Sine graphs but they get increasingly more AMAZING
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- Опубликовано: 4 окт 2024
- Here are my collection of amazing math graph with only sine function.
I use DESMOS to plot these graph.
Here is the link to the graphs so you can play with them yourself : www.desmos.com...
Music:
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Also check out my other collection of beautiful math graph:
Polar Graphs : • Polar Graphs but they ...
Math is Art : • Math is Art
Math is Beautiful : • Math Is Beautiful
Thanks for Watching.
Note:
I made a mistake in the video. I said that I only use the sine function, but that's not true. its not that i only use sine function, but more like 'I'm only using the sine function out of all other trigonometric functions." I hope this clears up all the confusion.
Note:
I made a mistake in the video. I said that I only use the sine function, but that's not true. its not that i only use sine function, but more like 'I'm only using the sine function out of all other trigonometric functions." I hope this clears up all the confusion.
U forgo cos in da vid
@@fortcraftgaming2136
TF are you saying?
@@RailsofForney "you forgot cosine in the video"
@@fortcraftgaming2136 sin(x+π/2) is equal to cos(x)
@the-mathwizard how do I make your profile picture as a graph?
I'm a musician and I was 100% expecting to hear these waves
if you're really a musician, name every song
Variations on the C Major Scale
@@sournois90 bruh what?
@SeeJay-ji7tqwhat about songs in microtonal tunings?
@SeeJay-ji7tq what about music that doesn't use western tuning?
I wish these could be rendered with full detail
i second this
Eh, working with Desmos you get used to it
Maybe GeoGebra could work?
if they actually could the line would be infinitely thin so invisible so a blank paper is a render with full detail kinda
Try buying a Raspberry Pi because the full version of Mathematica is free for the RPi. I’m guessing that it would do a better job of rendering these.
nothing could've ever prepared me for how smooth y = sin(x) + sin(y) was
2:13 ye
4:40
This is someone who has seen the true power of sine.
🤯
"At this point you know I'm obsessed with number 9"
Words of a Cirno fan, no doubt
Yuck, i could smell this touhou fan from a mile away
Deodorant aisle is that way
9 is beautiful, as it is the place value limit in our base 10 system. 9 does a lot of beautifully interesting things
@@ilovemitakaor you could just *leave?*
this is so cool and such a vibe with the music and little inbetween captions
I'm glad that people like slower, simpler, and calmer videos. Thank you.
fancy seeing you here looser, apparently we get recommended the same cool videos from smaller channels
@@the-mathwizard tbh anything slow is bound to bring people relief from the endless tiktok crap
I particularly enjoy y = x • tan(x²+y²), it makes a very nice spiral
You are right! owo
That's amazing.
I also like this one a lot, it doesn't look like something that would behave so nicely, even desmos has trouble rendering it. Why it creates a spiral becomes clear when we convert it to polar coordinates, we get theta = r^2, or r= +/- sqrt(theta). I also didn't expect it to be so simply expressed in polar.
i put a nice render of it on imgur a/7yRULrG
Nice
Changing it to y = x + tan(x²+y²) is pretty funny compared to that
A lot of these graphs look like that because of the limitations put on how precise they are to the real thing (since points are infinite therefore not every single can be rendered). It can be seen with the small missing pieces that should be there but aren't rendered.
@erin1569 -- I have often thought the same. I made my own graphing rendering decades ago, and have since recoded it on today's supercomputer PCs to be real-time, and comparing the output to online renderers shows that they make an attempt to "connect the dots". I have just uploaded a video with this video's equations shamelessly taken to see the difference, and to test my asymptote calculations. Have a look. Nyquist frequencies are still hit, which can be fun to look at, but it ultimately does not achieve the goal of showing "where are the solutions?"
4:06 is just sin(x)=sin(y) and 5:27 is just xsin(x²+y²)=1
(Except the forms shown in the video also have y=0 superimposed as a result of multiplying both sides of the equation by (y-0) )
imagine if we could see this in the complex plane
Loving this idea!
You somehow brought emotion to showing sine graphs and thats so cool
A lot of these are good easter egg designs
2:20 bro thats just tangent
i love the little comments with each function they’re so cute
Did i just make math cute?
@@the-mathwizardYou come from heavens if you can achive that, you must be Acute angle!
@@aeuludag..
Amazing 🤯I saw someone send the equation for a heart on a valentine card, but this is on another level. Please more.
Math wizard be like:
I'll have 2 number 9's a number 9 large
9
6
9
6
9
WE ABOUT TO LEARN _SINE_ LANGUAGE WITH THIS ONE
nice puns!
@@the-mathwizardbut still how do I make your profile picture as a graph?
How do I make it
Seeing y=sin(x^2) and seeing so clearly that for x~0 sin(x^2)~x^2 (the freaking parabola in the middle) and also noting it for all the other functions was so cool. I know it’s banal but that’s the beauty of math.
it goes wibbly wobbly
4:09 Is actually really interesting: y = y * sin(x)/sin(y) simplifies to sin(y) = sin(x), which can be solved to y = x + 2*pi*k, where k is any integer between -infinity and +infinity, giving a bunch of diagonal (y=x) lines spaced 2pi apart. Since sin(-alpha) = -sin(alpha) = sin(alpha + pi), this can also be solved to -y = x + pi + 2*pi*k or y = -x + pi + 2*pi*k, where k is once again any integer between -infinity and +infinity, giving a bunch of diagonal (y=-x) lines spaced 2pi apart, but translated by a factor of pi.
🤓🤓
😎😎
Intrusive thoughts winning 💀
real
What i dont understand
You could try "y=sqrt(1-x^2)*sin(10x)", it makes a sine wave that fits inside of a circle
00:11
Sine Wave
00:32
Frequency * 9
00:41
Magnitude * 9
00:52 & 01:01
Pitch Envelope
01:12 & 01:22
Magnitude, Phase, and Harmonics
I like these videos cause before the graph shows I take some seconds to think how the function will be, pretty interesting, keep up the good work
I love the part where the graph said “it’s cubin time” and then cubed all over the place
I do this all the time. I'll choose a function and guess what the graph will do as I add things. I am not alone!!!
It’s pretty cool that for any sine function, let’s say f(x) for example, whenever you multiply x and y it always leaves a line of non values around the origin that “cuts” the graph in two, almost like an asymptote in a hyperbolic function.
Such a nice video. Thanks for sharing cool functions you've found
Of course brother, you're welcome
The 4:05 graph is simple, sin(y)=sin(x)
Beauty lies in simplicity
@@the-mathwizardya I know, just pointing out
With the minor difference that sin(y) != 0 => y != kπ
Note: if you put "k" variable instead of nine, then the equation is: y=(sin(kx))+sin(x). And then you can make an animation of it
I’m not even going to pretend I understand why those graphs can be made 😂
1:00 IT'S CUBIN TIME!!!
My personal favorite sin curve is |sin((pi/2)x)|=y^2 because it makes a chain of what looks like perfect circles
Number 9 is the main character
Sure it is, agent 009😎
This is what the Beatles were talking about
Number 9, Burger King Foot Lettuce.
I like 2:00 Because this reminds me of how AM radio waves are transmitted. Kinda just a sine wave riding a sine wave.
4:05 the Ys cancel so ur basicqlly just solving sin x = sin y which will just be periodic straight lines
It's been nine days since this has been posted and I got reccomended it.
Learning sine waves 😪
Visualising it : 🤩
at 4:06 y=y*sin(x)/sin(y) simplify by y and you get 1 = sin(x)/sin(y) and then mutiply by sin(y) and you just get sin(y) = sin(x)
With the ones where there’s a y term on the RHS as well as the LHS being equal to y- how does that work? Is the graph not showing a function but just the set of all solutions to that equation? (I did a maths minor at uni but that was a couple years ago)
Yes, pretty much. You can simplify these equations to y= something, although the resulting formula definetely will not look as nice. Often enough it will also not fulfill the requirements of a function (each x-value is assigned to at most 1 y-value). Instead of that, the equation might be fulfilled for all y>x or similar.
It uses a numerical method to scan for all pairs (x,y) that solve the equation.
Coming up with such a numerical method is really cool and a fascinating problem. I recommend you read, at least the start of a wonderful introduction to Tupper's Algorithm: www.dgp.toronto.edu/~mooncake/thesis.pdf
Now put sum function at the beginning n=x and put any number on top
5:40 I was expecting the roblox epic face because “it’s over 9000” and that reminded me of “zomg so cool, but it’s ovah 9000”
naah, this is the true "it's over 9000" moment: ruclips.net/video/SiMHTK15Pik/видео.htmlsi=Zo_H0dJSCMw8ZALo
Funny enough, that's a meme based on a meme.
The original comes from an early English translation of Dragon Ball Z.
“Damn son” is my only reaction 😂
I’m in grade school and we use Desmos for our calculations, so whenever I get bored, I just go to Desmos and do something dumb, until it creates beauty like this.
Sine function on LSD!
Desmos is cool but Mathway graphing calculator renders the graphs much more precisely. Maybe give it a try.
Some of these are super cool and some of them make me viscerally uncomfortable with how imperfect they are
You should edit this as an sin(x) Iceberg!
Great vid!!
2:01
ITS THE KEYS
🔑 🔑
🔑 🔑
🔑 🔑
🔑 🔑
If you replace the number 9 with a higher number, you'll get even wigglier graphs
Friendly reminder that math is freaking cool
This is what happens when you piss
Biblically accurate sine wave
Let me toss you this one: sinx + sum from n=0 to infinity of n/10^n sin10^nx. Zoom in as much as you like, it will still look like a sine wave
I just tried plotting the graph, but after zooming in a couple times, it's not looking much like a sine wave. Could it be that I've entered the function incorrectly?"
Sine + sawtooth be like: 1:20
1:30 ok NOW it gets awesome
Would be cool to change the 9 by a variable and then animate that variable to go from 0 to 9. So that you can see how the figures form
That's a topic for a future video.
this is so cool
Normal graph: 😒
Graph with 9: 🤩
Y= Sin(9x)+sin(x) is what i call fractal sine or sine sine where the small sine wave from a big sine wave
Me when I get to class to do my maths test and I have to graph y=x•sin(x²+y²): 😮
(I'm going to humilliate myself more than ever)
When I tried the y=sin^3(x) in Desmos, I got an error saying “Only sin^2 and sin^-1 are supported. Otherwise, use parens.”
How unfortunate, still looks pretty cool on your end.
sin^3(x)=sin(x)^3
idk what im gonna do with this but at least now i know that i can confuse anybody without a phd in math with y=sin(xy)
4:08 That one makes sense actually; cancel the "y"s
I want to see this in Desmos 3D now
The third one in the thumbnail looks extremely scary
1;5x speed makes a cool beat
3:40 better infinity is "sin(x) = sin(y)!" (! - factorial)
you're goddamn right, how could I forget to add factorials
wtffff bro thats amzing
2:24 dude you can't fool me that's bacon
I wish you could do a f(x,y,z) sine function version, so we could see cool three dimensional versions of this.
sin(xy) is already three dimensional, in fact, a third variable would make the plot 4 -dimensional (though this would be impossible to represent). The reason why you see the xy functions in a plane in this video is that we are just seing a “level curve” (as if you cut the function at a certain height).
When I was trying stuff, I liked what sin²(x)=tg(y²) looked like
Bro this is awesome.
Bro I just started my trigonometry unit in geometry, this is cool
This was amazing, math wiz! do you have one with cosine? I had so much fun! I went from ABSOLUTELY hating trig to watching videos like these for fun!
y=2^{2sin(2x)}-2cos(y)
For a row of... *special items*
or replace the second 2 with 4 for some tall chess pieces.
I’m curious to how the computer is able to calculate y=sin(xy) since the dependent variable is in the equation
Desmond uses some numerical method to scan for all pairs (x,y) that solve the equation.
Coming up with such a numerical method is really cool and a fascinating problem. I heartily recommend you read, at least the introduction to Tupper's Algorithm: www.dgp.toronto.edu/~mooncake/thesis.pdf
isolate y or use a parametric
Magic!
i think it'd look better if the transitions were immediate, the function could be in a small box somewhere
y=sin(9x)+sin(x) looks so satisfying
no way this has only 1.7k, i thought this would be viral lol. even if you don't like math it's super cool
Thanks, soon those "k"s will turn to "m"s
You can do some equally interesting things with nested trig functions as well
5:26 - SOMEONE SPLIT THE WATER ON THE HILL!
ay try the dancing one - c = b tan(cos(x1)x)
y=y sin(x) /sin(y) looks like a linear transformation
Can we prove that those lines are lines indeed?
y = y sin(x) / sin(y)
1 = sin(x) / sin(y)
sin(y) = sin(x)
y + 2πn = x + 2πm; n, m are integers.
y = x + 2π(m-n)
When n = m = 0
y = x
So yes, those are lines. The 2π(m-n) term gives the graph its periodicity.
@@adiaphoros6842 I see. By the way, you ought to be careful when simplifying by y at the beginning since you can lose solutions. There is another line you are missing, the y=0 axis
Other than that, nice proof
add 1 to that and look at the graph :)
y=Sin(x^x)+sin(x) is my favorite (explicit too!)
You can make infinite infinities with 'sin(X)!=sin(y).
This video uses only sin, but cos looks better in my opinion because it's centered.
amazing video ❤, but switching from black background to white one so often hurts my eyes, would be better if it was only black or only white 😅
Awesome video! 👌
super nice man
My teacher uses Desmos to teach us
can anyone explain or link to smthn that explains how a graph can have multiple y values?
5:07 looks oddly perspective
(cos(x)*cos(y))^(1/3)>=sin(x)+sin(y)
I was shocked at y = sinx + siny because I thought that finally I found the "circular-sloped" sine wave when I noticed at the same moment that it's not.
What I mean by "circular" sine wave is that when every section is a perfect half circle.
Does such a wave exist?
Well try this sin(floor(x)×x)
I call that a sinsation
whoah never seen y^3 =sin (X) before
I Made The Duplicating Ramp
y = sin(xb) cos(xy) - ITS WILD