Just to be clear, I'm not a professional 'quote maker'. I'm just an atheist teenager who greatly values his intelligence and scientific fact over any silly fiction book written 3,500 years ago. This being said, I am open to any and all criticism. 'In this moment, I am euphoric. Not because of any phony god's blessing. But because, I am enlightened by my intelligence.'"
I'm really impressed at how you harmonize the music and the movements of this movie, and maximize the charms of these functions. I can't explain my feelings well with my poor English, but thank you for your great creation with mathematics.
These are absolutely insane. I know I don't realize how in-depth these equations are because they don't teach us them in school, but I'm sure this is amazing work and deserves appreciation. Math is very beautiful, but we did not understand its dimensions
Yeah they’re really weird because they’re combinations of many different math concepts but I really want to learn how I could make stuff like this and make it be whatever I want it to look. Anyone know any resources specifically on these types of graphs?
Numberphile has done a video on ”The ”Everything”-formula”, whose graph, supposedly, has every single image fitting to a certain-sized frame, from your family portrait to Mona Lisa 😮. I don’t remember the formula, though; but a little search should produce results pretty quickly.
@@Altair4611i remember that in the 1st year of uni, we had to work with these strange looking graphs and we had to be able to draw these things. The thing i was assigned with was crazy, it had ton of bends and had only 1 axis of symmetry. The parametrisation was ugly af. and derivatives of it were a long tangled mess. Just figuring out how to split it to segments to analyze its properties took me hours. These curves are beautiful, but having to analyse them is painful. And then after hours of finding inflection points, piecing it together to get the graph is even worse. That uni wanted to destroy all of us xD. They probably did that to test our patience. Its amazing and beautiful when an app can draw the graph for you, but when doing it manually, when you get to the point where you can begin to draw the graph, you're already so mad, that you will hate the outcome, no matter how beautiful it is.
This showed me that math isnt just only one graph or one formula. Its moving, breathing and the whole picture of the formula puts together a beautiful story. They have to show that in school...
@@wwatermelon15 100% Plus, people get this idea of being good or bad at math, but math is like any other subject of study. There’s no “being good” at math. There’s just being able to understand it and work/think through questions to find the answer.
Everyone is just appreciating his maths knowledge but no one is saying a single word about his editing and animation skills... Its totally insane bro.. 🤯
He didnt animate that. The graphs are animated by themselves i.e changing the values, u too can do it with the help of some graphing calculator shit like desmos
The amount of things you can create with maths is amazing! You are trying to get maths to be one of my favourite subjects and you are currently succeeding!
Don't worry, most of mathematical beuaty and magic is not visualizable anyway. And as a mathematician, I can't immediately grasp at first sight why do most of the graphs from the first half the video look the way they do.
@@ohayougozaimasu6424 I wish it was the only thing I didn't understand tho😅 I just have this huge gap of knowledge I missed during quarantine that I should be fixing. I just feel bad for my math teacher, 'cause she puts lots of effort into teaching, but most still fail
The beauty of Curves were so fascinating 💓🤩 this shows that functions with graphs are the one of the coolest thing to see and study in Mathematics. Mathematics is Universe in itself 😎. It is now 477k Remind me When, It will be 1M 🎉.
When we draw on paper, we draw strokes that would be comparable to piecewise functions - those piecewise functions make up the shapes we see on the paper. Mathematical art, can do that too, but more often I see people plugging in equations to get those same fun shapes. When we draw stars in real life, it isn’t because we have a complex parametric equation memorized- we draw vertex to vertex. Simplicity at it’s finest. I like mathematical art in this form too, because it inspires people, and because we can discover new formal geometric gadgets to develop new maths in the future. I just wanted to write that comparison.
Any time you get a sine or cosine function, the graph traces something periodic, and overlaying different periodic frequencies gets you these super cool patterns! Good job! Subscribed!
For some feedback i'd suggest that the equation for each graph be always shown instead of appearing and dissapearing suddenly for only a few seconds or at least show them for a bit longer
Beautiful, the capacity of representation of those simple things shows just how boundless those simple things can be, I feel this applies to life as well, with all the moments that make it up.
For those who don't know , here he use parameter curve and it'is different from a function, because in the definition of a function, a function has only on image for each inverse image unlike the parameters curve where inverse image can have multiple images.
Formally, they're all isomorphic to regular functions ( ℝ² →{0,1} ). The vertical line test thingy is useless past high school, pretty much all of mathematics is functions (until you learn what a morphism is)
Penultimate graph is something I’ve been looking for for a long long time, as that graph is normally graphed on a complex plane and it’s very useful for modeling two magnetic fields interacting, thank you random video, you get a like
How do you graph it in the complex plane? As a student of physics myself the mathematical equations for potential lines interests me also. Care to share where you got this information from?
This looks also like the electric field between two opposite charges. It is relatively easy to find a closed form for a single line of those, but finding a closed form for many of them, "equally spaced" like the one in the video seems a nice challenge!
Actually it’s quite easy in the complex plane, just use geogebra and do the equation tan(xi), many other trigonometric functions give a similar result, and I actually originally recognized it when I first made it I knew it looked like an electric field
Need one addtional disclaimer: t=θ I can accept r, x and y not being described because it's usually understood that the x and y are of cartesian coordinates and r for distance to origin, but most people use θ or Φ for angle.
One equation I'd like to mention is y=xsin(lnx), which essentially looks self similar at all magnitudes. Add a couple constants for spice. Found this one myself.
@@Nicomv-eu3pd if you really want to know, I was playing around with Desmos graph plotter and wondered if an equation could always have an appearance that isn't a straight line at all magnitudes. If you stretch sin x by multiplying it with x, it's a wave that oscillates between x and -x. The frequency increases as you zoom out, since you're increasing in magnitude with the constant frequency. So a lnx within the sin slows/speeds it at the rate you zoom in/out. Hence, xsin( ln(x)). And before you ask, no I don't have any friends.
I remember asking my teacher years ago what equations are nice for making shapes. We didn't have anything but circles at the time in the textbook. So it would be cool if it was more part of math teaching because it makes it a lot more practical
Really hope this video hits millions of likes and hundreds of millions of views. I often see math as underappreciated and those who don't appreciate it are missing out on an entire beautiful world. Many people immediately start thinking of school and become sulky when they even hear a slight bit of math but if we all can push ourselves further, we will all start really loving math. I say that as someone who is studying physics. Thanks so much for this video, hope it sparks interest in math in the mainstream audience
No, I calculated every single Y-value for every X-Value of all of these fuctions and constructed all of the graphs by myself 😢 Nobody is crediting me 😂
Very interesting and insightful! I’ve always tried to do this on my graphing tool to see what sort of cool shapes I can get. Just a suggestion for the next video, show the equations for two seconds longer so we don’t have to pause it to read, but great video!
Ever tried writing fragment shaders? It's literally just a function that maps each pixel on the screen to a color. You can make all sorts of funky stuff with it.
As a math fan, I think mathematics is a very important in our life, if I can't have any methods to solve the problem, I will use the function, I love functions and the calculus
I like the 3:45 graph Like one day, when human become super intelligent that will find out: Why magnetic flux of a magnet bar got that shape? Or why the opposite signed electric particles reacting to each other, made that graph? When human fully understand the graph, finding out more graph of more things in life, human may able to recreate the unknown natural
I can never help but wonder how people got to those equations... was it planned, or was it a coincidence that they were found... and what hasn't been found?
Math is art not because of the aesthetic of geometry and algebra but because the genius involved in representing the world in a mathematical way is artistic. Without artistic imagination of the minds that contributed to mathematics, it wouldn't have been possible.
@@homareyoshi4194 Nope, Manim is made to make math animations with code, so it's logical that DigitalGenius uses it there are other alternatives, such as Motion canvas, or Unity (yes, the one for making games) If you want to see how they look, here are some great videos made with each one: Manim: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-U_85TaXbeIo.html Motion canvas: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-WTUafAwrunE.htmlsi=-Y7tKrnGOQbiqG07 Unity: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Qz0KTGYJtUk.htmlsi=6G0gS4Xp31tfjIJo
Awesome video. I spent many months in high school representing functions, and years doing calculus in general. I wish somebody had explained me, back in the day, the concepts behind them or why they are so important. Years lost solving meaningless problems that could had been employed in building a much more solid mathematical base.
@@EliasRiveraReal realistically, complex dimension is just an additional dimension to whatever you were currently working in. So, if working in 3d, then yes complex plan would add a 4th dimension (multiple 3d level sets)
Absolutely amazing ! Can anyone help me explain how this is done ? I read somewhere that these are not functions in the classical sense - because functions cannot have multiple values for one value x for example - isn’t it ? So these work differently. I really would love to understand it better. There must be a cool way to also translate these to audio in some way … or make some kind of interactive game out of it.
I love videos like this and I even made one myself about langton's ant. Subscribed. Edit: How did you get fractions for lcm and gcd at 3:07? Also, these plots without t must use some local grid based algorithm to find where to find enough points to make smooth looking curves (obviously, it's easy to know which ones are neighbors when you have t)
