Amazing Math Animations

Amazing graphs dictated by mathematical rules, now in the animated format.
This video is a part of the series.
Playlist: • 🖋️ Maths
Graphing calculator - desmos.com/cal...
enderman.ch

[@ClaramayNivetta]

I really appreciate how the transitions are timed with the music

[@jeremywoolley]

YES! I am a massive fan of music sync! (I do cringe occasionally on your main channel when the big drop hits but nothing exciting happens)

[@aa-tx9su]

I really don’t appreciate you furry.

[@tentyp2]

comically synced

[@fentonflatt297]

Geometry dast

[@mozvi1436]

As a GD I thought I was dreaming when I heard at the speed of light lol I'm happy people enjoy this music

[@Zenzicubic]

That one at 3:18 is called a rose curve. They're pretty cool. If you want another thing like that, the Lissajous curve might be a good fit.

[@fandroid6491]

It exactly looks like what I draw with a spirograph!

[@heotapgym-piggym2460]

bloodlust

[@rosiefay7283]

@@fandroid6491 Spirograph curves are hypocycloids.

[@stcoops]

i believe they r similar to the logic behind fourier transforms

[@georgespalding5969]

Fun fact! The exact same graph can be found in the desmos examples under Polar:rose (i dont want this to sound sassy fyi)

[@bettercalldelta]

2:26 this actually kinda looks 3d, like running near a sine wave

[@assiddiq7360]

Omg, it does!

[@28rizzons]

It actually does lol.

[@baibhavpalit1085]

Yes...true...!!

[@notneo7898]

It's Opera Browser

[@bettercalldelta]

@@notneo7898 Opera Browser is before that

[@tentyp2]

well i certainly didnt expect at the speed of light to be the song edit: cant wait for an argument to start whether the song is from bloodbath, cataclysm, bloodlust or something different lmao

[@UN4YA]

hi

[@AkivaB]

*Bloodbath intensifies*

[@dogmania2892]

BLOODBATH WAT

[@tentyp2]

@@UN4YA hi

[@kodirovsshik]

No WaY

[@smiley6425]

Bit of an unfortunate choice of a song, it would normally be ok if it wasn't heavily associated with geometry dash and will now flood your comments

[@Smesper]

it's fine

[@RandomHandle-fun2rhymes]

As a GD player that knows nothing about this, I can clearly relate that this is an extreme demon Edit: was not expecting this to get 1k likes but ok

[@swagmoneybuge]

0/10 generic hell themed extreme

[@maces1]

The 1rt btw

[@stonkman7878]

too bad its extended list

[@igneousorgan6435]

What are you talking… _video starts_ Ohhhhh….

[@another_eu_player8035]

Nah medium demon at best

[@therattestofrat]

This is actually the coolest thing; I haven't seen a program like desmos do this before!

[@spyshead6217]

Desmos can get pretty nuts if you know how to use it to its fullest potential

[@jouzibar5112]

Muscle memory made me hit those triple spikes at 1:50

[@agentfelixscpit]

I smashed my keyboard hard a few times when I heard the start (the 7-13 wave is hard as hell)

[@staticchimera44]

One of my personal favourites is (x - a)^2 + (y - sin(x))^2 = 2. A little blob that follows an invisible sine graph. Another fun thing about this one, the larger you make the number on the right (the radius of the "circle", the more it will converge to an actual circle).

[@dundsdar]

Adding another one makes it look like blobs chasing each other

[@tesseract7586]

i found the sine graph its rolling on. its about sine(-1.41421)

[@staticchimera44]

@@tesseract7586 I don't quite understand what you mean. sin(-1.41421) is a value, not a graph. Could you elaborate?

[@Stuffinround]

@@staticchimera44 he might mean sqrt(2) times a sin function? I’ve put sqrt(2)sinx into Desmos and it’s pretty accurate.

[@staticchimera44]

@@Stuffinround Oh, if they mean the sine graph that the blob is following, then the sine graph should just be sin(x). sqrt(2)sin(x) is slightly off at the peaks and troughs.

[@identicalgd2446]

2:44 felt like an ancient message

[@MKB720P]

Ancient aliens message

[@The-pf4zy]

Wow! This is actually really interesting and I never thought that this was possible in Desmos. I was messing around in the calculator and found this: (a+x)(a+y²)=tan(x). You get an interesting animation where there's some change being transferred from line to line while a's value goes up and down.

[@greps4229]

You can graph a family of curves by typing into desmos things like a = [-5 ... 5] and you can do a lot of stuff with lists utilizing tools like list comprehension.

[@GodplayGamerZulul]

Kinda reminds me of a photon interacting with obstacles.

[@codoudou]

The song perfectly fits with the video

[@AkivaB]

At the speed of light also known in gd as bloodbath

[@AkivaB]

@@Victor_StudentOfFloppa who tf asked you?

[@AkivaB]

@@Victor_StudentOfFloppa I'm tryna help a person find a song the like

[@kenos911]

Ironically the aftermath part has the best ones

[@Orzeczenie.]

@@Victor_StudentOfFloppa me

[@ClimFreeFeelRain]

3:06 Galaxy ? *the whole big bang appearing*

[@MoonStudioAnimation]

OMG THAT IS SOOO COOL.

[@Tetracontakaitetragon]

it nearly destroyed my pc 8/10

[@GameristicForce]

“Oh, you dare challenge Desmos?” anime lines come into view and no I dont watch any 😅

[@StupidCupid627]

2:19 this video was sponsored by Opera GX!

[@ultimasvalk]

Tight wave spam 2:08

[@limenlemon3116]

I was messing with the graph at 4:10, and if you remove the plus sign in the middle of the two parentheses, you get a twinkling star. If you multiply the entire equation by big numbers, you make the star smaller. However, if you multiply by small numbers (above 0), you make the star bigger. Multiplying it by a number -n, is in fact, the same as multiplying it by the positive version n.

[@EvanLovesFoxes]

It actually works!

[@khorramzadeh5892]

So cool to see at the speed of light as the background music. First time I do and that feels great

[@martincampaner859]

3:12 the music is well named

[@palmossi]

Speed of light?

[@abstrick_]

1:42 How Italian make pizzas

[@SARMA360]

drawing the "galaxy" graph is 100x harder than beating bloodlust

[@The_GreenHub]

as someone who plays a lot of geometry dash and is literally trying to beat cata, i was not expecting at the speed of light to be playing

[@imavirginm8264]

I immediately searched the comments for a gd reference

[@comfykit_]

gl on cata!!!!!

[@lukarikid9001]

Thank you!!!! I use parametric to model some of my 2D animation and that “windy” graph is perfect for modeling a tail, wings or a tongue! Parametrics are my favorite!!

[@spoon7328]

1:32 was cool bc of the song

[@ozzienemo]

1:31 is better

[@quadroninja2708]

that clearly shows how a function can behave when a parameter is changed, very cool!

[@christinahamilton7676]

3:15 My favorite thing about this graph is whenever _a_ is a multiple of 5, you get all these cool flower patterns. If _a_ = 5 or -5, then you get a circle.

[@JMZReview]

Well yeah because then that means it's just sin of (theta multiplied by some integer)

[@crazy510]

Naw bro, those graphics are a whole bloodbath...

[@ilikespaceengine]

Frfr

[@sovietrodan5326]

1:14 bloodlust played

[@sovietrodan5326]

The video: math The music 🩸🛁

[@notthatntg]

One I like is xa+y/a=xy. Moving hyperbola which moves outwards when a is near 0. Also, xa+y/a=y is a diagonal line which rotates and swings back.

[@lemniscatecube8673]

2:00 quack

[@Toaster-jr5eo]

im never letting a geometry dash player access math again

[@vladnightmare]

Going into this the thing I least expected was At The Speed Of Light to start playing lmao

[@jacky2476]

4:00 that’s awsome

[@sonicwaveinfinitymiddwelle8555]

2:14 omg Opera GX reference

[@retiutheproto]

no just opera

[@andreimarentette6368]

1:18 The Worm

[@MoonStudioAnimation]

wiggle wiggle wiggle

[@Questiala123]

Why does it look so satisfying?

[@3_ormorecharacters]

hearing speed of light immediately triggered fear

[@AtomisXYZ]

Holy cow Bloodlust

[@AkivaB]

Bloodbath was first

[@adamdorsky5465]

@@AkivaB cataclysm

[@sahildas.]

1:44 bro just got born to vibe

[@bobingstern4448]

Try the Wierstrass Function, it wobbles and it’s really cool!

[@gabedarrett1301]

I second this, especially from n=0 to n=a since n=infinity might be problematic

[@andrzejthomas6494]

i love that when you add tangent to something it always messes it up

[@bigmartin343]

2:19 Should be Opera's logo animation

[@AymenZero]

1:31 that one just hit me like a truck. I was not expecting that

[@ForYouPlays]

0:16 the timing with the music god dang!

[@midnightsnacker3101]

Was not at all expecting a Dimrain track to play at the start lmao

[@sjthecreator]

“Galaxy” Me: Are ya sure ‘bout that?

[@kie927]

Try( tan θc)-c (the variable doesn’t matter). Also you can try different trigonometric functions with this equation and it produces some crazy cool stuff

[@tsurfa5278]

you mean r=(tan θc)-c?

[@alejotassile6441]

1:15 I can see a sine wave moving through space and this would be the slope at x=0 1:30 This one is like cutting a cone with a plane at different angles and seeing what would be left in the plane Damn, those two are really beautiful to observe

[@mahanp6993]

is there a way to average the x and y values of each point for the graph r=sin(a/5 theta)? if so this would help me a lot

[@egoworks5611]

In order to have the average r values you must do a double integral, first for theta then for a. The coolest thing is that the first one yields to a 2(sin(xπ))/x type of integral (depending on how many whole turns (N2π) you want for θ), and from here you can youse the Feynman's method to integrate (kzbin.info/www/bejne/qWLdmYx6ad1po7s) , but with a catch, and that is that you might have to do some workaround to find the constant, because the integral of the video isn't bounded to "a", the variable you want to have as a parameter for knowing the average 1/a' * \int_0^(a'){f(a)d(a)} But that's pretty much an analytical approach, thus you'll have to change coordinates and stuff. Also the turns are very important because with them, the expression is not a function(you might have many r values for the same theta) I would like to know what's the purpose/motivation for having the average with respect to the parameter a? if you're just looking for the average for a single a value don't mind me, I'm just curious

[@mahanp6993]

@@egoworks5611 so i wanted to create a way to visualize a fourier transform like 3b1b did but the normal e to the i theta integral doesnt work in desmos because desmos doesnt support imaginary numbers

[@purple_sky]

@@Andrewman r² = x² + y²

[@Djake3tooth]

@@mahanp6993 but it does support lists, so actually you can implement it using lists and functions of lists. I actually have a graph of the e^(i*theta) from that 3b1b video

[@TGKawikachu]

2:19 dude straight up made the opera logo

[@jonnytb212]

Hmm this song sounds like geometry dash

[@엑스비디오]

Draw two graphs with x^2+sin(ay)+y^2=0 and x^2+sin(ax)+y^2=0, set the range of a to -100~100, play it, and set the radius. Draw this one-person circle.

[@sirmanki]

Pretty cool! I'm waiting for more

[@ShellPois]

This vide is so clear and it is simple and fast as the speed of light, i admire the lambotistic of this level, this made me took a bath.

[@kodirovsshik]

How did you make it so smooth? It is beefy PC or you had to render some parts much slower and then speed it all up?

[@Jaojao_puzzlesolver]

Anybody : Math is boring Me : *Shows this*

[@sussy8579]

Holy cow geometry dash song

[@maces1]

Supersonic ?

[@sussy8579]

@@maces1 At the speed of light

[@maces1]

@@sussy8579 BLOODBATH !!

[@maces1]

@@sussy8579 im so stupid

[@sussy8579]

@@maces1 lol its ok

[@MochiClips]

What I love about x^a is imagining thr curve on the negative side whizzing in circles and popping into existence again when it hits the real plane lol

[@tescowifi]

these graphs give me a good bloodlust

[@Turmoil101]

Damn this level looks like an Extreme demon

[@slesser6373]

At the speed of light. Great song

[@raulvelez3475]

Increíble, como es posible que la matemática pueda hacer eso, algo inimaginable, un saludo @Andrew

[@thebiggaklipa]

I like the fact that he used "at the speed of light" for a math vid

[@badRandy2100]

I love this and would have understood math so much more in school

[@ninjacodertech]

the r = sin((a/5)theta) except with tan instead of sin is so cool

[@youlookinalittlesussyovert4260]

If you graph r=cos(nθ) or r=sin(nθ) and make the graph animate extremely slow, like make 2 numbers for the animation domain at most 0.1 apart and slowest speed, and zoom into the center, you can see random hypnotic patterns from lines intersecting each other.

[@youlookinalittlesussyovert4260]

Never mind, don’t think it works anymore😪

[@Logarithmic-Spiral]

Awweee@@youlookinalittlesussyovert4260

[@neutrogemax8494]

@@youlookinalittlesussyovert4260 math 2 just dropped they fixed it thats why it doesnt work anymore

[@TT2009]

The song is called "At The Speed Of Light".

[@архиввевекекса]

thank mr obvious

[@TT2009]

Im not mr obvious

[@kodirovsshik]

@@архиввевекекса bruh

[@inawolovitz4990]

I love (t+cacos(2πt+c), tcos(2πt+c)). Makes a nice winged effect

[@DamienRamirez]

2:53 seen that one in GLSL & HLSL Well very similar, cool effect!

[@ultimade9610]

This is one of the best math videos I've ever seen. 2: 14: It seems the Opera logo.

[@cosmozone31]

Normal people: focuses on the video Me: heart beat intensifying because of the music*

[@applemelonsugar]

As a both Geometry and Geometry Dash lover I can say it is extreme calculus demon

[@joshdot9244]

The microsecond I heard the music I went from being mildly interested to laughing my ass off

[@Cat-yz1tk]

1:31 syncs with the music

[@memerboi69.0]

this equation contains fine detail that has yet to be resolved

[@ishikani]

i did not expect the song to be atsol but damn those are some nice syncs

[@AVerySkilledShadow]

These graphs are so cataclysmic! After these i feel like in a bloodbath, I just can't believe the aftermath

[@meraldlag4336]

1:14 that line is definitely moving to the left you can’t change my mind

[@debug8377]

do "y ≥ sinax + asinx + cosay + acosy" and zoom in really close to one of the blob edges

[@Arseniy-4660]

\sec\left(x^{2} ight)+\sin\left(\sqrt{a}x ight)+\cos\left(\sqrt{a}x ight) changing the a from 1 to 10, it creates wave that gets steeper

[@xlthecoolguy-lz7uh]

One of my favourites is y=(cos(x)*-(tan(x)+sin(x^2)))^2, it's very clear near (0,0) but gets muddier the more you move away from the origin and eventually forms a line of heart-shapes.

[@scientistvwoman4970]

it works without the negative sign as well :)

[@gutiiplayz]

IM GOING TO TAKE A BATH FULL OF BLOOD AFTER THIS VIDEO.

[@Succativiplex]

As a smart guy, I can confirm this is extremely demonically a extreme demon

[@aegon1807]

This video gives 2010 vibes. Loved it!

[@luigibudd]

2:22 Opera GX is the world's first and only browser made for gamers.

[@bobirika1233]

2:20 Opera GX logo showcase? Didn’t expected that!

[@AlixL96]

well that's a fascinating way to learn that a cool animation from a flash game I once played actually comes from a mathematical formula

[@yarpasandalan]

Waves: \sin\left(x+a ight)^{2}+\cos\left(y+x ight)^{2}>y

[@UznKe]

if u try that sin curve with a/5 times theta and change the sin with a tan, u get a very goofy new function

[@fran3283]

i like the fact that the video is sync with the music

[@ilovenumberblocksandMSM]

the music is just *BLOODBATH*

[@Robisquick]

That last one looked like the reflection of the sun on a pond

[@Bitter.Bitter]

the thing that i love is the moment i opens this i knew the song, i need help

[@mygills3050]

r=mod(a,θ) results look cool near the center around a=6600 onward especially if you run two of the function with separate color due to lag

[@skylardeslypere9909]

This is an amazing video. I'm glad it popped up in my recommended.

[@bloctans_4]

the equation at 1:22 ends at about 1.4 x 10^154

[@Zerlot]

This music sounds like boss music for a fantasy RPG and it's awesome.

[@logan3102]

geometry dash

[@김영찬-c8g]

y = x * floor(kx) (0 < k < 50) is funny graph too.

[@robloxsigner148]

3:21 the a = - 14.986 is really cool

[@master_blueboi]

3:24 Reminds me of playing a Slinky

[@Qstate]

Sometimes, it really feels like you are seeing the shadows of higher dimensional functions

[@dx243_]

2:20 as an opera gx user, i like this