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...
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!
@@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.
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
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!
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.
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 😂
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.
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
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
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.
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
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
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 🎉.
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.
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.
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!
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?
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.
@@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: ua-cam.com/video/U_85TaXbeIo/v-deo.html Motion canvas: ua-cam.com/video/WTUafAwrunE/v-deo.htmlsi=-Y7tKrnGOQbiqG07 Unity: ua-cam.com/video/Qz0KTGYJtUk/v-deo.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.
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
@@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)
Now I want to see an equation that would make an image of something like let's say a stick man, then we can go up from there to something like the equation of a line art of Mona Lisa.
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)
![Why you didn't learn tetration in school[Tetration]](http://i.ytimg.com/vi/Ea1_1aVfwl4/mqdefault.jpg)
Don't think of maths as problems and exams, think of it as a playground with unlimited freedom.
This quote better be official, if it hasn't already been claimed then it will under your name, even if it's only under your username
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.'"
@awsomebot1 good try. Youre on the right path. Since your young, your goal should be to clean that quote up and put it on the map.
Best of luck.
I try to lol it was easy in 8th grade but 9th grade it’s kinda ridiculous
@@awsomebot1bips bedora
Imagine someone drawing an entire portrait using just functions.
That’s not how it works math creates patterns not specific features
@@joshstudiospresentFunctions. Multiple ones. People have made images using graphing calculators like Desmos already too.
@@tnapeepeeluYeah you can probably use piecewise also for more specific details
@@animationcity8178 someone is actually doing artpieces using mathematical functions, i dont remenber their name but it was really impresing
@@joshstudiospresent Restricted Domain and Range 🙂 we can create an art but it's just too hard
I can’t believe this only has 5,000 views, when I clicked on it I expected it to have millions. This is insanely cool
honestly, same, let’s hope the algorithm does it’s job ig
fr
its going up soon
We’re probably the ones to see a video right before it goes insanely viral. We’re the chosen ones thIs time :O
About that-
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.
Poor English you mean great english
I felt the same way like you
1:15 I like how the 2D shape gives a 3D effect just because of the closer spacing of the lines as we go farther from the origin
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.
parameteization is taught in college math
@@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.
you didnt know this because you didnt go far enough into math. This is the first lesson of parametric equations in calc 2
Math is art when I’m not dying on a midterm trying to figure out wtf arcsec of arccos of 192pi/6
💀
1/sine of it silly
Kid named calculator
Skill issue tbh
1.
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...
When artists are out of inspiration they don't randomly swing brush to paper, they write random equatoins and enter them to desmos.
When an artist and a mathematician fall in love
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!
Life is *MATH* !
Sure am
Math is truly art.
Sad that the education system only gives the student stress and fear instead of showing the true art of mathematics
@@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.
No.
@RepentandbelieveinJesusChrist5 shut up
╭╮╱╱╭┳━━━┳━━━┳╮
┃╰╮╭╯┃╭━━┫╭━╮┃┃
╰╮╰╯╭┫╰━━┫╰━━┫┃
╱╰╮╭╯┃╭━━┻━━╮┣╯
╱╱┃┃╱┃╰━━┫╰━╯┣╮
╱╱╰╯╱╰━━━┻━━━┻╯
As an artist, this is absolutely insane and beautiful. I kinda feel bad for understanding math at a mid level
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.
"They cannot comprehend anything of Her (Allah's) knowledge, except as much as She (Allah) wills." (Holy Quran, 2/255)
@@motherlandmars5999 she?
@@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
I understand math at the lowest lvl hahhahaa
It’s like you can see that every pattern has it’s own unique personality. Amazing.
What I like about these is any normal person can just “draw” it but with equation it will always be perfect
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!
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.
This seems like something midwits put on their Pintrest so they can feel like they created something.
Math art is polynomograpghy
If I told an algorithm to draw something, it's not art. If I draw something even badly, it is. The difference is one has soul.
@@Pappycap74 If only you had a time machine, to go tell that to the headmaster of a certain Austrian Art Academy 😅.
@@icidemart5046 couldn't disagree more
This is one of those legendary videos which will be in everyone's recommendations few years from now 🙂
I'm guessing that too
I'm then glad to be early here. Good job UA-cam for recommending me this early!
@@vedantsridhar8378i’m late but glad for youtube
Guess so.
Also try "y = x × sin(y) × sin(x)" makes really cool triangular group of squares and circles that meet in the center
This is better than 99.99% of "ASMR Sleep Conjuring".
The second to last one looked like the field lines of an electric field. So cool to see math in reality
That’s what I was thinking too! So cool!
so true
As someone with the name Matthew, I can confirm that math is truly art
Real
Me to
Math-ew
@@ShabudanaYour family-ew
@@Unlimit-729 Who hurt your feelings?
3 blue 1 brown would be proud🔥
This is fire, well done! Especially the animated ones🌟
The math exam be like, "sketch the graph"
Computer that makes this possible is just beautiful and thankful.
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 😂
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.
I used t because: θ - theta
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
@@trashatf hn but how he made that in that motion ??
@@Uchihaitachi_7 screen record and made it to 2x
@@trashatf lol no
The animations were likely programmed with Python.
@@axeldewater9491 ohh ic oopsie
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
just press the space button and the video will magically freeze
@@iliagozalishvili2803 gets kinda annoying when you have to do it every 4-5 seconds
Agreed. These graphs are cool but the pacing is off.
這樣節奏會太長
@@NoName-rd6etslow the video down to 0.5
Well presented. What graphing tool is this?
man math is just the heaven of unlimited freedom and bro people take math to the extreme sometimes
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.
stfu@RepentandbelieveinJesusChrist5
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.
Thanks, I was wondering how it was possible
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)
Was searching for an explanation, thanks. So the equations of circle, ellipse etc. Aren't functions?
Nope.
Before accusing me of saying false information check you all of you definitions and information.
This is gorgeous - probably the most beautiful implementation of Manim I've ever seen
Subscribed
Suffering = math = patterns = art = great conclusion? SUFFERING IS GREAT!!!
Never knew math can make cool attack animations.. damn, this is the only thing that is going to make me like math
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
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.
People actually made actual art using graphs
how do people even find this stuff
@@Nicomv-eu3pd well its not that hard using comp algorithms ( using pen n paper its tedious to figure out such equations)
@@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.
@@Thomas-vn6crThe function is really beautiful. Thank you
Honestly expected for a lot more views for such a cool idea and a high quality video. Good work! This was really awesome to see.
Gotta love how most of these beautiful graphs come from sin, cos and tan
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
Trigonometry + Exponents + Modulus + Number Theory = Art
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
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 🎉.
And its not the only beauty of math, math is full of it.
You can try [sin(x²+y²)+cos(x²y²)]
2:08 i like how it syncs with the song
What even is the song there? IM DESPERATE FOR ITT
Song ;(((?
He meant music
Imagine giving a math equation to your art teacher
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.
Teachers should show this to students in school to inspire them!
Yeah, hopefully they won't be half asleep when the video is on
3:46 looks like a magnetic field with north and south poles. Cool!
Yeah
My man can make a butterfly out of a math function HOLY SHIT
Technically it’s the other way around, art is math, since everything can be described using some form of a mathematical statement
Technically it’s the same both ways
Sooner or later, UA-cam algorithms will give this video the millions of views it truly deserves.
so true
Aged like wine
2:09 to 2:11 was just so brain smoothing
Mandlebrot Set is still one of the most intricate pieces of mathematical art I've ever seen, makes you wonder who drew it.
It was generated on a computer
Imagery
@@mr.p2665that's the how he drew it , we want the who , who did it first , who created this set ?
Я получил настоящее эстетическое удовольствие не только от визуального ряда, но и от прекрасно подобранного музыкального ритма. 👍
1:48 light when the booklet's plastic cover is dented
Seriously tho this is amazing
Seriously show this stuff in schools, if they'd shown me this stuff back than I'd definitely pay attention
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.
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!
this is why i like math and want to learn it
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
It's an pattern, formed by an equation, made by humans, we already know why the equation produces that specific pattern.
I love art and love math. This was amazing
Wow
It changed my perspective of maths
Mind-blowing 🤯
This deserves to have more views
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?
Once you do it a few times, you can get the gist of it and just input a random equation and it'll always produce some kind of pattern.
2:08 i love how the curve matched the beat
Is there any practical value in those, or just fun?
What tool/software did you use to get such high detail?
manim
Most of these aren't functions, but they sure do look like fun
Idk, they look pretty func-y
@@wafflesauceyehehehehehehheh
@@wafflesaucey👍
@@wafflesauceybro is him
function sum(a, b) { return a + b; }
Whether you like it or not, math is the only one that truly blows your mind.
0:37 who would've thought that a simple star is described by such complex formulas...
Yeah
it's not that complex lmao
5 little happy stars
props for this channel for creating Earthbound backgrounds. what absolute legends
What you learned in class:5x5=72
The test:
Lol, that's kinda relatable, not in math class for me, but many times I recall having learned wrong info in class.
This is great! Can you share tbe source code for the animations in this video?
0:42 I see why I was recommended this now. 10 karma symbol. If you know you know.
If I don’t know I don’t know (I dont know)
Rain world?
When you wanted to be artist but your ASIAN parents forced you to be a mathematician
I can say that mathematics is not only science ,it s also ART ............
If one person decides to put one of these functions into his painted painting, people would buy it for thousands or millions of dollars.
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.
Consider the graphs that are drawn as sets of points (x,y) in the plane that satisfy the relation between the x and y shown in the equation.
3:36 no equation
What software do you use to make the graphs?
Python, Manim library
wait not desmos..?
@@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: ua-cam.com/video/U_85TaXbeIo/v-deo.html
Motion canvas: ua-cam.com/video/WTUafAwrunE/v-deo.htmlsi=-Y7tKrnGOQbiqG07
Unity: ua-cam.com/video/Qz0KTGYJtUk/v-deo.htmlsi=6G0gS4Xp31tfjIJo
@@homareyoshi4194desmos wouldn't render any of these properly
@@homareyoshi4194 desmos can't really do the animation part
This gave me a new perspective for math 😊
there is a function in solidworks where you can hae these patterns on surfaces instead of just a plane surface imagine how cool is that
At 1:08 the equation at end is sin(2t-pi)/24 not sin(4t-pi)/24
Still great .....
What's the equation at 3:35?
doubling question
Tomato equation
great quality of content!
Try “ z(x) = ix “multiplied by any number, you can create grids.
dis proves math isnt boring like i thought
This is like 10 million subscriber editing
2:30 I Love this.
Fm
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.
Why this video didn't get 1M views? The Math is truly the masterpiece.
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
As soon as something loses practical applicability it becomes art
2:39 sharingan 😐
Math truly is art. All of these are 2d slices of 3d objects (the 3rd dimension is imaginary numbers). Would be so cool to see the 3d ones!
meh might as well just graph 3d functions and not need imaginary numbers
Shouldn't it be 4d or do mathematicians only let one of x or y be complex and the other real
@@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)
@@saveerjain6833 thanks for in insight man.
Truly mathmagical.
Now I want to see an equation that would make an image of something like let's say a stick man, then we can go up from there to something like the equation of a line art of Mona Lisa.
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)