this would turn into a whole wall of text, and as much as i'd enjoy writing that, i don't think it would be quite as fun to read.)
Really enjoyed your reaction to this animation! Was good in math but I had trouble following what was going on in the video. Keep up the amazing content! Hope you are having a fantastic day! Take care.
Gotta smash that like button,you just made my day. Oh and that 6²=36 it means 6×6=36 the ² means multiply the number by itself so for example 6³=216 that means 6×6×6=216.
e^iπ is Euler's Identity and its equivalent to -1 (search it up cause it can get complicated) - √2 is irrational, which is why it has a lot of digits √-1 can't really work, so somw mathmaticians came up with i which means imaginary. - i * i * i is simple(ish). Since we know i * i is -1, we can change it to i * -1 and then to i * e^iπ - The number tries to get out by multiplying itself by i, but the orange guy (TSC) throws another one making it turn into -e^iπ. e^iπ = -cos(π)+isin(π) e^iπ-π = e^0, so it pivots around (0,0) - Too much to go through on 6:39 - Funny little thing after that, TSC makes a bow with 2×2, so it shoots out 4 e^i(pi/4) makes it rotate 45 deg counterclockwise - (the dot) Complex plain Unit circle, yippeee! 1 rad = 57.3 deg which is why it has 6.28 radians Arclength of 1 radian = 1 = radius Radius increases making the circle bigger using theta*r The thing about moving the theta is pure fun Ratio of arclength to radius at 180 deg = pi (which is also why e^i(pi/4) goes up 45 deg) cos(t) + sin(t) for unit circle i sin(t) rotates the sine curvs by 90 deg Cos(π) + i sin(π) = e^iπ fun fighting scene!!!! 2*(-π) rotates it by 180 deg twicw The thing that it turns into is the Taylor series of e^x for x = iπ TSC makes a circle then multiplies it by π to create a circle or a shield thingy 8 × π × r^2, making it a cylinder e^iπ = -1 so r-(-theta) = r+theta TSC teleports by negating his position - Too much at 10:18 for me to handle :( TSC makes f(x) = 9 tan(pi x) funny fight until 10:56 :) - i think TSC multiplies the angle by pi, making it rotate 180 deg Adds i7 to the dot making it go up by well, seven. TSC upgrades his funny shotgun by adding infinity 11:41 is just impossible to explain Integrals can handle infinites if it has a limit more FIGHTING!!!!!!! 9i shifts it up, etc. the cos(circle) + isin(circle) makes the waves from earlier, and tan just destroys everything TSC multiplies 10×10 making r=100 and the laser bigger Euler's Identity: imma head out TSC: lets make a circle and WEEEEEEEE The whole world is rotated 90 deg when multiplied by i (i dont really know why, it just does) The square roots you saw from the cracks are fully imaginary Multiplies it by i going back to the normal world - i^4 = 1 The nth term is the n-dimentional volume for a unit n-d sphere For example, 0d is a point, 2d is a circle, and so on and so forth The sum simplifies to -1, ans TSC is gone. Oh and by the way, if you want to ask questions do NOT send them here. I am not a mathmatician and I am only writing this by my findings. If you want to ask a question, go to Gallium-Gonzolium and many other explenations. They explained it very well and even i took the explenation from him!
At the end MR ._. So what happened.... he spelled exit with the letters by the e then x is the multiply symbol and the I with is already there and for pie, he blocks the right side to make it look like a t which spells..... EXIT! So orange wanted to get out of this math universe to go back for minecraft probably XD💀😳💀😳
The cool thing to me at least is that it shows how orange "broke reality" with math and its accurate to how in pretty much every simulation possible it can be broken with math/infinity if there are no set limits or boundaries
Numbers were really hard to learn for me too. I used to think like you do. I'm a man of words not numbers. I was really good with foreign languages and literature and I thought it doesn't have anything to do with numbers. Then I discovered computer languages! I discovered math itself is a kind of language! The one thing I was missing, the one thing that I needed to understand math was A REASON! In school, I was always taught the theoretical never the practical.
at 14:25 the thing you said its a somekind of equation its actuallly spells exit and alan did not make this animation the lead animators are all behind of this animation and yes they are nerds🤓🤓🤓
Also the reason why the the square root of -1 equals i is because before i was a number you couldn't take the square root of -1 so they just invented a number to make it possible I'm pretty sure this also adds to every single other negative number
The symbol ‘i’ stands for imaginary numbers, or any numbers that don’t have tangible value, and are thus considered “not real numbers”. The square root of negative one is the basis for all imaginary numbers, or ‘i’
I didn’t necessarily hate math, I was interesting, it was just excruciatingly hard, the only class I hate more than anything, is science, EVERYONE in my class is bad at science, we can never get more than like, 55.5% on science exams, the assignments are somewhat ok,
I did a collage math course to brush up... Euler's Identity doesn't show up in it. Like at all. So don't worry about it, you'd need to really get into math to encounter it.
I watched this video, and immediately went and watched a bunch of math videos. from algebra to theoretical type stuff. Was quite fascinating. also made me want to make a game based off of this animation.
Square root is like multiplications but reversed lets take an example: in the multip we say 2×7 = 14 in the sq root its 2 or if you put sq root on 14 it will be 7 if you put sq root on 21 (3×7) it will make 14. Sorry bcs my explanation is not clear im just 15 turned 16 last week so i rlly tried my best :) have a great day
i is denoted as an imaginary number. It is just a representation. Any negative number under a square root is generally denoted as non-real. Using "I", we get into the realm of complex numbers and the complex plane. It can get complicated. But for now, note that "I" is equal to -1. And for those of you unfamiliar, e^(i*pi) = -1 is known as Euler's Identity.
According to some videos, there are some equations there that were a mistake or just not possible. Well if his lead animator gonna explain it, then the equations would make sense.
that guy who said that there were mistakes is wrong btw every equation in alan beckers video is completely legal and that other guy does not know some things
9:30 if your wondering “what is dat symbol and what does it do?” Well it's called “Sigma” and I'm not joking, it is called sigma I don't know alot about it so i will just say the thing i so far learned it, so its basically looking for the sum of cn 4 | 3 Sigma k=1 = 3+3+3+3 = 12 The i you saw on “√-1=i” means a imaginary number and it just no way to give a actually answer. The e^iπ is a number so you can find a answer for it but add a i at the start making ie^iπ and now it there is actually answer for it
*WOAHHHH! Who knew Math could get so intense and aggressive! Apart from me being an absolute dumb dumb, I enjoyed the awesomeness behind this animation!*
*Ok that division one was a mistake! I'm not that much of a dumb dumb!!!!*
Book Me! www.cameo.com/eckosoldier
Creator: www.youtube.com/@alanbecker
Video: th-cam.com/video/B1J6Ou4q8vE/w-d-xo.html
more AB reacts - th-cam.com/video/-0KuBPR3OuI/w-d-xo.html
Same
ya this video dumb founded me
E
i cant wait for language vs animation o wait imagine music vs animation green vs a musical note would break the internet
You aren't the only one confused about math I graduated but I looked up every math question
What’s hilarious is that Alan managed to make all the math problems in this video valid
Alan actually didn't plan the animation his animation leader did since the animation leader loved math so much.
@@MicherGDReal🤓
Some of the math isnt actually valid i think
@@NotathreeletternameOnly one minor thing he did. Everything else is mathematically accurate
@@violentwhite0 who uses the nerd emoji, is thou nerd emoji
1:07 law of equality
1:26 discovery of the digit "0"
2:23 every number is unique
2:36 discovery of subtraction
2:46 discovery of negative numbers
2:51 -1=e^iπ (i=imaginary, which unlocks graphs)
3:03 (based on math graphs) a line (x) multiplied by i, the line (x) will be rotated 90 degrees or π÷2 radians, which in this video, it just teleports you in another dimension
3:36 discovery of multiplication
3:47 discovery of division
3:48 representation of the easiest way to divide natural numbers (1, 2, 3 etc.)
4:01 division by zero is invalid
4:17 6^2=6*6=6+6+6+6+6+6 (the sign "^" represents the power of n, and if you didn't know, n is short for number)
4:27 our 3D cube but made out of the digit "1"
4:29 4D hypercube made out of the digit "1"
4:33 5D hypercube made out of the digit "1"
4:35 n^0=1
4:43 n^-1=1÷n
4:50 n÷(1÷2)=√n (√n means square root of n)
4:55 discovery of irrational numbers (and that huge number isn't simplified)
5:45 discovery of complex numbers
5:56 remember e^iπ? i said that e^iπ=-1, and it was shown 2 seconds ago that i*i=-1, so i*i=e^iπ. so basically, i*i*i=i*-1=ie^iπ.
6:07 (based on math graphs) if a line (x) is multiplied by 2i, the line (x) just gets reversed.
6:11 e^iπ=cos(π)+isin(π) (formula for e^iπ)
7:13 discovery of graphs
7:31 representation of a circle in mathematical graphs
7:36 2π radians can actually fully complete the circle
7:46 1 radian arc is enough to calculate the radius of the circle
7:53 θ appeared for no reason, it's like going to a party without even being invited
(from 8:17 to 8:23) for people that are still at school, DO NOT DO THIS IN EXAMS
8:43 sine and cosine waves discovered
9:05 the i*sine wave makes a type of a 3D tube with a bunch of gaps
9:13 the combination of cosine and i*sine leads to the formula that made e^iπ
9:30 expansion of e^iπ
10:10 he multiplied a unit length by 4 to get to the white line and throw himself up, then he got the dot from the white line and hit the expansion of e^iπ with an infinite sine wave
10:18 e^iπ=cos(π)+isin(π)=e^iπ+e^-iπ÷2+e^iπ+e^-iπ÷2i
10:28 he just made a mathematical gun, nothing to explain here
11:25 Today, we're sponsoring... THE INFINITY GUN!!! Unlimited bullets, unlimited range! Buy now! 🤣🤣🤣
11:55 the E-MECH
11:57 YAEEEEH! (starts the battle)
12:30 mathematical laser :)
12:45 the mech can't handle multivariable things so it got destroyed
13:01 radius 100 laser
13:19 e^iπ goes into the 90 degree rotated dimension but the stickman also known as TSC follows e^iπ into the dimension
14:09 TSC begs for e^iπ to show him the exit
14:20 TSC spells "exit" with e^iπ's symbols
15:20 TSC banishes out of existence
if this helped you (except 11:25, 11:55, 11:57 and 12:30), give this a like!
Thank you so much for pinning the comment! (or at least i think its pinned)
Albert Einstein Be like. 😂
🤓
52nd like
Genious....
I am no math person but when TSC confronted the giant "mech" equation, he tried to shoot it with his function of the tangent infinity gun, only to be stopped by it with the integral limit. Limits are self explanatory as it only allows equations to be done at a certain "limit". However, later on, TSC modified his gun to use the cosine and i sine as the trigger, making the function of tangent infinity gun a multi-variable shot, which yields the values of cosine, i sine, and tangent, which the "mech's" integral limit shield cannot handle as it can only do single variables.
Let me explain all the things you were confused about in the video. I'm doing this from memory so I hope I won't make any stupid mistakes.
I'll be using programming math notation, so here's what it is:
= is the equal sign
+ is addition
- is substraction
* is multiplication
/ is division
^ is power (2^4 is two to the power of four, so 2^4 = 16)
2:50 - Euler's formula. e^(i*pi) = -1. In a more general sense, e^(i*x) = cos(x) + i*sin(x) (in the case of x = pi by definition cos(pi) = -1 and sin(pi) = 0, so e^(i*pi) = -1 + 0*i = -1 + 0 = -1). The constant e is what's called Euler's number, one of the most important mathematical constants. It is equal to 1 + 1/1 + 1/(1*2) + 1/(1*2*3) + 1/(1*2*3*4) + 1/(1*2*3*4*5)... which equals around 2.718. The constant i is what's called an imaginary number. i^2 = -1, which seems impossible as two negative numbers multiplied by each other always equal a positive number. Pi is also a very important constant in math, equal to around 3.142. It is the number you get if you divide the circumference of any circle by its diameter. For now however you only need to know that e^(i*pi) = -1.
3:00 - Euler's number multiplies itself by i, making it an imaginary number and transporting it to the imaginary number space.
3:46 - This is a method of of quickly dividing large numbers. You substract the divisor from the divided number multiple times until you are left with a number smaller than the divisor. The solution is the number of times you substracted plus the number you are left with divided by the same divisor. This breaks with dividing by 0 (which is left undefined because everything suggests that the solution is infinity, but that would make all numbers equal to each other; I won't explain it here, just google why you cannot divide by 0).
4:34 - You seem to be confused about taking something to a power higher than 2. This is actually quite simple. x^5 for example is x*x*x*x*x, so 4^5 = 4*4*4*4*4 = 16*4*4*4 = 64*4*4 = 256*4 = 1024. Taking something to the power of 0 is shown later. Every number except 0 that is taken to the power of 0 equals 1 for reasons I won't get into here. Negative powers are later shown, which are also very simple. x^-y = 1/(x^y). So 4^-2 = 1/(4^2) = 1/16.
4:50 - Square root. A sqaure root is synonymous with taking a number to the power of 1/2. In programming you usually write the square root as sqrt(), but in math it's written like in the video. It's sort of like a reverse to squaring a number. The sqrt(4), the one shown first in the video, is equal to 2 because 2^2 = 4. The sqrt(9) = 3 because 3^2 = 9. The sqrt(1) = 1 because 1^2 = 1. Sqaure roots of numbers that are not perfect squares (0, 1, 4, 9, 16, 25, 36...) will be hard to write with an unending sequence of numbers after the decimal separator (the little period signifying a non-whole number). The sqrt(2) shown in the video is equal to around 1.414, but the actual number is infinitely long if you want to write it. It is however very useful in math. For example the diagonal of a square is always sqrt(2) times the edge of the square.
5:44 - As I previously stated, this is the constant i. i^2 = -1, so sqrt(-1) = i.
6:08 - Orange throws an i at the Euler's number, which is trying to multiply itself by another i to escape to the world of imaginary numbers. This causes them to combine into i*i, which are equal to -1 by definition. This makes the Euler's number equal to -1*-1 = 1, which is not an imaginary number. This is why it gets thrown out back into the world of real numbers.
6:10 - Here Euler's number uses Euler's formula to become cos(pi) + i*sin(pi), which I explained earlier.
6:18 - Euler's number takes out its own pi, which is equal to 180 degrees in a unit of angle called radians (a radian is a unit of angle in which 1 is equal to the legth of the radius of the circle that the angle creates; this means that by definition pi is half of the circle). More of this will be seen later.
6:50 - Here Euler's number has its pi divided by 4, which makes it move by 45 degrees, which is in radians equal to pi/4. Again, more on this later.
7:02 - Orange uses i to rotate him 90 degrees. This is not because of some radian calculation (i cannot even exist as a value in geometry), but because the imaginary and real axis of number are usually shown together on a plain of so-called complex numbers. The axis of the imaginary numbers is vertical and the axis of the real numbers is horizontal, so by multiplying any complex number by i you "turn" it by 90 degrees anticlockwise. This will be shown more clearly in a second.
7:13 - This is when the plain of complex numbers is shown. The first axis drawn by Orange is the imaginary vertical one. The second is the real horizontal one.
7:34 - These are the radians I talked about earlier. The circle can be divided into six segments the size of one radian (one length of the radius) and a small part that makes the total circle slightly larger. This is because the total angle inside the circle, or 360 degrees, is by definition equal to 2*pi, or around 6.283.
7:39 - Orange takes out a single radian, which, as I said, is the size of the radius of the circle.
8:00 - Here the r is the radius of the circle and the weird 0 with a line through it, which is a Greek letter called theta, is the most common symbol used for an angle, especially in physics, but also in math. Orange uses them to get the angle at which the radius is orientated, which is pi at 180 degrees (facing left).
8:38 - I'm not really sure how exactly Orange got the trigonometric functions here, but the sine and cosine functions are highly connected with pi, as the waves of both create sort of "circles" and go through the x axis in intervals of pi.
9:04 - Again we see the sine function multiplied by i to turn it 90 degrees
9:29 - This symbol that Euler's number turns into here is called sigma, and it is again a Greek letter. It is used to not do what I've done while explaining what e is at the beginning and write out a sum with an ellipsis at the end. It is used to write a sum of any large amount (potentially infinite) of numbers if there is a rule that connects them all. For example to get the sum of all the natural numbers up to ten with each number divided by 2 you start with the big E-like thing (sigma), you write the number you start with below the sigma, starting with n= (in this case n=0, which means you start with 0), then you write the number you end at above the sigma (in this case 10). Finally you write the formula to get the specific numbers to the right of the sigma (in this case we want each number to be divided by 2, so we write n/2). I will from now write it as sigma(below: n=0; above: 10; function: n/2). In the case of the video we use the sum from the definition of e, which is e = sigma(below: n=0; above: infinity; function: 1/n!). The ! sign in math is called the factorial and is the multiplication of all numbers up to that number starting from one. So 3! = 1*2*3 = 6, 5! = 1*2*3*4*5 = 120, 1! = 1 and 0! = 1. In the video we see a different sum because the number that is equal to the sum is e^(i*pi), not e. This is why we get sigma(below: n=0; above: infinity; function: (i*pi)^n/n!) in the video. You can also see that the missiles shot by the sigma sum are actually the elements of the sum one after another ((i*pi)^0/0!, (i*pi)^1/1!, (i*pi)^2/2!...).
9:58 - This is actually a thing in math. A negative vector is its positive version rotated in a vector space. The video later confirms that this is a vector space, which I will point out.
10:25 - Orange divided the sine by the cosine of the same angle (pi or 180 degrees), which equals the tangent of the same angle. In mathematical notation: sin(pi)/cos(pi) = tg(pi). I think this is all combined into a tangent function times 9i, but even if it's not, it's definitely some kind of function even though it doesn't have an x parameter. You can actually see the bullets of the weapon leave a trait of tangent functions if you look closely.
10:57 - Here pi is used to rotate the radius by 180 degrees.
11:34 - This confirms that the circle is indeed a vector space.
12:12 - 9i is used to move the circle up by nine (remember the imaginary axis?).
13:21 - Orange and Euler's number end up in the world of imaginary numbers as they have been multiplied by i. They also end up rotated 90 degrees counterclockwise, which is again the result of them being multiplied by i.
14:22 - Orange spells exit here using the Euler's number as e, a multiplication sign as x, the i constant as, well, i, and a half-covered pi as a t.
14:58 - n! is turned into the gamma function, which I will describe as gamma(n - 1). By definition of the gamma function gamma(n) = (n - 1)!. It is not really that important, just explaining what the weird letter in the equasion is.
15:08 - Euler's number adds more and more "volume" to the circle with each use of the function. It's too complicated to explain in a TH-cam comment.
15:28 - The different letters here are different constants in math. I am not really sure what the tall bouncing one is, it is the Greek letter zeta but there is only a zeta function, not a zeta constant. The weird o with a line through it one the left is phi, the famous and very useful golden ratio. Phi = a/b = (a+b)/a = around 1.618. The flying letter is delta, the first Feigenbaum constant, which is too complicated to explain here, but it equals around 4.669. The giant letter at the end is aleph, a type of infinity (yes, there are different types and sizes of infinity in math). There is an infinite amount of alephs, the most commonly used one is aleph-zero, the sum of any infinite set of whole numbers
I know this is all very simplified for the math nerds reading this, but this is a very long comment and I just want to finally finish writing this.
Wow very long comment
is f in tsc's gun also a constant?
@@nothpx It's a function, which takes the variable in brackets, plugs it into a formula and equals the solution of that formula. For example: f(x) = x^2 + 2x + 3. That means that f(2) = 2^2 + 2*2 + 3 = 11. And that f(3) = 3^2 + 2*3 + 3 = 18. You can use a plain to visualize a function, so that the horizontal axis are all the possible x's and the vertical one are the f(x)'s that are given out for each x. This particular function will create a curve known as a parabola (google it if you want to see one. But for example f(x) = 2x + 3 will simply create a diagonal line, f(x) = 2^x will create an exponentially growing function, f(x) = log(x) will be the opposite, creating logarithmically smaller and smaller numbers getting closer to 0 (which is in this case what's known as a limit - a maximal value the function will reach at a certain point, in this case at x = positive infiniry). f(x) = sin(x) will create a sine wave and f(x) = tg(x) will create a weird rotated S-like pattern. Functions are what's covered in the branch of maths called the mathematical analysis.
Holy smokes now that’s the kinds of comments I love to see!!!!
@@ecko dayum
everything in this animation is suppose to be as mathematically correct, which is shocking
🤯
Most of it is, but there are some small errors in some of the advanced equations. Just some nitpicks though
@@panrex2451good gods y'all found mathematical mistakes in the video
@@brothdian fax lol
Densebysebyhdehhn
The creativity in this is amazing, and it actually makes sense! All of the equations and operations listed have correlation to what's happening!
Oh don't get me wrong this is a masterpiece
14:20 TSC spelled out the word “exit”, telling Euler’s number that he wants to exit this weird universe.
For me is like a dimension
Like He is on the 1° dimension
But He belongs to the 4° dimension
Thats What i understand
@@gustavofabiani5153Not quite. The mathematics exists on a range of dimensions. But he is not in the correct one. The gamma function used to send him away accounted for infinite dimensions and then flipped it over to the imaginary.
The symbol at 5:02 is the square root. It's kinda the opposite of squared. (Remember that a number squared means a number multiplied by itself once)
For example, 2 squared is 4 so the square root of 4 would be 2. The square root of two would be a decimal since no whole number multiplied by itself is 2.
Hopefully that makes sense; I'm not great at explaining.
What is the giant N at the end?
nvm
What is the N?
@@MrKneeBeeYT Aleph
Where u learn this
14:24 that ain't an equation. A lot of people mistake this, but Alan himself stated that the consecutive characters spell out 'exit' as TSC (Orange) wanted a wait out of this "math dimension"
Math is surely complex and interesting at the same time, just lacks fun to be fully understood and this is what I call Math being fun. And now I saw or just had a witness or preview of whatever else Math has prepared ahead for me and for everyone else like me.
Did you know what those things in the end? It was the Greek math symbols. for example: the long thing was 7 the s combine with the o was 4 o with a line was 21 and the big thing was infinity
u mean zeta and delta and stuff? those have other uses other then being normal number (they can be used for stating numbers beyond infinity like omega (w)
the big thing would be aleph
aleph_0 being the smallest cardinal infinity
@@Walker74382zeta is also the symbol for the rienmann zeta function
@@HokoraYinphineyeah and omega would actually be infinity
@@Idk71568 omega isnt in the video though?
I love how he can just press together the equal sign and it automatically does the equation even though its already solved
The equal sign compresses it
If I learnt math like this I would like math more
Edit: the e with pi symbol represents -1 or imgainary unit and the e means euler
So if e i pi is -1 and TSC is 1, is that the reason they're fighting? As opposites? And the ending -1 had literally subtracted TSC?
@@Red_MOON187 no based on the story of the episode -1 is being chased by orange because he wants to get out but it could also be your explanation
@@theanimator6890 I know why they're actually fighting. I just found the opposites idea interesting.
Summery :)
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 the orange guy 5:01 the bow is made up of two twos, a multiplication sign, and an equal, 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.
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
7:53 circle and cylinder
8:11 orange guy 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
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 Handel 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 nole (smallest infinity)
IF I MISSED ANYTHING OR GOT ANYTHING WRONG PLZ TELL ME :)
-nerdy highschool freshmen
@@MathOverChemistry I think its basically the Series of e^x because e^x = x^n/n!, Gamma (n+1) Equals to n! Because Gamma(z) = the integral from 0 to infinity from t^(z-1) *e^-t dt. Then you can say that gamma (z+1) = t(z-1+1)*e^(-t). Now do partial Integration. U= t^z, v‘= e^(-t) v= -e^(-t), u’ = z*t^(z-1)Then do u(x)*v(x) - the integral from u‘(x)*v(x). So that we have -t^z*e^(-t) from 0 to infinty + z*the integral from 0 to infinity from z*t*e^-t dt. -t^z*e^-t goes to 0 if t=infinty. At the end we have Gamma (z+1) = z* the integral from 0 to infinity from t^z-1*e^-t dt. So basically z*Gamma(z). Now we calculate Gamma (1) which equals to the integral from infinty to 0 from t^1-1*e^-t dt. Which is the integral from 0 to infinity from e^-t dt. The integral from 0 to infinity from e^-t = 1. Now we say that Gamma (n) = (n-1)! Because Gamma (1)=1 which is as you probably know 0!. In total we have now Gamma (n+1) = n*Gamma(n). n*Gamma(n) = n*(n-1)! Which is n!. When 2n= Infinity then is n = infinity/2 as well so gamma ((infinity/2)+1) is the same as gamma (n+1). If i*pi is x Then we have (i*pi)^n/n! = e^i*pi. I hope you already did partial integrations. Anyways there is a Formular that can be used to calculate the volume of a n-dimensional sphere which is quite similar. (Pi)^n/2/gamma(n/2+1). I Hope I was able to help you. I know its probably difficult to read that over the screen. (And please dont take it too seriously, if I have made a mistake. Even for me it was hard to write everything down)
@@philipp1779 Ahhhh that makes more sense, Thanks :)
@MathOverChemistry Youre still in high school right? That is actually quite Impressive.
@@philipp1779 thanks 😀
1. 14:22 "EXIT"
2. The "i" means imaginary numbers (numbers that don't exist)
3. Ei pi ( 2:56 ) equals to -1 idk how to explain but it does
e to the i*pi is kinda easy to look at if you are kinda nerdy (its still hard to see how and why it works like that)
e to i*n is equal to cos(n) + i*sin(n)
and because n is pi, it makes the cos equal to -1 and the isin to i * 0 so its just -1 + 0 and thats why e to the i*pi is -1
@the_m_original you're Incredible
Secret ending: it turns out the black void, was Alan’s calculator, and he’s like: Guys, what happened to my calculator? And TSC is just:……..*silently walks away*
Wheather you love math or not, the fact is you still use it almost everyday mainly without knowing e.g. Did you get the right change after purchasing a burger at McDonald's.
In the mean time here is a simple question for you!
2 × 2 ÷ 2
TSC was fighting something called the Euler's Identity, which is SUPER important in the whole of MATH (just like how Pi is important), and that's probably why TSC keeps getting it by mixing random operations and numbers.
The Euler's Identity consists of 3 important variables.
e = 2.71
and e is raised to ( i multiplied by Pi )
i = A special symbol for Imaginary; Hence it is the answer to the square root of -1. It's imaginary but it is still represented by something
Pi = 3.141592 obviously
15:00 he uses infinite amount of dimension to make him return
The only reason I watch these reactions for this video is just to see people trying to get the math lol
The symbol you see at 5:00 is called Square root. Correct me if I am wrong, but it opposes the concept of how exponents work.
At 14:21 you can see it says “exit” not really a math equation, but I can see why people may think it was a math equation lol.
e^i(pi) is equal to the huge floating Taylor series seen shooting out numbers as they are equal to -1 so that is basically a Taylor expansion of e^i(pi)
In the end where tsc is teleported each new circle represents a new dimension (0d for a point, 1d for a circle which is a line, 2d another circle and so on) and when e^i(pi) adds an i the whole equation is simplified into -1 equals to -1
in the end the huge grey thing is called Aleph null (0) which is basically all natural numbers (normal numbers) in 1 so from 0 to the end of the number, it is a inaccessible number as you cannot get it by any means it is also the smallest infinity there is.
edit: omg im kinda famous
and i is a short form for imaginary number which is equal to squareroot of -1 so 4i would be 1 as 2i cancel the square root and 2i x 2i would be 1 so 2i would be equal to e^i(pi) so when ie^i(pi) goes through a portal tsc throws another i into it turning back into -1 making it impossible to go through the portal
btw also e^i(pi) is equal to -1 and also cosine(pi) x isine(pi) and those can be expanded to create even more -1s (e^i(pi))
and lastly the dot represents the complex plane
So you’re a numbers kinda guy then 😂
@@ecko no haha not really i just like watching documentaries
edit: i like science so thats why
If i had a math class like this im alaways awaken no skiping this is masterpiece
I knew some people would love this, I’m just a letters person not numbers 😂
@@eckothen do 2a + 7b and 6ab • 4c lol
@@eckobtw where is ur discord server?
@@eckothe symbol u last used when u was 15 was a carrot/square root
@@noatouwthe algebra you stated is just an expression, not an equation.
To “do” 2a + 7b is a meaningless request, therefore you must be jokin’ m8!
14:20 that wasn't an equation, it spelled "exit"
4:59 That's the Square Root Symbol. Easiest way to remember is to tell yourself: what times itself will be equal to the number inside the square root?
Euler’s identity, Limits, and Integrals are all like, college level math, so it’s understandable you might not have seen them.
Limits and integrals are like 11-12 th grade math bro
Only if you go to a good school
I see a math teacher smiling ear to ear watching this animation
Also the orange stick man is called The Second Coming. Just letting you know
Things you didn't know:
1. It was square roots
2. Yes, √-1 = i
3. cos(pi) + isin(pi) = e^i (pi)
4. The dot makes a circle
5. R = radius
6. T in PI means 0
7. E ^i (pi) can turned into Tylor series (hope i type it right)
8. E^i (pi) can multipled himself
9. This part i can't help, for some reason e^i(pi) turned into 0 after being shotted
10. E^i(pi) made a giant robot which even infinity can't handle back
11. 9i with move the circle
12. Cos with isin on tan will destoyed everything on it's sight
13. Imaginary numbers falls down
14. Multyplying will i will go back to the real dimension
15. It spells Exit
16. i × 4 = 1
17. Yes, e^i(pi)
18. Zeta, phi, delta and aleph arrive
19. Don't tell everyone why aleph is huge
Final (20). You're clueless 😂😂😂😂😂
I like how he’s confused by division
when you start dealing with i, your 1-dimensional number line becomes a 2-dimensional number plane. adding i to something is basically just moving it upwards, and multiplying by i is basically rotating it 90 degrees counterclockwise. rotate 1, and you get i. rotate i, and you get -1. (anything more complicated than this would turn into a whole wall of text, and as much as i'd enjoy writing that, i don't think it would be quite as fun to read.)
Really enjoyed your reaction to this animation! Was good in math but I had trouble following what was going on in the video. Keep up the amazing content! Hope you are having a fantastic day! Take care.
too many references to be made!! brain overloading!!!!!!!!!!!
Gotta smash that like button,you just made my day. Oh and that 6²=36 it means 6×6=36 the ² means multiply the number by itself so for example 6³=216 that means 6×6×6=216.
Yeah
e^iπ is Euler's Identity and its equivalent to -1 (search it up cause it can get complicated)
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√2 is irrational, which is why it has a lot of digits
√-1 can't really work, so somw mathmaticians came up with i which means imaginary.
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i * i * i is simple(ish).
Since we know i * i is -1, we can change it to i * -1 and then to i * e^iπ
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The number tries to get out by multiplying itself by i, but the orange guy (TSC) throws another one making it turn into -e^iπ.
e^iπ = -cos(π)+isin(π)
e^iπ-π = e^0, so it pivots around (0,0)
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Too much to go through on 6:39
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Funny little thing after that, TSC makes a bow with 2×2, so it shoots out 4
e^i(pi/4) makes it rotate 45 deg counterclockwise
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(the dot) Complex plain
Unit circle, yippeee!
1 rad = 57.3 deg which is why it has 6.28 radians
Arclength of 1 radian = 1 = radius
Radius increases making the circle bigger using theta*r
The thing about moving the theta is pure fun
Ratio of arclength to radius at 180 deg = pi (which is also why e^i(pi/4) goes up 45 deg)
cos(t) + sin(t) for unit circle
i sin(t) rotates the sine curvs by 90 deg
Cos(π) + i sin(π) = e^iπ
fun fighting scene!!!!
2*(-π) rotates it by 180 deg twicw
The thing that it turns into is the Taylor series of e^x for x = iπ
TSC makes a circle then multiplies it by π to create a circle or a shield thingy
8 × π × r^2, making it a cylinder
e^iπ = -1 so r-(-theta) = r+theta
TSC teleports by negating his position
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Too much at 10:18 for me to handle :(
TSC makes f(x) = 9 tan(pi x)
funny fight until 10:56 :)
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i think TSC multiplies the angle by pi, making it rotate 180 deg
Adds i7 to the dot making it go up by well, seven.
TSC upgrades his funny shotgun by adding infinity
11:41 is just impossible to explain
Integrals can handle infinites if it has a limit
more FIGHTING!!!!!!!
9i shifts it up, etc.
the cos(circle) + isin(circle) makes the waves from earlier, and tan just destroys everything
TSC multiplies 10×10 making r=100 and the laser bigger
Euler's Identity: imma head out
TSC: lets make a circle and WEEEEEEEE
The whole world is rotated 90 deg when multiplied by i (i dont really know why, it just does)
The square roots you saw from the cracks are fully imaginary
Multiplies it by i going back to the normal world
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i^4 = 1
The nth term is the n-dimentional volume for a unit n-d sphere
For example, 0d is a point, 2d is a circle, and so on and so forth
The sum simplifies to -1, ans TSC is gone.
Oh and by the way, if you want to ask questions do NOT send them here. I am not a mathmatician and I am only writing this by my findings. If you want to ask a question, go to Gallium-Gonzolium and many other explenations. They explained it very well and even i took the explenation from him!
correct them not me ;)
Can I just say that SC made a friking DEATH STAR.
🧐
Multivariable infinity, which not even integrals (the "sword" of Eurler's number) can counter.
how math teachers see math
They actually see it as fun but we see it as “explain why the triangle is a triangle by using rocket science in 2 minutes.”
@@GoofyAhhBoxy"explain this (8>6)"
I think what Alan becker is pointing out is Math can be cool. Most of the time
For the fact Alan had to do the maths to make this video is crazy!
It was his lead animator who made the script and had the idea.
Not alan.
Unpopular opinion but I LOVE Math! So this was great for me!
Same
Unpopular opinion indeed.
math is really cool but the way it's taught in schools is horrid
i kinda like math
@@therealtailsprower true lol
ecko, your not alone with your hatred of math.
At the end MR ._. So what happened.... he spelled exit with the letters by the e then x is the multiply symbol and the I with is already there and for pie, he blocks the right side to make it look like a t which spells..... EXIT! So orange wanted to get out of this math universe to go back for minecraft probably XD💀😳💀😳
11:54 congratulations you have found a boss from dark souls ⚔️
even a stick figure can learn everything in math in just a matter of minutes 💀💀👍👍
The cool thing to me at least is that it shows how orange "broke reality" with math and its accurate to how in pretty much every simulation possible it can be broken with math/infinity if there are no set limits or boundaries
Every math teacher be like:
Make a war.
Me:ok that's easy.
The math teacher:
With math
Me:wha-the the wha-t
This is the new fighting technique called Math-fu
Numbers were really hard to learn for me too. I used to think like you do. I'm a man of words not numbers. I was really good with foreign languages and literature and I thought it doesn't have anything to do with numbers. Then I discovered computer languages! I discovered math itself is a kind of language! The one thing I was missing, the one thing that I needed to understand math was A REASON! In school, I was always taught the theoretical never the practical.
14:22 he meant "exit" in there if you see the spelling :)
this is the forth time im as- wait, he actually finally reacted, LESSGO BOIS, HE REACTED TO IT
The square route of a number (for this example we will use 4) its the result of a number times itself, so √4 is 2
at 14:25 the thing you said its a somekind of equation its actuallly spells exit and alan did not make this animation the lead animators are all behind of this animation and yes they are nerds🤓🤓🤓
Fun fact for those who somehow didn't know: This was made with the help of a math nerd
*THINK FAST! WHAT'S THE SQUARE ROOT OF A PINECONE?!*
An acorn! :D
Also the reason why the the square root of -1 equals i is because before i was a number you couldn't take the square root of -1 so they just invented a number to make it possible I'm pretty sure this also adds to every single other negative number
The symbol ‘i’ stands for imaginary numbers, or any numbers that don’t have tangible value, and are thus considered “not real numbers”. The square root of negative one is the basis for all imaginary numbers, or ‘i’
Are you glad ur not in school anymore Ecko?
I loved school but I hated mathematics so much 😭
@@ecko my fav subject was science what was urs?
English, history and PE
@@ecko pe isn’t an actual subject tho-
@@ImMrNugs It was in my school as it was a sports school :)
that giant grey Aleph walking away is the stuff of nightmares
He spelt out the word exit dude!!!!! 14:20
I think that guy is the guy who make the math the hardest subject
Eko: Percentages
Me: But thats division
I am back from a long break! I hope you're doing great!
2:50 the reaction is legit and sussy too how -1 transformed to his giant form
I didn’t necessarily hate math, I was interesting, it was just excruciatingly hard, the only class I hate more than anything, is science, EVERYONE in my class is bad at science, we can never get more than like, 55.5% on science exams, the assignments are somewhat ok,
The Second Coming: I was forced to learn math today and I’m gonna make it everyone else’s problem
I loved math and I only understood 13% of what happened
Yeah this animation was insane
I did a collage math course to brush up... Euler's Identity doesn't show up in it. Like at all. So don't worry about it, you'd need to really get into math to encounter it.
animation: spells exit, him: idk what equation this is
Same bro same..
I watched this video, and immediately went and watched a bunch of math videos. from algebra to theoretical type stuff. Was quite fascinating. also made me want to make a game based off of this animation.
How did orange escape the facility…😂
I liked this comment
Bro defined whole of reality using math😂
Dude is a death star
5:05 that’s a square root sign it’s basically the opposite of the of squaring a number
Square root is like multiplications but reversed lets take an example: in the multip we say 2×7 = 14 in the sq root its 2 or if you put sq root on 14 it will be 7 if you put sq root on 21 (3×7) it will make 14. Sorry bcs my explanation is not clear im just 15 turned 16 last week so i rlly tried my best :) have a great day
Wrong. Completely
I imagine math teacher will give student this video to make them motivated
i didnt even know math has alot of learning
5:52
nothing squared can become -1, so it becomes imaginary, standing as I
It's called a square root 5:01
17:02 its collage level pretty much, e^i*theta converts from radians to complex numbers
At least I go to a private school so I know most of this.
I LOVE YOUR REACTIONS.❤
i is denoted as an imaginary number. It is just a representation. Any negative number under a square root is generally denoted as non-real.
Using "I", we get into the realm of complex numbers and the complex plane. It can get complicated.
But for now, note that "I" is equal to -1.
And for those of you unfamiliar,
e^(i*pi) = -1 is known as Euler's Identity.
Now we are connected more with eckosoldier 😂😂😂😂😂😂
"Metroplex" cybertronian ultimatum
No your not Dumb your PERFECT
According to some videos, there are some equations there that were a mistake or just not possible. Well if his lead animator gonna explain it, then the equations would make sense.
People always like to dig deeper, regardless if there are any mistakes. It shouldn’t take anyway away from this masterpiece
that guy who said that there were mistakes is wrong btw every equation in alan beckers video is completely legal and that other guy does not know some things
I dont see any errors. Only the last equation had some weird notation, but I understood the reference it was trying to make
Ecko and everybody else reacted to this video have Very similar Thumbnails.
🧐
ECKO: "What are we watching?!"
Answer: Genius. Sheer genius.
THE SPEED AT WHICH I CLICKED
5:00 a square root
Question, do you think you could create two playlists of you reacting to Alan Beckers Animation vs Animator and Animation vs Minecraft
5:00 it called speauz root or something like that
This video is accurate to how hard maths is in collage right now I don't understand looking it old computer dial up noise
14:21 it spells 'exit' spelled by the e, x, i and TSC covering up half the pi so it looks as a T.
9:30 if your wondering “what is dat symbol and what does it do?”
Well it's called “Sigma” and I'm not joking, it is called sigma
I don't know alot about it so i will just say the thing i so far learned it, so its basically looking for the sum of cn
4 | 3
Sigma k=1 = 3+3+3+3 = 12
The i you saw on “√-1=i” means a imaginary number and it just no way to give a actually answer.
The e^iπ is a number so you can find a answer for it but add a i at the start making ie^iπ and now it there is actually answer for it
5:49 Yep. That's the symbol for imaginary, which is a complex number.
The weird sign is called a square root and tysm for making this video 🎉