Amazing Math Graphs

Why did I make this video? I don't know, visualized math is satisfying to me. Why not give it a try yourself, especially if you are a pre-calc student like me and know most of the trig and some basics of calculus? It is really mesmerizing.
This is the first part of the series.
Playlist: • 🖋️ Maths
Hi Shibacchi - / @hishibacchi5357
Graphing calculator I used: desmos.com/cal...
enderman.ch

[@サンゴ礁Scleractinian]

For those who are unaware, most of the jagged lines/dots/shapes in the more complex curves are not actually 'real', they appear because the function changes so rapidly (or where the computation involves such large/small numbers) that Desmos' numerical solvers stop working properly.

[@oosmanbeekawoo]

They are complex?

[@primalaspie]

@@oosmanbeekawoo It's complex in the sense of literal complexity, not the complex plane. (This isn't to say that there aren't complex solutions; that just isn't what I think OP meant)

[@thatwasme7197]

@@primalaspie welllll ackshually they are all complex since R ⊂ C ...... 🤫🤫🤫🤫🤫🤫🤫

[@jpsalis]

at some point it has a hard time dictating where lines should be drawn, and where they should be separated too.

[@matthewfala]

Aliasing

[@noneofyourbusiness4133]

4:43 *me waiting for thr sorting algorithm video to start*

[@Fire_Axus]

real

[@priangsunath3951]

5:28 seems like a really easy way to generate alien alphabets. It's crazy how each column looks like a fully fleshed-out alphabet that you could easily imagine seeing scrolled in some ruins on a distant, deserted, and desolate planet out floating in space.

[@_abdul]

Absolutely loved the way you think. Nice One.

[@Nulono]

00000000OOOOOOOOoooooooooooooo

[@atomchild2619]

Thought the same, maybe it's the one which amazed me most

[@lucyc5844]

damn that's what I thought when I first did that

[@priangsunath3951]

@@Tzlil-jw1fg exactly, so don't use the proper graph, use the desmos one

[@gabrielko2147]

The problem with desmos is that when equations get too hard to process it starts processing less points. This can be avoided by just zooming in, you get less of the equation but if it is not crazy hard to calculate it will be accurate. For example tan(x^2 + y^2) = 1 is an infinite series of circles with the center (0,0) with their radius approaching the previous ones radius. Zooming in this becomes evident but when zoomed out it just becomes a jumbled mess. If you start increasing the number 1, the rendering becomes so hard that desmos limits the points of the equation calculated so that it looks like there are just a few random dots (points). After a certain number nothing at all is rendered.

[@feepants4495]

I just made my own graphing software in python that's only limited by hardware lol

[@liquidgargoyle8316]

@@feepants4495 lol, same here but used gm2.

[@codoudou]

Teacher: "The exam is going to be easy!" The exam:

[@ReirtoRRNTX]

Yeah

[@enderxity]

Is this hell?

[@SylvainBerube]

Guilty.

[@elliotc4268]

it's not very hard to throw around random functions in desmos to create some cool stuff like this

[@だつみん]

But some of them still can solve and drow with derivation such as "x^3/y = x" ,and " y = e^sin x + 1" (I don't say it's easy to solve)

[@Tama-sg7sv]

POV: you closed your eyes in math class for 5 minutes

[@BedrockBlocker]

When I was still in school, I imagined this must be what university calculus must look like. Was not prepared for the epsilons

[@alganpokemon905]

We signed up for Extreme Integration 5001 not this epsilon crap!

[@BedrockBlocker]

@@alganpokemon905 Hehehe exactly

[@Sg190th]

I imagined this could be Calculus 4 if it existed 😭

[@BedrockBlocker]

@@mynameusedtobelong What do you mean?

[@Lilly-Lilac]

@@mynameusedtobelong epsilon looks like this ε, and is used commonly in real analysis (and plenty of other analysis fields I presume)

[@dudenope5357]

for anyone who wants it, the music is "synchobonk" by steventhedreamer, who's the father of a youtuber named 3kliksphilip

[@RightJackAtYa]

Thank you!

[@stutavagrippa8690]

Some of these equations might have been drawn wrong by desmos. Still, awesome.

[@cara-seyun]

Are there any ways to find the true shape?

[@stutavagrippa8690]

@@cara-seyun I'm not sure.

[@cara-seyun]

@@stutavagrippa8690 possibly if you run it multiple times on different devices, you’d see what remains the same and get an idea

[@pwouik9784]

The main problem is the function varying too fast and desmos interpolate wrong

[@anushrao882]

For example tan(x²+y²)=1 (thumbnail) should just be infinite concentric circles centred at origin getting arbitrarily close to each other as the radius increases, but desmos can't interpolate it properly.

[@d4rksonic474]

"Dad, how are babies made?“ Dad: 1:03

[@ThatONEKid-uv5fe]

excuse me what-

[@givrally7634]

1:18 I mean you can, you just have to separate the case where x=0 beforehand. You get y=1/x², and along with x=0 that makes the whole graph.

[@alexandrosweeb8059]

Damn, didn't see yours... commented the same lmao

[@fabrizioperini288]

Can't you moltiply by 1/x and it becomes y=x^2?

[@neijrr]

@@fabrizioperini288 multiplying by 1/x is same as divinding by x, and you cant divide by variable if you dont consider the x=0 case (unless x cant be equal to zero for other reasons)

[@fabrizioperini288]

@@neijrr ok now I understand thank you

[@senthilpuliadi6599]

@@neijrr in equality you can divide by variables. You cannot divide by variables in inequality

[@toyama3307]

the way you put them in video, the message between, and the music choice. they all, together, make this video feels like good old online flash game. totally love it. what a nostalgia

[@ugiswrong]

Was worth the pre-hemorrhoid

[@notmilenakos]

Alternative title: brain hurt% glitchless math sub category wr

[@TheEncrow]

Is that kliksphillip's music?

[@DanielVCOliveira]

Some of these look like a slice of a 3D object (similar to a human tomography). I wonder if there's something going on in the complex number axis that we're unaware about. Beautiful work anyway.

[@Rudxain]

Exactly what I was thinking. This is related to elliptic curves. If Desmos used arbitrary precision and supported complex numbers, domain coloring, and maybe a 3rd axis, we would get the full picture

[@anlev11]

Good point

[@pawetwardowski839]

They actually are (at least most of them), but this has nothing to do with complex axis. If You look for example on the equation tan(x^2+y^2)=1 it is just a set of points where plane z=1 in the three-dimensional Euclidean space crosses the graph of the function f(x,y) = tan(x^2+y^2), which itself is a two-dimensional surface "living" in a three-dimensional space. And this can be applied to the other graphs too. If You have for example the equation y=cos(x^x), You can rewrite it as y-cos(x^x)=0, and then the graph is just the intersection of plane z=0 with the graph of the function f(x,y)=y-cos(x^x). There is actually an entire branch of calculus dealing with the behavior of such curves, called implicit function theory.

[@musa4539]

these can be continued to the imaginary numbers so yes

[@DatBoi_TheGudBIAS]

Oh man, if it's a mess in real axis, imaginary would be inimaginable

[@Anthrubicon]

I tried the graph at 5:40 out myself and it's really simple; It just looks trippy because the calculator's having a bit of a stroke. It's supposed to be just a bunch of circles of center (0,0) with increasing radii.

[@potath10e]

yeah it's not loading pixels properly

[@sammy3212321]

5:43 Huh, this one reminds me of the rippling patterns formed when you approximate a sphere in discrete voxel space

[@YOM2_UB]

That's very closely related, as the look of the graph is very much the result of Desmos discretely approximating circles. In polar coordinates the function reduces to tan(r^2) = 1, so it should be infinite concentric circles with less space between them as you go away from the origin. (which is what you see when zooming in on the graph and reducing Desmos' workload). In fact, for each y value that the line x = 1 passes through the graph at 5:55, there's a circle centered on the origin with that length of radius. In other words, the circles get _very_ dense _very_ quick.

[@kristyandesouza5980]

That's what i thought about when i saw the thumbnail

[@daffa_fm4583]

me too

[@guy_th18]

glad someone else saw the connection. wonder if there's something deeper at play, and also if it's possible to recreate the effect of the circles on the voxel sphere "flowing" the more detailed the sphere becomes, but in this 2D space. somehow.

[@rogogo1244]

Did you see tze KZbin Video?

[@tinyseal3085]

i used to do something like this, but with 3d graphs, in school. instead of paying attention in math class or whatever, i'd find cool patterns and shapes. i made snowflakes and very surreal aqueduct-like designs. at some point i had a somewhat intuitive understanding of what caused what. zooming in and out would garner "unique" results within the same function. it's very fun to mess around with!

[@JMUHC]

The one tan(x2+y2)=1 is pretty curious though cause it can be solved using polar variable change. We got r=sqrt(pi/4+kpi) so the solutions should be circles of different radius

[@username4835]

And they are. Any zooming changes the where the “circles” are. It’s just a combination of the estimations of Desmos’s solver in infinite detail and screen limitations on the same.

[@fabiovezzari2895]

Amazing

[@ru5b]

@@bruceleenstra6181 the link works

[@goggs7714]

true, i used my algorithm from scratch to plot this equation and it did just a bit better than desmos strange that "Abs(left / right)

[@goggs7714]

also here's a showcase to the equation... pasteboard.co/7W885ydbhwMY.jpg

[@Kyanki113]

2:16 yes i am feeling cosy, thanks for asking

[@SHIN2024_official]

Do you mean cozy?

[@Angelthe4th]

@@SHIN2024_official jokes aren't meant to be fixed.

[@chopianist5226]

It gets even crazier if you mix in the hyperbolic trig functions, those are always fun to explore

[@xoxoheartz]

Imagine mixing complex numbers or z axis…

[@Xarr3]

I also know very complex maths, simaltanoes equations and that

[@newaccount-cz6tb]

@@xoxoheartz wait I thought complex numbers don't exist in the normal cartesian coordinates. Pls explain me

[@xoxoheartz]

@@newaccount-cz6tb i do not remember but there was a method to graph complex numbers using Cartesian plane but it was really specific.

[@bitonic589]

@@Xarr3 same, I'm 6th and understand all trigonometry

[@junetyle]

I'd never thought I would hear 3kliksphilip music here

[@tommy5965]

same hahah

[@Bruhmoment42O]

I was gonna say the same thing 😂

[@footlover9416]

3:50 gows crazy it looks like an impractical futuristic gun

[@professionalidiot8161]

5:00 i tried saying this one out loud and the furniture started floating

[@Shreyas_Jaiswal]

5:38 In this one, the graph is actually many concentric circles but the graph plotter is not able to render it properly, so it looks like this. 😁

[@trinityy-7]

what i find more interesting is instead of the circles becoming more defined they actually dissapear

[@trinityy-7]

so actually you are wrong

[@mathieugouttenoire9665]

@@trinityy-7 except he is not wrong. The software used is just having a hard time rendering everything properly. solving tan(x^2+y^2) = 1 by hand isn't hard, and what you'll find is that the graph will be concentric circles of radius sqrt(pi*(k+1/4))

[@mynewaccount2604]

@@trinityy-7 The graph is obviously radially symmetric so it's easy to see that the graph's wrong

[@trinityy-7]

@@mathieugouttenoire9665 i forgot what concentric meant when i commented that

[@josephwilkins238]

5:52 this one is my favorite. I remember just randomly finding it and being amazed

[@cuberdc9641]

Your video makes me, a student very love Maths, now is more interested in my subject and even your Windows videos. Thank you so much, Andrew (or Enderman)!

[@valentinozangobbo]

Minecraft "Cave sound" will be even more fitting than music 😅

[@patrlim]

Credit 3kliksphilip for the music in the comments

[@ks2091]

The factorial function is also fun to use!

[@spooksicola]

Nice use of the exclamation point

[@nogussy]

I'm really happy to see this music being used, and it's perfect use of it. Kudos, great video

[@becausewhynot8004]

Where can I find this music?

[@atla5263]

@@becausewhynot8004 The song is synchobonk by SteventheDreamer.

[@alaas1041]

Reminds me of 3kliksphilipp videos

[@Danicker]

My favourite is y=sin(1/x) (not in this video) because it has an infinite number of turning points in a finite region of space

[@lesarXD]

if you type: f(x) = sin(1/x) f'(x) = 0 you can actually see them

[@LetsSitTogether]

@@lesarXD Yeas bró

[@Torenu]

f(x) = sin(1/x) and f(0) = 0 is actually a great example of non simple-conneced but topological connected space!

[@Tu4zd6t7etrh]

You here?

[@topeka321]

that graphs pretty troll it just oscillates to 0 xD

[@momom6197]

Some of the later equations are not nearly as complicated as they appear. For example, tan(x²+y²)=1 can be thought of as y=tan(x) intersected with y=1 in 1D, then rotated around the z axis. The one before can also be described pretty thoroughly: you can easily find a (sort of) grid of points and show each point is encircled by a shape that is itself bounded near the coordinates of the point, although it's only visible towards the lower left. x = tan(y²) looks impressive, until you realize it's y=tan(x²) rotated 90°. Others however are genuinely man-boggling, and I'd love to study them more in-depth! My favorites are 2:23, 3:36 (which both have intriguing similarities) and the two afterwards, which I just can't wrap my head around!

[@igxniisan6996]

5:41, tan(x² + y²) = 1 or, x² + y² = tan^-1(1) = π/4 or, x² + y² = π/4 But in 1st equation tan function repeats itself along x axis.. thus generating such effect when having a complicated multiple variable inside it. Another way to get the logic is that you have to pick any random possible value for x² and y² pair such that the tangent of their sum will always be 1.

[@lmaothenametm]

@TheMainataur study math

[@mehdithezer0_985]

So we know that tan(π/4)=1 its also: tan(π/4)= tan(π/4+πk) with k being a Rational number so when removing the tan we get: x^2+y^2=πk+π/4 try it in desmos it will look the same as the first formula

[@tobiacremona4340]

*Paste in desmos:* \left|\frac{xy+a}{x}\left(0.01+x^{b}y^{c}\left(\sin\left(x^{d} ight)+\cos\left(y^{d} ight) ight) ight) ight|

[@toolbgtools]

I had worked on many math art equations , but never seen such big collection of terrifying equations. its awesome

[@iantyner7520]

I feel like you could by playing with these equations enough you could stumble upon an entirely new form of math

[@_Guigui]

No one: The netflix intro: 4:14

[@shannonelmer3860]

It looks like enchanting table language at the end of it at 5:06

[@Purely_Andy]

cos(x^tan(y))/sin(y^tan(x))=0.5

[@victorfunnyman]

It looks so grainy??

[@ecksdee9768]

@Progreshbar ok

[@proloycodes]

@Progreshbar which one?

[@Mono_Autophobic]

Logs : i make most difficult graphs! E : really? Mod : don't listen to them! Sin cos : lol have you even seen mine? Tan : So cute

[@ilaymuchnik]

5:38 the graph is actually very simple - it's a bunch of concentric circles - all circles are just around the origin!! and are perfect circles. desmos just draws this very wrong. proof: tan(x^2 + y^2) = 1 substitute theta = x^2 + y^2 tan(theta) = 1 theta = pi/4 + pi*k for some integer k x^2 + y^2 = pi/4 + pi*k right hand side is some constant which is at least sometimes positive, so x^2 + y^2 = c^2 the equation of a circle. different k values correspond to different radii.

[@Teemaino]

To all who want to know what those graphs mean: 1:34 Gauß' approximation of prime numbers 3:51 some manufactured small parts 4:33 A OCD-Test (the lines are not parrallel) 4:40 Your Routers Bandwith Diagram 5:10 T̵h̷e̴y̷ ̸A̵r̴e̷ ̷C̵o̷m̴m̸u̵n̸i̶c̵a̷t̸i̴n̵g̴ ̴W̵i̵t̵h̸ ̷U̵s̶ 5:19 A Map to T̸͔̙̖̩͇̓͂̓̑̕ͅh̷̥̭̲̻̀͗̎̽̚͜͝e̶̞͖̟̫̋̉͛̆m̶̜̆ 5:32 First 2 Coloumns are Wingprofiles 5:43 A 2D-Wave on a 3D-Object

[@raphaelr.5904]

How do you write those symbols on top the letters?

[@rwfrench66GenX]

This is very cool, thanks for uploading the video! When I was 14 in 1980 my dad brought home a TRS-80 Color Computer running Microsoft BASIC with 16KB of RAM, no internal hard drive, it required a cassette deck for recording programs or playing games. There was a game port and a place for two joysticks but many games were available on cassette. Anyway, I mainly used it for animated graphics and because of the limited memory you had to choose between having more colors and more pages but lower resolution, or higher resolution and fewer pages and colors. To draw a circle you would input the center of the circle on the column and row graph based on the resolution you chose, then you sin/cos to draw the circle and you could make an arc by putting a certain number between 1 - 360, if you wanted to do a full circle you could then add a command to fill it with a color, but if you wanted to do an ellipse you could add a command for the ratio of height to width, then you could add the command to fill that with a color, that was always the last command. These commands were always line numbers like line 10 line 20 line 30 and you spaced them apart by 10 so you could go back and add additional lines if you wanted to tweak it by adding sounds or GoSub commands, although GoSub's were usually already planned. GoSub was a subroutine that you built in like a macro to do something after your main program did most of what you wanted, like if you had it pick lottery numbers the subroutine would put them in sequential order and then display them.

[@cc3]

is this music from 3kliksphillip's dad?

[@xanthoconite4904]

6:00 me: *spams "zoom out" button* my laptop: *explodes*

[@rando5673]

The weirdest part is seeing some of these patterns and recognizing the real world physics they resemble

[@aronma2765]

that's super interesting, can you give an example?

[@ht8038]

^

[@riudoms222]

12 yrs old: WTF IS THIS?????

[@techcube7291]

14 yrs old: y axis is up and down and x axis is left and right Square root of 2 is 1.41blabla That is all i know

[@odyishere1828]

Cant wait to ask these questions to my tutor

[@nano_dank]

4:35 I crashed my GeoGebra tab 😂😂 Literally, Chrome showed the "tab is not responding" pop-up for a few seconds before finally graphing the equation

[@victorfunnyman]

It's just so many almost straight up and down lines close to each other, it can't handle it

[@glitchydemonfairy3171]

5:51 - The math is now speaking in alien lenguage.

[@helloitsme7553]

I'm now studying analysis on manifolds , and there it says that it's a fact that {(x,y):f(x,y)=C} is a manifold if the Jacobian at all points in this set is of full rank. This means there is a way to do calculus on some of these graphs. Imagine doing calculus on these graphs

[@MrRenanwill]

Algebraic geometry?

[@infamedepatates2502]

Welcome to general relativity

[@polinamoskvicheva2523]

yep all C^1-graphs look locally like when you draw it with pen with measure=1, some theorem from calculus about measure of jacobian=0 points=)

[@Puffman728]

0:33 Fun fact, the point where the two of them intersect is ( _e_ , _e_ )

[@SHIN2024_official]

which is also (2.7182,2.7182)

[@harsh0522]

But why?

[@RajJaiswal538]

I like how the strictness and precision of maths still creates such natural and random looking shapes

[@igoigo8656]

5:35 looks like an Alien language ,out of the earth

[@kanuos]

2:32 *Lisp programmer:* Finally, an worthy opponent. Our battle will be legendary!

[@Brahvim]

Thanks! As someone who does generative art as a hobby, I really like these.

[@bena2.014]

I did not expect that music on this video

[@ericmilnesoto2727]

You not only corrupt Windows, you also like to corrupt the cartesian plane as well.

[@belegarironhammer3200]

In x/y = x^3 : of course you can divide by x on both sides, it's y=1/x^2. This is never negative.

[@legendgames128]

5:44 so that's one way to map the sphere to the Euclidean plane... (referring to Henry Segerman's video of circles on cubic approximations of a sphere.)

[@SHIN2024_official]

Credit to henry

[@chrisbarlow6335]

@5:30 I believe it says "Amenhoptut owes me 180 bushels of wheat and 60 cattle, to be repaid on the spring equinox next year"

[@ПриветКакдела-с1э]

Эти функции специально придумали, чтобы передавать сообщения на древне-каком-то-там

[@gong65771]

2:31 when you program with Lisp

[@SHIN2024_official]

((((((((()))))))))

[@thepianokid9378]

((((((((()))))))))

[@tamaz88]

5:28 we’re making it out of the pyramids with this one

[@_wetmath_]

4:50 and 5:39 and 5:51 seem like such cute, peaceful, harmless equations. and yet...

[@Tom-u8q]

5:39 and 5:51 can be quite easily sketched by hand and so can 4:50 with a little more thought, assuming you are familiar with the behaviour of cos(x^2)

[@_wetmath_]

@@Tom-u8q i am not

[@null_s3t]

Can't wait for the sequel, Eldritch math graphs

[@garethmansfield9364]

Most of the later ones are just desmos being glitchy, they don’t actually look like that. Like tan(x2+y2) should just be a bunch of concentric circles around the origin

[@yuyy8565]

Yeah I was thinking the same thing. Also two variables functions are in a 3 dimension space and we only see a plane that cut the graph on the origin so those 2d graphs can be misleading sometimes

[@garethmansfield9364]

​@@yuyy8565 I made a typo; the equation is tan(x2+y2)=1, so in theory a 2D graph is fine (We're not plotting a function's output, but rather the set of values in R2 where that function is equal to 1)

[@flyingpenandpaper6119]

And around x^2 = π etc. by periodicity, right?

[@b_hav_6365]

Just makes you realize that a single equation can store a whole map worth of info. Also that basically anything you draw can be represented by some sort of equation.

[@StefaanHimpe]

If you haven't seen it yet, have a look at this: kzbin.info/www/bejne/eHfPlWd7d7RliKc

[@DatBoi_TheGudBIAS]

5:22 me wondering HOW THE FUK did it got graphed, does the computer slaps all numbers in x and get an y and graphs the results? how did he got that point mess in the top of the graph lol

[@스머프-s7g]

im not sure how they do it, but one solution could be to just base them off of the pixels on your screen.

[@agfd5659]

It basically takes many samples over a region that you want graphed. Say you want the region to be [-1,1]x[-1,1]. It could then sample points (maybe one point sample per pixel, although more samples would be preferred) from this region to see whether they satisfy the given equation (with some small error) and if that error is small enough, then it knows that that pixel should be colored in. This works well for "standard" functions and equations, not so well in this case, so that's why a lot of these are not correct graphs.

[@samegawa_sharkskin]

holy shit i love hi shibacchi Nice to know that you're making one as well!

[@jackm.1628]

It's pretty cool to actually graph these equations in 3D. Meaning if you have f(x, y) = g(x, y), graph z = f(x, y) and z = g(x, y). You see not only the intersection (whose projection on the xy plane is these graphs) but also so much more.

[@kaladinstormblessed3472]

I’m just waiting for someone to come out with an equation that maps out the whole earth

[@Zinaida7224]

Congrats, you made me even more curious on the trigonometric graphs I will abuse them as much as I can now

[@chico_obliq]

The one at 5:29 seems like a time travel representation of a mountain that evolves itself in a city full of skyscrapers with floating objects that connect the earth to the sky, millennium after millennium.

[@nishantpatil1847]

Its good if we take screen shots afyer going to the settings, remove the axes grids and reverse the colours itll be awesome wall papers

[@kamboojie7811]

1:10 Am i the only one?

[@user-se2we]

butt s*x

[@Somting_IDK]

no.

[@hdjdjdufjid]

No

[@retiutheproto]

no :3

[@iamanoob99axolotls-withtem97]

Math: Me: Task failed Successfully

[@Blahblahblah-s9x]

I didn't expect to hear Synchobonk outside of SoundCloud or a Kliksphilip video.

[@meirihagever9132]

When I first saw the graph of y = x! It actually made me want to learn why it looks the way it looks.

[@meirihagever9132]

@nnnoooo Not y = x, it's y = x! ("!" Means factorial)

[@nepp-]

Kindergarten: What's 1+1? 12th grade: *casually decoding the secrets of the universe via math*

[@lukan2]

I don't know any single thing about calculus, just looking at the nice squiggles on the graphs. :)

[@QuantumScratcher]

Me too.

[@aulosrazr_7285]

If ur wondering what song this is, its called Synchobonk by Steventhedreamer, I recognized the music because of 2kliksphilip's Going Low in CSGO series lol

[@01yomi_1]

2:50 if you do sin(x^y)>0 the result is weirder

[@MrKristian252]

5:17 this one is amazing, looks nearly like pure randomness at the top

[@meowcat7124]

I know this video is old, but there's definitely something wrong with some graphs. For example, 4:16 is intended to be a graph of a function that doesn't define Y at all, so all the lines should be infinite and vertical. Great video nevertheless!

[@agfd5659]

True, it wouldn't surprise me if most of them were wrong actually. Desmos just isn't good enough for these sorts of graphs. It would be interesting to compare this with how other software draw these graphs

[@volpilh]

Man, this vid's got some fuking old KZbin vibes to it. Switch out the tasteful white writing, black background transition cards with that one blue background Windows movie maker transition ( you know which one ), and this is bona fide 2012 content. I love it. It's simply lovely.

[@charlie43229]

2:22 Desmos can make wood? What the heck

[@prasham_shah]

tan(x²+y²)=1 has just circles with center (0,0) & with radius pi/4+n(pi) , n is an integer

[@GoodSmile3]

I remember experimenting like this during my first year of university. This is really cool and fun!

[@marasmusine]

As a student in the 90s I used to have a graphing calculator, and I use these kind of equations for sequence to use with Takens attractor recontruction, because I liked pretty patterns with fine structure. I felt pretty clever. My calculator was stolen from my coat pocket one day when we were playing Laser tag before a physics exam. I felt pretty stupid, never really recovered.

[@ugiswrong]

Doesn’t matter that you were careful with the plastic battery panel

[@reflex9216]

This is honestly amazing I wonder how some of these would act in any 3d environment

[@gabrielvanderschmidt2301]

POV: your sleep paralysis demon is also a calculus teacher.

[@Pepa14pig]

As a math student, I’m pretty sure I got some of the easier ones or similar functions to check continuity and if they’re differentiable 😂😂 They’re always impossible to draw but since we “only” had to check limes, they were always so so complicated

[@Sokobansolver]

Teacher: your summary of curve sketching exam won't be that hard The exam:

[@trevorallen3212]

At 4:56 it reminds me of GPR (Ground penetrating radar) scan. Very useful in surveying.

[@edwinpatassini3658]

that and 5:53 actually Did remind me of Anime for some reason... maybe large mobile machines and the like.. thought that wasn't weird! 😄😄

[@cblpu5575]

I think the graph in 5:36 is extremely misleading. This is because we have tan(x^2+y^2)=1 =>x^2+y^2=arctan(1) =>x^2+y^2=π/4,5π/4,9π/4,.. So it should really be a bunch of concentric circles (centered at the origin) with radii π/4,5π/4,9π/4,... Not sure why desmos gives circles centered in other places as well.

[@zealot4325]

with every equasion you are getting closer to the discovery of the Matrix

[@JosaxJaz]

It's amazing how simple some of these equations are for what they create in a graph

[@TheCookiePup]

4:40 Looks like it could use a sorting algorithm

[@khai6061]

1:07 Why did I giggled when I saw that 🤣🤣🤣🤣🤣🤣

[@honoohane]

3:07 is absolutely an art