A Complete Over-Analysis of Alan Becker’s Animation Vs. Math
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- čas přidán 25. 06. 2023
- **Read here first**
I know this video is from the channel Alan Becker. The animations his team make are phenomenal and I am simply doing an analysis (more generally a criticism and review) on it.
Please watch their original video first before commenting that I didn’t make this :)
Original Video: • Animation vs. Math - Zábava
It makes infinitely more sense when you stop thinking of TSC as a stick figure, and start thinking of him as the numerical value that he is: *frames per second.* He is innately math meeting visuals.
That’s why, for example, the multiplication sign speeds him up: it increased his play rate.
I never thought about it like that, but yeah they are canonically an animation, and that makes sense.
Yeah! That makes alot of sense😮
What is he being multiplied by? Two?
There wasn't a 2 there and the multiplicative identity is 1 (1x=x), so without any multiplication factor it seems like it essentially should've just done nothing...
@@FireyDeath4 I know that's a far reach, but if he's f.ex. 24 frames/second he could do 2×4, making it 8 frames/second. This would lead to this effect from old movies, where everyone is moving slightly faster than in reality, because you need to speed it up to get a flowing image.
Genius
I think the reason symbols work on TSC is because he's using the number on his attributes, such as speed and position, the two attributes he edits in the animation. He isn't a number, but he's composed of them, like atoms.
Makes sense, he's a computer code
imagine making vector graphic version of TSC *exact details i mean exact is his outline orange sprite same thickness as Alan when drew him in Alan his painting editor if you look closely in desmos somthing..
@@a17waysJackinn Flash animations use vectors, TSC is already that.
Which makes sense why "exit" is a higher dimension for euler... Cuz TSC is literally a higher dimension being, made up of numbers
@@a17waysJackinn
Flash animations are vector based
So he is already a vector shape
You see that a youtuber makes a really masterpiece when even the university teachers are talking about it.
Wow, ok, I was not expecting that but at least I know my whole middle school is talking about that video but I was not expecting it to leak to the univerity teachers at all
@@weirdskunkI'd wish people from my school watched Alan Becker.
Well to be fair, Alan Becker is an absolute master of not just animation but also visual storytelling, script writing and all the other things that a master movie director would do, and he is really way beyond just a CZcamsr in terms of talent and skills. I think he chose to still only make projects that have a scale appropriate to CZcams and only posting his videos on CZcams instead of making one of those cash grabs called Hollywood movies in 2023 and charge insane amount of money, because he is humble and has integrity, NOT because he doesn't have the capacity to lol
@@xuanyizhao4952well that scaled quickly
get it? scaled? as in *matrixes*
There's a lot of people who are going to finally understand concepts by seeing them in visual form. This is incredibly well done
I don't have maths as majors nor did I ever tried to understand these concepts , but it still looks baffling from what i can make out. So epic , it's an endless universe.
lol this vid was what i used yo explain to some of my friends the of complex numbers
I'm always so shocked to see the attention to the tiniest of rules and details in their videos. Most of the tricks we saw in the Minecraft series could be done in-game, which is insanely cool as the videos serve an "educational" role too in that regard. Same with this video, just nothing but tremendous praise
These guys really know their attention to detail!
I don't think the animations really serve as educational, they're just really cool. The only reason I learned anything from the video was because it made me want to learn what it meant, not because it taught me itself.
@@godlyvex5543for me that really counts as educational
@@godlyvex5543 The basic concepts and the circumference basics I think could be used to exemplify a teacher's point honestly
This level of attention to detail reminds me of that Oscar-nominated Tom and Jerry Piano Animated Short
10:04 something interesting about the integral is that it leaves behind a trail because the integral is the area under a curve
I didn’t even notice that. Yeah that’s so much cooler.
Good point, another thing I hadn't realized but makes sense in hindsight.
@@gallium-gonzollium 3 equal equal equal equal D
@@davidarvingumazon50248 year old trying to look cool in front of a genuine mathematician
@@pixelgamer6199 ...not quite.
THE MATH LORE
0:07 The simplest way to start -- 1 is given
axiomatically as the first natural number (though in
some Analysis texts, they state first that 0 is a natural
number)
0:13 Equality -- First relationship between two objects
you learn in a math class.
0:19 Addition -- First of the four fundamental
arithmetic operations.
0:27 Repeated addition of 1s, which is how we define
the rest of the naturals in set theory; also a
foreshadowing for multiplication.
0:49 Addition with numbers other than 1, which can be
defined using what we know with adding 1s. (proof
omitted)
1:23 Subtraction -- Second of the four arithmetic
operations.
1:34 Our first negative number! Which can also be
expressed as e^(i*pi), a result of extending the domain
of the Taylor series for e^x (\sum x^n/n!) to the complex
numbers.
1:49 e^(i*pi) multiplying itself by i, which opens a door
to the... imaginary realm? Also alludes to the fact that
Orange is actually in the real realm. How can TSC get to
the quantity again now?
2:12 Repeated subtraction of 1s, similar to what was
done with the naturals.
2:16 Negative times a negative gives positive.
2:24 Multiplication, and an interpretation of it by
repeated addition or any operation.
2:27 Commutative property of multiplication, and the
factors of 12.
2:35 Division, the final arithmetic operation; also very
nice to show that - and / are as related to each other as
+ and x!
2:37 Division as counting the number of repeated
subtractions to zero.
2:49 Division by zero and why it doesn't make sense.
Surprised that TSC didn't create a black hole out of that.
3:04 Exponentiation as repeated multiplication.
3:15 How higher exponents corresponds to geometric
dimension.
3:29 Anything non-zero to the zeroth power is 1.
3:31 Negative exponents! And how it relates to
fractions and division.
3:37 Fractional exponents and square roots! We're
getting closer now..
3:43 Decimal expansion of irrational numbers (like
sqrt(2) is irregular. (l avoid saying "infinite" since
technically every real number has an infinite decimal
expansion...)
3:49 sqrt(-1) gives the imaginary number i, which is
first defined by the property i^2 = -1.
3:57 Adding and multiplying complex numbers works
according to what we know.
4:00 i^3 is -i, which of course gives us i*e^(i*pi)!
4:14 Refer to 3:49
4:16 Euler's formula withx= pi! The formula can be
shown by rearranging the Taylor series for e^x.
4:20 Small detail: Getting hit by the negative sign
changes TSC's direction, another allusion to the
complex plane!
4:22 e^(i*pi) to e^0 corresponds to the motion along
the unit circle on the complex plane.
4:44 The +1/-1 "saber" hit each other to give out "0"
sparks.
4:49 -4 saber hits +1 saber to change to -3, etc.
4:53 2+2 crossbow fires out 4 arrows.
4:55 4 arrow hits the division sign, aligning with pi to
give e^(i*pi/4), propelling it pi/4 radians round the unit
circle.
5:06 TSC propelling himself by multiplying i, rotating
pi radians around the unit circle.
5:18 TSC's discovery of the complex plane (finally!)
5:21 The imaginary axis; 5:28 the real axis.
5:33 The unit circle in its barest form.
5:38 2*pi radians in a circle.
5:46 How the radian is defined -- the angle in a unit
circle spanning an arc of length 1.
5:58 r*theta -- the formula for the length of an arc with
angle theta in a circle with radius r.
6:34 Fora unit circle, theta /r is simply the angle.
6:38 Halfway around the circle is exactly pi radians.
6:49 How the sine and cosine functions relate to the
anticlockwise rotation around the unit circle -- sin(x)
equals the y-coordinate, cos(x) equals to the
K-coordinate.
7:09 Rotation of sin(x) allows for visualization of the
displacement between sin(x) and cos(x).
7:18 Refer to 4:16
7:28 Changing the exponent by multiples of pi to
propel itself in various directions.
7:34 A new form!? The Taylor series of e^x with x=i*pi.
Now it's got infinite ammo!? Also like that the ammo
leaves the decimal expansion of each of the terms as
its ballistic markings.
7:49 The volume of a cylinder with area pi r^2 and
height 8.
7:53 An exercise for the reader (haha)
8:03 Refer to 4:20
8:25 cos(x) and sin(x) in terms of e^(ix)
8:33 This part +de net tnderstand, nfertunately... TSC
creating a "function" gun f(x) =9tan(pi*x), so that
shooting at e^(i*pi) results in f(e^(i*pi))= f(-1) = 0.
(Thanks to @anerdwithaswitch9686 for the explanation
- it was the only interpretation that made sense to me;
still cannot explain the arrow though, but this is
probably sufficient enough for this haha)
9:03 Refer to 5:06
9:38 The "function" gun, now 'evaluating" at infinity,
expands the real space (which is a vector space) by
increasing one dimension each time, i.e. the span of the
real space expands to R^2, R^3, etc.
9:48 logl(1-i)/(1+i)) = -i*pi/2, and multiplying by 2i^2 =
-2 gives i*pi again.
9:58 Blocking the "infinity" beam by shortening the
intervals and taking the limit, not quite the exact
definition of the Riemann integral but close enough fo
this lol
10:17 Translating the circle by 9i, moving it up the
imaginary axis
10:36 The "displacement" beam strikes again! Refer to
7:09
11:26 Now you're in the imaginary realm.
12:16 "How do I get out of here?"
12:28 Den't quite get this-One... Says "exit" with t being
just a half-hidden pi (thanks @user-or5yo4gz9r for that)
13:03 n! in the denominator expands to the gamma
function, a common extension of the factorial function
to non-integers.
13:05 Substitution of the iterator from n to 2n,
changing the expression of the summands. The
summand is the formula for the volume of the
n-dimensional hypersphere with radius 1. (Thanks
@brycethurston3569 for the heads-up; you were close
in your description!)
13:32 Zeta (most known as part of the Zeta function in
Analysis) joins in, along with Phi (the golden ratio) and
Delta (commonly used to represent a small quantity in
Analysis)
13:46 Love it - Aleph (most known as part of
Aleph-null, representing the smallest infinity) looming in
the background.
Welp that's it! In my eyes anyway. Anything I missed?
The nth Edit: Thanks to the comment section for your
support! It definitely helps being a math major to be
able to write this out of passion. Do keep the
suggestions coming as I refine the descriptions!
Comment credit goes to @cykwan8534
😮
🤓
@@starsyt3164 “you call me a nerd, therefore I am smarter then you” 🤓
@@NySx_lol bro realize its a joke reply that your serious onto
@@starsyt3164 that reply was a joke too…
It’s insane that this animation about math is not only flashy, but also makes sense! Props to Alan Becker’s team for making this animation, and to you for giving an in-depth analysis!
Imagine this is like a game, where you discover maths and the dialogue explain to you endlessly
This is real. Math is real.
@@PSIChrisMath is not real. It's just paints on paper
@@vAR1ety_taken is language real?
@@PSIChris As math, language exists for communication
@@vAR1ety_taken Is logic real? Do you think that logic exists?
Math is essentially logic.
If you think logic exists, then it is real; then math is real.
Math isn't something tangible, it exists as an abstract concept. It exists anyway, so it is real.
While I don't like maths all that much, I used to and this brings a smile to my face. This is amazing.
they do it very often, animators, storyboard artists, etc are overworked by such a high demanding industry
@@NO_ir777 if you mean the Alan Becker channel, I agree with you, their animations are always top-notch!
@@NO_ir777overworked
Ok syg tq cikgunanti tolong bagi tahufaris zafran saya datang
I think we don't like how it is teached, or how it effects on world in real-time. Video games does that that's why people prefer that then plain maths
This reminded me of why I started to like math in school, before college ruined it. Feels nostalgic.
Grade's 1-3: You Said It's Ez
Grade's 4-6: It's Getting Harder Now Like My Vitamin D💀
Junior High: There Are Gonna Be More Canon Events
Senior High: You Better Read And Study Or Else...
Before College: SUMMER BRAKE B****ES!!!
During College: See You In The Next 4 Years P.S. Study Hard, No Phone, No Sleep Etc.
After College: Time To Find A Job...
Interview: We Don't Talk Abt That...
The Job: It Depends But You Gonna Work Your Back, Eyes, Hands, Legs, Feet, Etc. For 20 Years 💀
Retirement: You Can Now Rest But For How Long?...
as someone who hated doing math but loved learning the concepts and what math can do, this video is amazing; visuals are so important for learning and being able to see it in form helped me learn what I couldn’t in class. Your analysis really helps!!
0:27 I think you should’ve added the fact that the “motion blur/blending/in-between” frames actually have an equals sign! I find that really neat and fascinating, because they took the 1 = 1 concept and smudged it in with animation!
Oh i never noticed that-
I thought its just like playing with clay, things stretch like this before separating TwT
Yeah I noticed that, there's so many hidden cool things in this man, like this is actually amazing. It's already blowing up, but I can't wait to see this blow up even more
Only 350k views! This deserves 10 million at least...
@@user-xw4mu6nz4tGAINED 5K IN 5 MINS
This is stolen. This animation make Alan Becker
5:04 in this case, TSC Is considered as X, since he is not a number, the "math dimension" has to do something with him if he include himself in an equation of sort, so TSC is X, making X rotate 90° on the axis, so watever his position was (if x was a point on the axis), it is rotated by i
Yeah, that makes sense.
Oh yeah that makes sense. My theory was since he was a drawing made in Adobe Flash/Animate, which is a vector based drawing program, that he was a collection of bezier points that have numerical values that can be manipulated with the math in this dimension.
Yours make just as much sense and is easier to understand though.
@@AstarasCreatorI was thinking something similar, they are eventually tied to the code in some way or another, in fact, when TSC first appeared he was in the files, which my amateur brain can only assume boils down to a form of code.
12:25 Well, the fact that TSC was able to get X from his pocket to spell out "exit"..
@@Aftonny i think that was a multiplication sign actually
As a physician who loves physics and maths, I absolutely love this gem of a masterpiece ❤️
Honestly I was scared looking at all this without an explanation, fearing I forgot “how to math” but once I saw this I understood I had an understanding of the math because I recognized it, I’m filled with calm now that I can understand this level of math, thank you?
I knew that there was a lot of math in this video that was going directly over my head, but I trusted the animator to have done their research.
I'm glad to see that I was correct.
I'll have to send this to some of my engineer friends and see what they think.
Actually, according to the comment he pinned on the original video, Alan Becker's lead animator was the math nerd behind that, so yeah he was able to do all of this.
@@user-38rufhoerh3id His name is Terkoiz and it's revealed in the description below.
@@ryukokanami7645 Oh thanks. Didn't know that before you told me
You have managed to condense trigonometry, algebra, introduction to calculus, and all the fundamentals required for those subjects within a single animated video with an entertaining plot of 14 minutes. Outstanding work. Definitely will be sharing this as a reference for anyone I end up teaching some math to.
To be crystal clear, I made a criticism and review on Alan Becker’s latest video. You can find the video in the desc. Reason why I am saying this is that I don’t want to take credit for an animation I didn’t make, it was simply an analysis I added over the top.
@@gallium-gonzollium yeah in hindsight i realize that it was one of Alan's animations so I feel sheepish over that. Still, its noteworthy that you managed to find the mathematical principles to back it up which still falls in line with what i said before minus the video animation.
@@gallium-gonzollium I always love someone with integrity👏.. Great work in the explanations by the way.
@@gallium-gonzollium 3 equal equal equal equal D
It is not even his video
Python with Prosper also covered this animation frame by frame and with some historical explanation. The effort being put into the animation and analysis is insane.
8:51 got me dead 😂 " someone touched that radius again"
Of all the analysis videos I've seen on this animation so far, this one is definitely the best
the video does not belong to him, he simply stole it from the original artist to gain views
@@mapelli547 Care to tell me who the original is then?
@@infernianthedragoon6210 Alan Becker, but i Just misunderstood things and it's not Just a resposted video, sorry ;w;
@@Nubbdz.v2 yeah, sorry about that
this is the result of not paying attention to things😅
That's a really good video! It explained everything in a good way, and was the first one that came in the recommendations that actually says something smart about the math. As a big math fan, I learned today some new stuff. The Tailor series, the small integral references etc. were all incredibly helpful. Thanks for the video!
This explanation was so incredibly made, I'm just here for when it blows up
A Complete Over-Analysis of Animation Vs. Math
Es de Alan becker el vídeo
*Taylor. I would know, it's my first name. No offense, of course, and I know that the “Taylor” of the Taylor series is a last name, but still.
yreeeees
This definitely helped me understand some of the math I didn't know in this, still a lot I don't know, looking forward to learning that and understanding the rest of this beautiful animation made by Alan and spectacularly analyzed by you!
Thank you!!!!! I’ve been waiting for someone to do this! ❤
I loved the Aleph at the end.
I have dyscalculia but love the concepts of math. So frustrating!
It was so nice to see all this laid out like it was and I was just hoping someone would label all the different functions and formulas!
10:32 had me stumped for a while, but I think the interpretation is that he's feeding every point along the circumference of the circle (sinx + cosx) into the tan function simultaneously, so every point along the circumference of the circle is emitting the tan death ray at once
then it wouldn't be confined to a circle, it would spread to half the screen, like the tan function did
then it wouldn't be confined to a circle, it would spread to half the screen, like the tan function did
I think if you remember earlier I the video, when the circle was smaller, the "amplitude" of the resulting wave graph was equal to the diameter of the circle it was mapped from, and bigger amplitude = more power.
@@aguyontheinternet8436the circle acts like a border, e^i 𝝿 used the circle to bring tsc near it, and while tsc was using the tan function + infinity the wave wasn’t crossing the circle, it collided with it, creating the span thingy, basically, the circle restricts the wave in some form, and that’s why it didn’t fill up half of the screen, also, by the animation’s logic, that would have completely broken e^i 𝝿’s realm, which didn’t and wouldn’t have happened
also when tsc brought out the tan function, it didn’t even have the infinity, which is the part which makes it fill up half of the screen
Everything Alan Becker touches is given full respect of the concept
I watched this and was like "Well, here's clearly copying Alan Becker, can't wait to see the comments of people complaining"
Kept watching and was like "Aight, you get a pass."
@@user-xw4mu6nz4tcopying how? He's breaking dow the video
@@muh.suudcandra5231 the guy was high
12:59 - I'm not sure if it's intentionally, but when e is stood next to the circle and beckoning TSC to enter, the "iπ" part overlaps with the circle and looks like it says "in", which is where it wants TSC to go.
A freaking god
Thank you for this! I loved the original video but knowing more of the context behind it is great
Now when it's explained like this, i would love to have a game that makes us use maths like they did in the animation. Learning maths like that would have been way more fun!
The video really is just “what if Math could also be a military grade weapon?”
@@ThaCataBoiLMAO
@@ThaCataBoi E=mc²
@thacataboithefurret4038 It already is.
N U K E
If u were to make it vr and then use it in an actual school math lesson, it would be everybody's favourite lesson
You sir, are a hero, spreading our word of math to the world. Goddamn, now everyone can appreciate the beauty of math :)
This is Allen Baker's video
@@theyeetfamily2668 No, I know it's Alan's video (and I love his AvA and AvM series), but a lot of the math details that are in the Animation vs Math video can happen in 1 second - there's been a few times where I had to rewind just to see a tiny detail in the weapons that either e^(i*π) or TSC uses (that includes the pi bombs, the sigma sum machine gun etc).
And lots of people sadly wouldn't understand why a lot of the attacks and movesets in Alan's video are the way they are, which is why this video is great, because it explains nearly all of them.
more things to note and perhaps clarify,
4:22 graphically, using a negative sign on the x coordinate of a point in space flips it about the y-axis. Here, it flips TSC around. This happens again at 8:03 but relative to the graph's (0,0).
6:01 θ and r are polar coordinates. Where θ is a phase and r is a magnitude. The equation θr equals the arclength the dot travels from a reference direction.
7:04 the highlighted area is equal to the area of the unit circle. This becomes more significant at 10:38, when it projects into an area of effect.
7:30 subtraction of radians when depicted in the complex plane results in a clockwise rotation, which is the direction that the slash arcs travel.
7:45 The formulation for this is a little confusing. 2πr is the equation for circumference, while πr² is the equation for a circle's area. The way TSC forms his shield suggests that his shield has a circumference of 4, and an area of 4π, which isn't possible. A circle with an area of 4π has a radius of 2, and the circumference of a circle with a radius of 2 is 4π, not 4. (But interestingly enough, a circle with a radius of 2 has the same circumference and area.)
8:26 Personally, I would depict e^(-iπ) as cos(π) - i*sin(π) because that negative symbol bears a lot of significance when working with signals. Sine and cosine have this weird relationship with negative symbols. cos(x) = cos(-x), but sin(x) ≠ sin(-x). Instead, sin(x) = -sin(-x).
4:34 I believe this is mostly a velocity thing where instead of TSC’s speed Accelerating by let’s say 1.2units(or Meters)/second, by adding a Multiplication Symbol to their legs, TSC’s Acceleration is now x1.2ups instead of +1.2ups.
7:26 This is fun because the Number just normally clashes with the Arclength/Radii, unlike the Number Sword Clashing Earlier. The Radius Length is a defined term, and therefore cannot be “deducted” or other similar variables would also have to adjust to this truth. However, the Arclength(of r=1), is as strong as a 1 +/- sword, and will be deflected by a 2 or higher.
note at 8:52 "what a traitor"
@@dacomplex1Yuhanhan.hanna-Xia those damn e^i(pi)’s….
100th like! :D
3:16
power is repeated multiplication (which itself is repeated addition)
5:05
the bow that TSC uses is actually just '2x2=' oriented differently (idk how to explain it), which is why the projectile is '4' (answer)
It is orientated like a crossbow, from 2 2’s and a multiply sign.
@@gallium-gonzollium if it were to be a crossbow, then it would be shaped 'horizontally' more
also, you can in theory calculate TSC's 'number' by using pixel measurements
you look at what the length of 'i' is, then you compare that to TSC's normal pose, (i think TSC's length is 2i), now that you have TSC's length, you can use it as a glorified ruler to calculate how much i's TSC has gone upwards, then just divide the 'height' by i and you get TSC's 'number'
@@hanchen267it's a bow, not a crossbow
@@DatBoi_TheGudBIAS it's technically a "cross"bow
@@master_yugen7278 ba dum tss
0:08 Everything starts with 1
0:15 a=a
0:18 Addition discovered
0:28 You can add as many numbers as you want
0:33 2-digit numbers discovered
0:45 2 = (1+1)
0:48 You can add any number
0:58 3-digit numbers discovered
1:24 Subtraction discovered
1:35 Negative numbers discovered
1:39 -1 = e^i(pi)
2:05 Negative numbers are unique too
2:23 Multiplication discovered
2:35 Division discovered
2:48 a ÷ 0 = undefined
3:03 Square numbers discovered
3:17 a³ = area of cube with side length a
3:29 a⁰ = 1
3:30 a^-1 = 1/a
3:37 a^(1÷2) = sqrt(a)
3:43 sqrt(2) is irrational
3:50 sqrt(-1) = i
3:57 i + i = 2i
3:59 -1 = i × i
4:46 -1 + 1 = 0 (Look at the swords)
4:53 2 × 2 = 4
part 2 at 5 likes
Best explanation on the video so far, a lot of others I found missed more intricate details and the ending concepts
so glad this is here! i'm really happy with how much i was able to recognize the first time (aleph, complex plane, ∞-dimensional ball) but the slightly more in depth explanations of the sum figure and the integral staff helped a lot!
that will tecnically mean that the ''real world''or the computer at least,it is a infinite dimensional structure,or even beyond the cardinalities(at least the aleph)
8:25 I think you might have put sin(x) and cos(x) the wrong way round? Still the best explanation of this I’ve seen, with so many easy-to-miss details!
Yep, I did. Thanks for the correction!
I think there's also a mistake in the original video: when isin(π) is expanded it has 2i in the denominator, but it should be 2 (the i is eliminated). Technically both identities are correct because the numerator equals zero, but still...
1. **Coefficient**:
• Coefficient is like the number that hangs out 😎 in FRONT of a Variable ❎ in a math expression.
• It’s like the price tag 💲🏷️ on an item in a store - it tells you HOW MUCH of the Variable you have.
(For example, in the Expression 3x, 3 is the Coefficient of x.)
2. **Base**:
• Base is like the foundation of a math operation, especially in Exponentials and Logarithms.
• It’s like the bottom of a building 🧱 - everything else rests on top of it.
(In the Expression 2^3, 2 is the BASE.)
3. **Exponent**:
• Exponent is like the little number floating above ☁️ the base, telling you how many times to MULTIPLY✖️the base by itself.
• It’s like the power that makes things Grow ⬆️ or Shrink ⬇️ in Math.
(In the Expression 2^3, 3 is the Exponent.)
4. **Variable**:
• Variable is like the mystery number in a math problem that can CHANGE or VARY 📈📉.
• It’s like a box that can hold different things depending on the situation.
(In the Expression 3x + 5, x is the Variable.)
5. **Constant**:
• Constant is like the unchanging part of a math expression, always staying the SAME ✅.
• It’s like the fixed number that NEVER MOVES in a game.
(In the Expression 3x + 5, 5 is the Constant.)
6. **Monomial**:
• Monomial is like a simple math expression with just ONE term, like a single ingredient in a recipe.
• It’s like a SOLO player🧍♂️in a game, doing its OWN THING without any partners ❌👫.
(For example, 3x or 5y are Monomials.)
7. **Polynomial**:
• Polynomial is like a more complex math expression with MULTIPLE TERMS added or subtracted together.
• It’s like a team of players working together to solve a problem 👫🧑🤝🧑.
(For example, 3x + 5 or 2x^2 - 3x + 1 are Polynomials.)
8. **Relationships and Differences**:
• Coefficients, Constants, Variables, and Exponents are ALL PARTS of Expressions, while Base is specifically related to Exponentiation.
• Monomials are a specific type of Polynomial with just ONE TERM, while Polynomials can have MULTIPLE TERMS.
• Coefficients and Constants are similar in that they’re BOTH FIXED numbers, but Coefficients are associated with Variables while Constants stand aline.
(Tips and Tricks:
• Remember the “C” connection: Coefficient, Constant, and Constant Base (in Exponentials).
• Think of Variables as the “variable villains” that can change their value anytime!
• Monomials are like “mono” (single) and Polynomials are like “poly” (multiple) - simple and complex, respectively.)
In summary, these Math Terms are like building blocks that help us understand and manipulate expressions and equations. They each have their own role to play, but together, they create the rich tapestry of mathematical concepts and problems we encounter.
There is still a lot of stuff with which I struggle in here (everything that involves the radian gives me a headache) but there are some stuff that I finally begin to grasp when given visual form. Alan truly outdid himself with this one and your explainations are very welcome.
I still can't believe that is literally a lot of math explained just on one video!
5:04 I think he uses i with his arrow to make the translation upward (2x2xi) but since he was running so it makes an arc. That also explains why he can't sustain his elevation like e and falls down right after.
Please make more of these, I know you didn't animate this but it adds so much to the video, really cool
I was thinking the video was going to explain more the maths, but its very cool like this !
My question is how TSC learnt math so fast, enough to use things people who have been studied for years cant remember
TSC is the smartest animation drawn by Alan Becker, change my mind
For a stick figure with it's own consciousness made by it's creator, it definitely learns fast.
Maybe it's an effect of "things" gaining it's own consciousness and able to learn fast.
Kinda like how in stick figure vs minecraft, it was able to adapt real quick.
TSC is crazy smart.
@@ZliarxTSC has the power of very fast machine learning
I think it's because he watched math as a weaponry, not some boring test paper. And we know TSC is a fighter.
10:00 One point i think you missed is right after the integral appears, there's some expressions that appear on the left and right of it. The integral is 5 separate integrals, which are in the exponents of the e^...i on the left of the integral, each of the top 3 evaluate to π/2, the fourth goes to 3π/8, and the last to π/3, meaning that each of the five expressions evaluate to e^iπ. Also at 8:30 i didn't realize why the tan function was cancelling out the e^iπ since I didn't see the π that was multiplying in the tan function, good job spotting that. And at 13:04, while i knew the formula for the volume, It just didn't connect for me, so overall great job of explaining it.
Alan Becker and his team are Genius 🤯🤯
this is literally the best analysis of it I've seen so far
9:59 this my favorite part of you commentary, really nails what happened
"Handle". Literally
This was exactly the mathematical breakdown I was looking for. Thank you so much for posting it!
1. **Sine (sin)**:
Imagine you’re on a roller coaster going up and down.
The sine function tells you how high or low you are at any point on the ride.🎢
In a triangle, if you divide the length of the side opposite an angle by the length of the hypotenuse (the longest side), you get the sine of that angle. It helps us understand how steep or gentle a slope is.
(For remembering, think of “Sine” as “SLIDE” - it’s like sliding up and down the roller coaster.)
2. **Cosine (cos)**:
Cosine is like a buddy to sine. It tells you how far you are from the starting point on the roller coaster. 📏🎢
In a triangle, if you divide the length of the side adjacent to an angle by the length of the hypotenuse, you get the cosine of that angle. It’s like measuring how far you are from the starting line.
(For remembering, think of “cosine” as “COZY” - it’s like getting cozy with the starting point.)
3. **Tangent (tan)**:
Tangent is like a secret agent that loves to climb. 🧗
In a triangle, if you divide the length of the side opposite an angle by the length of the side adjacent to that angle, you get the tangent of that angle.
It helps us understand how steep a slope is compared to how far you move horizontally.
(For remembering, think of “Tangent” as “TANGLED/TRIPPED” - it’s like getting tangled up and getting tripped down in how steep the climb is.)
These functions are super important because they help us solve all kinds of problems involving triangles, like figuring out the height of a mountain 🏔️ from a distance or the angle a rocket 🚀 needs to launch into space.
And guess what? They’re not just for triangles! They’re like Swiss army knives of math - you can use them in all sorts of shapes and situations to figure out Angles and Distances. 📏📐
So next time you’re on a roller coaster or climbing a hill, remember, Sine, Cosine, and Tangent are there to help you understand the ride!
1. **Cosecant, Secant, and Cotangent**:
• Cosecant, Secant, and Cotangent are like cousins of Sine, Cosine, and Tangent. They’re related but have their own unique roles.
• Cosecant is the reciprocal of Sine, Secant is the reciprocal of Cosine, and Cotangent is the reciprocal of Tangent.
2. **Relation to Sine, Cosine, and Tangent**:
• SINE, COSINE, and TANGENT are like the original trio of trigonometric functions, representing the ratios of different sides of a right triangle.
• Cosecant, Secant, and Cotangent are like their mirror images🪞📐, showing the inverses or reciprocals of those ratios.
3. **Usage in a Triangle**:
• In a right triangle, Sine is the ratio of the side opposite an angle to the hypotenuse, Cosine is the ratio of the side adjacent to an angle to the hypotenuse, and Tangent is the ratio of the side opposite an angle to the side adjacent to the angle.
• Cosecant, Secant, and Cotangent can be thought of as the “OPPOSITE” reverse ratios: Cosecant is the ratio of the hypotenuse to the side opposite an angle (Opposite of Sine), Secant is the ratio of the hypotenuse to the side adjacent to an angle (Opposite of Cosine), and Cotangent is the ratio of the side adjacent to an angle to the side opposite the angle (Opposite of Tangent).
4. **Importance and Purpose**:
• Trigonometric functions are crucial for understanding and solving problems involving angles, triangles, and periodic phenomena. 🔺
• They’re used in Geometry, Physics, Engineering, and many other fields to model and analyze real-world situations involving Waves, Oscillations, and Rotations 🌊🔉🔁.
• Cosecant, Secant, and Cotangent help us understand different aspects of right triangles and trigonometric relationships, providing a more complete picture of the geometry involved.
(**Tips and Tricks**:
• Remember the RECIPROCAL RELATIONSHIP: Cosecant is the reciprocal of Sine, Secant is the reciprocal of Cosine, and Cotangent is the reciprocal of Tangent.
• Think of them as the “OPPOSITE” 🪞📐 functions to Sine, Cosine, and Tangent, providing additional insights into the geometry of triangles.🔺)
In summary, Cosecant, Secant, and Cotangent are like the “other side” of Trigonometry, providing complementary information to Sine, Cosine, and Tangent.
Together, they help us understand and solve problems involving triangles, angles, and periodic phenomena, making them essential tools for mathematicians, scientists, and engineers.
Just like pieces of a puzzle, each trigonometric function fits together to create a complete picture of the geometry of the world around us!
You are the best explaining everything in this video and helping me understand this!
I still remember calling math an easy subject when I was 1st, 2nd grade etc. But oh boy! Match is much harder than I thought it would be.
I personally thought the reason why the circle increases is because more E^i[pi] enters it, thus 'adding' to the radius. I only noticed with multiple watches, but as more enter the circle, it increases in size. I don't think any of them are actually touching the equation-just that their mere presence is adding into it!
I think so too!
At 8:37,you could see the radius was lying around. Later on at 8:42 the eulers were taking them. They might've used that to change the radius
Then.... Shouldn't it have been reduced as e^iπ=-1?
@@DimkaTsvremember at the end e produced 4 i's and made a 1 out of it? Could use that to add to the radius... Or just two e^iπ 's multiplied to each other...
@@jonathan_herr √(-1)^4=1
It showed that you cannot just stack "i" to travel dimensions as each other will cancel first.
1. **Reciprocals**:
• Reciprocals are like the mirror image🪞or opposite of a number, but FLIPPED UPSIDE DOWN 🙃 in a fraction.
• If you have a number like 2, its RECIPROCAL is 1/2. It’s like turning the number UPSIDE DOWN 🙃 and making it a FRACTION 1️⃣/2️⃣.
• Reciprocals are like partners in a dance 🕺💃 - they’re different, but they fit together perfectly ✨.
2. **Usage in Math**:
• Reciprocals are used in math to solve equations, simplify expressions, and perform operations like division.
• For example, when you divide a number by its reciprocal, you get 1. It’s like dividing a pizza 🍕 into equal parts - you get one whole pizza.
3. **Usage in the Real World**:
• Reciprocals are used in many real-world situations, like when you’re cooking and need to adjust a recipe. 🎂 If a recipe calls for 1/3 cup of flour and you want to make THREE TIMES 3️⃣✖️ as much, you’d use the RECIPROCAL (3/1 or just 3) to multiply the amount of flour needed.
• They’re also used in measurements, like converting between different units of measurement. For example, if you know that 1 mile is equal to 1.609 kilometers, you can find the reciprocal (1/1.609) to convert kilometers to miles.
4. **Tips and Tricks**:
• Think of reciprocals as the opposite numbers that complete each other, like puzzle pieces fitting together.
• Remember that when you multiply a number by its Reciprocal, you get 1. It’s like UNDOING the operation you started with.
• Reciprocals are like friends who always have each other’s backs - they’re different but always there to help out when needed.
(In summary, reciprocals are like the FLIP SIDE of numbers 🪞, essential for solving Equations, simplifying Expressions, and performing Operations in math and the real world.
Whether you’re dividing pizzas 🍕 or converting measurements ⚖️📏, understanding Reciprocals helps you navigate the world of numbers with ease. Just remember, they’re like the Yin to the Yang ☯️ of Mathematics, always ready to lend a helping hand!)
Let’s simplify these Mathematical Concepts for you:
1. **Calculus**:
• Calculus is like a superpower in math that helps us understand how things change and move.
• Imagine you’re driving a car and want to know how fast you’re going at any given moment. Calculus helps you figure that out by looking at how your speed changes over time.
2. **Derivatives**:
• Derivatives are like the magic glasses of calculus that let us see how a function changes at a specific point.
• Picture a roller coaster - the slope of the track at any point tells you how steep the ride is. Derivatives do the same thing for math functions, showing us the slope or rate of change.
3. **Anti-Derivatives/Integrals**:
• Integrals are like the reverse of derivatives. They help us find the total amount or area under a curve.
• Imagine you’re filling a pool with water. Integrals help you calculate how much water you’ve added by looking at the rate of flow over time.
4. **Number Theory**:
• Number theory is like a treasure hunt in math, where we explore the properties and relationships of whole numbers.
• Think of it as solving puzzles with numbers, like finding prime numbers or figuring out patterns in sequences.
5. **Euclidean**:
• Euclidean geometry is like the basic building blocks of geometry, dealing with points, lines, and shapes in flat space.
• It’s like playing with blocks and building structures in a 2D world, where everything follows simple rules.
6. **Topology**:
• Topology is like the study of shapes and spaces, but with a twist - it’s more interested in the properties that don’t change when you stretch or twist them.
• Think of it as studying rubber bands and playdough, seeing how they can be squished and pulled without changing their essential properties.
7. **Game Theory**:
• Game theory is like playing chess but with math. It’s all about making strategic decisions in competitive situations.
• Imagine you’re playing a game of rock-paper-scissors. Game theory helps you figure out the best strategy to win, even against tough opponents.
8. **Linear Algebra**:
• Linear algebra is like the superhero of math that helps us solve systems of equations and understand transformations in space.
• Picture a Rubik’s cube - linear algebra helps you figure out how to twist and turn the cube to solve it, using matrices and vectors.
(Tips and Tricks:
• Think of Calculus as the detective, derivatives and integrals as its tools for understanding motion and change.
• Remember Number Theory as the treasure map leading you to hidden mathematical gems.
• Visualize Euclidean Geometry as building blocks and Topology as rubber bands and playdough.
• Picture Game Theory as a strategy guide for winning games, and Linear Algebra as a toolkit for solving puzzles in space.)
In summary, these mathematical concepts are like tools in a toolbox, each serving a different purpose but working together to solve problems and unlock the mysteries of the universe. Whether you’re exploring the properties of numbers, analyzing strategic decisions, or understanding shapes and spaces, mathematics is always there to guide you on your journey of discovery!
Seriously somebody better make a game based on this animation as I'm pretty sure it can be a real entertaining way to teach kids of any age Mathematics how i know I'm pretty sure mathematicians and math teachers would agree to the idea
I'm a computer programmer, maybe I can try that sometime.
This would be a sick VR game w/o a doubt
But I mostly do front end...
@@ZerickKilgoreadd it with a deep story like this:
A not ordinary human suddenly wake up in a destroyed laboratory
He went outside to see the world real dead, no signs of life, ruins of everything humans have built
No more atmosphere
This male character doesn't need to breathe
He wanders around back to lab, but when he touched the number 1 written on the board, it attached to his hands
He tried to remove it but it just got divided into 2, resulting in 0.5
He's wandering what's happening
His vision starting to look some sort of not natural, seeing some settings or inventory, but it's actually just a slot of discovered math symbol, equations or formula he have seen
Because he seen number 1 and and 0.5 , his artificial vision makes his discovered slot appear on screen(his vision)
He start to walk around to calm himself and see a piece of paper
When he flipped it, he sees some basic math symbol and numbers:
+, -, ÷, × and numbers of 1 to 9
And it automatically collected by his "discovered slot"
Now it's up to you what the character will encounter and discover in his journey
But I would like the ending to be him floating in space discovering he is a equation, a numbers. He is the math.
He suddenly see a dark red light approaching, and consuming dead planets and blackholes while he's floating, his last solution if he can do anything because he is the math
Maybe he can restart the universe. So he rush to make the equation of making or restarting the universe.
It's for the player to think the equation for restarting the universe. Any equation, symbol or number the player typed will cause 3 outcomes:
1. Equation didn't work. So Game Over
2. Instead of restarting the same universe, it created a different universe.
3. If the equation got right, the universe will restart and will start showing the character's background story.
Edited version:
A man wakes up in a destroyed lab and finds out the world is completely dead. After wandering around, he goes back to the lab and the telescope catches his attention. He looked at it and saw that some sort of shockwave was approaching to planet millions of light-years away, and it was getting faster than the speed of light. He feels that he is in danger so he hurries up to save himself and suddenly sees a book filled with only half of the entirety of the math. He also discovers that he can manipulate things using math with his hands. The first thing he did is add the same object and created two objects. Fast forward, he now solves half of the math. Finds out he is the math itself, he is an experiment. Now the shockwave is very near the cluster of galaxies where the milky way galaxy is. He hurries ups to get to the point where he can make an equation to restart the universe because he knows he can manipulate anything. He's rushing to make equations until he gets the right formula. Closed his eyes and throw the equations at the approaching shockwave at the speed of light and the universe restarted.
@@johnlourencecarlos9620 That's a good idea, I'll try to remember that one.
Was completely expecting text to show up at 1:00 saying "Math sends you to the void" or something lol
Where the heck did you come from, and why are you receiving little attention???
haha yea!
I learned new things out or Alan's animation and your explanation, thank you very much!🎉❤
"The smallest cardinal infinity (hence why its so big)" you realize how insane that sounds right /pos
AVM has me in a chokehold man. And watching this video explaining the things in it just made me love it even more. Thank you so much!
As someone who took honors math classes throughout high school, the fact that recognize almost all of these mathematical concepts both amuses me and horrifies me.
This is by far one of my favorite animations of all time, because it combines two things I love: math and epic battles.
ITS stolen
@@riccardomeyer3294
aint no way
@@riccardomeyer3294from who
@@thatoneguy9582yes it is
@@hie3800Alan becker (Original)
Note that at the third appearance of Euler's Identity, when they're fighting, TSC uses the arc of the radian, which is the radius, of 1. This is why the swords cancel each other out.
This was really nice. I recognized most of the math in the animation, and at least understood what sorta math most of the rest was, but this really filled in the blanks in an understandable way, thanks!
respect for this guy for putting hard work for this so the kids can understand some stuff
ITS stolen
@@riccardomeyer3294It’s got the original link in the description, and everyone already knows about this video. It’s just an explanation of the mathematical properties within the video. This still took effort and research on gallium’s part.
@@Asterism_Desmos ok
@@riccardomeyer3294 I do want to point out that if you suspect a video being stolen, you should mention it. I was just saying that this one specifically isn’t :)
Finally someone that can explain it easier and straight to the point, great job!
you could be clearer at 7:50 that hpi*r^2 is the cylinder volume formula, so 8 units is the height
Dude that was boss. Loved it. I was happy to have already learned 99% of that stuff otherwise it would have be way harder to follow along. Still had to slow down the speed to .5 to really grasp what was happening though. made me so happy watching this.
Thank you for doing an analysis of this.
Seeing all of this makes me realise just how visually striking this animation is in terms of what it conveys, such as 8:15 and 9:57
I'm surprised how much of this I actually totally understood after just a little explanation lol. And THANK YOU, the mystery of Aleph has been itching my brain for days. Couldn't figure out how to even search for it by visuals.
Good job on going viral! you deserve it
extremely amazing the way you expresses all these
I love it that you chose this form of anaylsis with editing in text instead of stopping it every time something comes up, much better
Also releasing an analysis in less than a day, pretty impressive!
4:41 "By the power of addition, i compels you -e^i(pi) !!"
I have watched many analyses on this subject, but none of them noticed the exponential relationship with dimensional shapes like you did. Impressive stuff.
Let’s break it down these Calculator Symbols 🔢 step by step:
1. **MC, M+, M- and MR:**
• MC (Memory Clear) clears the memory in the calculator.
• M+ (Memory Plus) adds the current number on the display to the memory.
• M- (Memory Minus) subtracts the current number on the display from the memory.
• MR (Memory Recall) retrieves the number stored in memory and displays it on the screen.
Example: Let’s say you’re adding up a list of numbers on your calculator. If you want to store a number in memory, like 10, you would press “10 M+”. Then, if you want to recall that number later, you press “MR” and it will show 10 on the screen.
2. **Rad:**
• Rad switches the calculator to “radians” mode for trigonometric functions. Radians are a way to measure angles, like degrees but slightly different 📏⭕️.
Example: If you’re solving a math problem involving trigonometry in radians, you’d press “Rad” on your calculator to make sure it’s using the correct mode.
3. **Sinh, Cosh, Tanh (Hyperbolic Functions):**
• These are special functions used in mathematics, especially in calculus and geometry. They are related to exponential functions and have applications in various fields.
• Sinh (Hyperbolic Sine), Cosh (Hyperbolic Cosine), and Tanh (Hyperbolic Tangent) are used to calculate values based on hyperbolic functions.
Example: Imagine you’re studying a rocket’s trajectory 🚀. Hyperbolic functions might help you understand the rocket’s acceleration or velocity over time ⏳.
4. *X!:*
• This symbol represents factorial, which is the product of ALL positive integers up to a GIVEN NUMBER ⛓️. For example, 5 factorial (written as 5!) is 5x4x3x2x1=120.
Example: Let’s say you want to calculate how many different ways you can arrange a set of 5 books 📚 on a shelf. You’d use factorial:
5. *In:*
• This is the Logarithm function with base , where is Euler’s number, an important mathematical constant approximately equal to 2.71828.
Example: If you have a problem involving exponential growth 📈 or decay 📉, you might use the natural Logarithm function to solve it.
6. *Rand:*
• Rand generates a random number between 0 and 1. It’s useful for simulations, games, or any situation where you need randomness 🤪.
Example: If you’re playing a game that involves rolling a dice 🎲, you might use Rand to simulate the randomness of the roll.
7. *e and EE:*
• is Euler’s number, a mathematical constant approximately equal to 2.71828. It’s used in Calculus, Exponential Growth and Decay, and many other areas of mathematics.
• EE is often used on calculators to represent POWERS OF 10 in scientific notation. For example, can be written as .
Example: If you’re calculating compound interest, you might use as the base of the exponential function to represent continuous compounding 💹.
(*Tips and Tricks:*
• Memory Functions (MC, M+, M-, MR): Think of these as a calculator’s way of keeping track of numbers for you, like a little notepad 🗒️.
• Rad: Remember “Rad” as short for “Radians,” which are like a different kind of measurement for angles ⭕️📏.
• Hyperbolic Functions (Sinh, Cosh, Tanh): These are like cousins of the regular trigonometric functions, but they’re used in different situations, like when dealing with curves that look like bows or arches 🏹.
• Factorial (X!): Think of it as “multiply all the numbers from 1 up to this one.” It’s like making a big chain of multiplication⛓️.
• Natural Logarithm (In): This is like the “logarithm version” of the exponential function. It helps undo exponential growth or decay 📈📉.
• Random Number (Rand): Use it when you need to add a little bit of unpredictability to your math 🤪.
• Euler’s Number (e): Remember it’s a special number like 3.14 but even more special because it shows up all over the place in math 🧮.)
By understanding and using these symbols and functions, you can solve a wide variety of mathematical problems and even have some fun along the way!
6:22 When a circle is stretched like that, it turns into an ellipse. So, any ellipse with major and minor axis greater than or equal to the radius of a circle and be created by stretching said circle.
9:57 "Integrals can handle infinites". Bro is saying it like he's a marvel supervillain or something
This really helped me understand the math founding this animation. Thank you for your work!!!!
That's like impressively well put together.
Noone's talking about this, but in 5:53 TSC multiplies itself with the radian(or seems like it) making another copy of it impling that TSC's value is 2 in the "math dimension".
Just theory crafting over here lol
This is why we're calling it The 😊*2nd* Coming
I loved this analysis!
Detail: in this fight 7:23 stickman grab as a sword the lenght unit (1) and the "e" fights with -1 and that is 0. Then "e" transform the -1 into 2 that is the double of 1. That's why stickman it's pushed back. 2 is more than 1.
Wild, might use this to refresh myself on basic stuff before college classes start this week
WHERE'S THE VIEWS THIS IS SO GREAT
i subbed
It was only published two hours ago
i love how you could throw this into the first math video ever made and people just learn it right there
makes math so much easier
A best content always get a explanation that some people dont get it. Thanks man
Amazing. this is being added to my favorites.
This truly explains a lot about how Alan Becker is truly one of the best Number Lore creators of all time. ✊
His lead animator was the math nerd in all of this
2nd comment:
This analysis video is incredibly amazing. It made the animation more impactful knowing what it is happening and what it all means. Most of all the last part explaining what was the big thing is and that gave more impact to the animation.
10/10 analysis video
You and Alan have just made the best math tutorial video in Human history
Okay, thank you for breaking this down. Most of it's over my head, but I love how you explained everything.
That was amazing. Thanks for the analysis, I learned something from this.
Oh wow, this is a really good video! It explained everything in a good way and was the first one that came in the recommendations that actually says something smart about the math. Likewise, this is the only animation that goes past kindergarten math and involves Calculus, Trigonometry, and Complex identities. As a big math fan, I learned today some new stuff. The Tailor series, the small integral references, etc. were all incredibly helpful. Thanks for the video!
Also 13:45, I never noticed the giant Aleph 0 (Aleph Null) in the back because it was blended in the Background
I guess it is big since it is the smallest infinity among all of the infinities
There's a BIGGER infinity?
Infinity is already infinity. How is there anything bigger than that???
Math just has the "I use the stones to destroy the stones" type of energy going with it at all times.
@@ZRovas117 Well, I think it's something like, imagine having 0 and 1, the difference between 0 and 1 in decimals is infinite, because an infinite number of decimals can fit between them (you can have 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 001 or have 0.9999999999999999999999999999999999999999999999999999999999999999999999999999999) more or less towards could explain a way to have "infinity greater than infinity".
or another example:
You can have an infinite universe, but that infinite universe is a number among the infinite universes in a multiverse.
@@ZRovas117Infinity is yes still infinity, But some infinitys are smaller than other infinity’s. Considering you don’t know this enjoy your time before you enter high school.
@@ZRovas117 thinky this, there are infinite integers right? But there are also infinite real numbers, and we know there are more real numbers than integers.
@@ZRovas117 yes, there are infinity's bigger than others. Aleph null is the sum of all numbers. Since every number is contained in that number you would count things ordinally for example instead of making stuff like ∞+1=∞ you would do stuff like 1st, 2nd, 3rd... etc all the way to all the numbers past. The next "ordinal" number you would see after all the numbers is omega (its in the greek symbol). Next is omega+1 then +2 etc until its omega plus itself making it times 2. And then times 3 and 4 and all the way to omega times itself, making omega squared. next is omega cubed, omega to the 4th power and all the way to omega to the omega. then you could do omega to the omega to the omega, and till there is an infinite power tower of omega's, repeated exponentiation is called "tetration" so its omega tetrated to omega. you can keep replacing over and over but no replacement will ever reach the next infinity, an irreplaceable infinity: Aleph 1. The next ordinal number outside aleph 1 is omega 1. You can keep going doing infinite orders of magnitude from aleph 2, aleph 3, aleph 4.... aleph omega ... aleph omega 1... aleph omega omega ... aleph omega omega omega omega omega... and you can keep going to even more crazy and absurd infinities, but there will always be an infinity that will be irreplaceable from all the infinities below so ironically there won't be an end to the infinitys as you can just add more and more things to it to grow bigger and bigger
1. **N-dimension**:
Think of dimensions as different directions you can go. In our world, we have three dimensions: up-down, left-right, and forward-backward.
But in math, we can have more! N-Dimension means we’re talking about ANY number of dimensions, NOT JUST THREE. It’s like having more roads📍to travel on a map 🧭 🗺️
2. **N-d sphere**:
Imagine a ball, like a basketball. 🏀 Now, picture this ball existing in MORE than just our regular three dimensions.
An N-Dimensional sphere is like that, but with more dimensions than we can easily imagine.
It’s like trying to picture a shape that’s not just round, but also has directions we can’t see. It’s a mind-bending concept! 🫨
3. **What they do in mathematics**:
N-Dimension helps mathematicians explore and understand shapes 🏀and spaces in more complex ways.
It’s like giving them a bigger playground 🛝to play in, where they can imagine and create new things that we can’t even see in our regular three-dimensional world.
It’s crucial for studying things like Geometry, Topology, and even Physics.
4. **Real-world concepts**:
While it might be hard to imagine objects existing in more than three dimensions in our everyday lives, concepts from N-Dimension mathematics actually help us understand things like how the universe works on a fundamental level.
For example, theories in Physics, such as String Theory and Quantum Mechanics, rely on ideas from N-dimensional spaces to explain the nature of reality.
5. **What would happen if it didn’t exist**:
If N-Dimension didn’t exist, mathematicians would be limited in their ability to describe and understand many phenomena in the universe.
It’s like trying to navigate a maze with only a few paths instead of having the whole map available. Without n-dimension, our understanding of mathematics and the world around us would be much narrower.
To remember, think of N-Dimension as a magic doorway🚪✨ to worlds beyond our own, where mathematicians explore and discover new wonders. Just like exploring a new video game with endless possibilities, N-Dimension opens up endless possibilities for exploration and discovery in mathematics and beyond!
Man how much time you edit this video? This is super amazing because there's always something in this video I don't understand but you explain it very carefully
Truly good work man 👌😎👌
Took me 1h nonstop? I don’t have that much time at my computer (I am constantly away from home) so it took 2 days from start to finish :)
This video made me realise how much detail they put in ! Even the having the "bullet" make a tangent wave !
wait what when was that
@@TheProGamerMC20 8:30 :)
One other little thing at the very end: Aleph numbers aren't just infinities, but (one of them) also represents the size of the set of all numbers, which I think is why aleph is filled in the same way the complex plane was
Let’s explore the differences between Parabolas and Hyperbolas in a simple way:
1. **Parabola**:
• A Parabola is like a graceful curve ⤴️ that looks like a smile 😃 or a frown 🙁, depending on its orientation.
• It’s the shape you get when you graph a quadratic equation, like .
• Picture throwing a ball into the air 🏈- its path forms a parabola as it goes up and then comes back down.
• Parabolas have a special point called the VERTEX, where the curve changes direction. It’s like the peak of a hill 🏔️ or the bottom of a valley.
2. **Hyperbola**:
• A Hyperbola is like two mirrored curves🪞⤴️ that stretch out to infinity ♾️, forming a symmetrical shape.
• Imagine two branches of a tree 🌲 that grow apart from each other, but NEVER touch ❌.
• Hyperbolas have two SPECIAL LINES called ASYMPTOTES, which the branches get closer and closer to but never actually touch ❌. It’s like chasing after a dream that you can never quite reach.
(Differences:
• Parabolas have a SINGLE curve ⤴️, while Hyperbolas have TWO distinct branches ↩️↪️.
• Parabolas can open upwards, downwards, left, or right, while Hyperbolas stretch out horizontally or vertically.
• Parabolas have a Vertex, while Hyperbolas have Asymptotes.)
(Similarities:
• Both Parabolas and Hyperbolas are types of conic sections, which are shapes formed by SLICING a cone.
• They’re both used in mathematics to model various phenomena and in engineering to design structures like satellite dishes and reflectors.)
In summary, while both Parabolas ⤴️ and Hyperbolas ↩️↪️ are curved shapes, they have distinct characteristics that set them apart.
Parabolas are like graceful smiles or frowns 😃🙁, while Hyperbolas are like mirrored branches stretching out to infinity🪞📏♾️.
I like how when hes pulling numbers apart their still displaying logic.
Pulling one away from one has two "strings" still holding them together: an equals sign