You probably know this, but you can change desmos graphs into degrees instead of radians. Just click the settings tab in the top right corner. Looks like a wrench. Love the videos btw!
@@Skittleplays891 I know this, but I'm curious about how you can project a 3d rotation on the 2d plane, that's what was talked about at the end of the vid
Incredible work. Love when creators SHOW THEIR WORK. So much fun to follow. Cannot wait until you do your 3rd video with projections from a third dimension.
I adore learning about these fun math problems. Showing graphs and math as something less abstract (based on simple principles) helps tremendously in understanding them. From part 1 equations slowly grow more complex but you did amazing job at showing the stages and reason behind them eliminating any confusion.
Hey man, I just have to say that the best thing about your videos is how you made a simple question that anyone could have asked in school. Then you went through and solved it in an easy to follow way. Keep it up, I’m sure many others will love it as it is.
Just discovered your channel today, via part 1 in this series. Love your way of presenting these ideas, you make it sound like we're discovering this together! From this first impression, your channel is criminally underappreciated, keep up the good work!
Using a browser extension that (among other things) allows me to transpose the audio, I figured out that you use a transposition of "+3" (out of 12, of course), so 3 half-steps, in order to set your voice pitch in post.
Thank you, your videos are understandable and this is a pure pleasure to watch it. Keep going like that. We can see the quality and know that the work behind each video is massive. Your channel is 30 days old and this is one of the best that I have ever seen. Thank you again. One of your french fans.
At 5:30, the equations are applying the transformations incorrectly. They should be: (x, y) : start (x + a, y + b) : move the graph away from (a, b) (xcos(θ) - ysin(θ) + a, xsin(θ) + ycos(θ) + b) : rotate about the origin ((x - a)cos(θ) - (y - b)sin(θ) + a, (x - a)sin(θ) + (y - b)cos(θ) + b) : move back towards (a, b) On a related note, if you want the windmill at 7:02 to keep its shape, you should be using: (x - cos(θ))sin(θ + L) + (y - sin(θ))cos(θ + L) + 0.37 = 1/5 sin(5((x - cos(θ))cos(θ + L) - (y - sin(θ))sin(θ + L) + 2.64)) Or better yet, to rotate it at a different speed than it orbits the origin: (x - cos(θ))sin(3θ + L) + (y - sin(θ))cos(3θ + L) + 0.37 = 1/5 sin(5((x - cos(θ))cos(3θ + L) - (y - sin(θ))sin(3θ + L) + 2.64))
Thanks to part 1 of this series i was finally able to find the reason why the graph x^2 - y^2 = 2 is the same as 1/x rotated clock-wise by 45 degrees You literally just rotate 1/x by 1/4pi and you indeed get x^2 - y^2 = 2 Very cool.
Love the video, this sort of stuff is exactly what I used to think about in my math classes, just trying to rotate a graph because I feel like it’s possible, and trying different things out to see if I can. I know the ‘t’ equations aren’t suitable for animating the graph in the way you were trying to show, but I didn’t think they were any less interesting than when you don’t use it to draw the graph, it’s just a different way to animate the graph by changing the lines themselves. If you could calculate the right coefficients for t then I’m sure you could use it in some interesting ways. I already thought the ones you showed were quite cool-looking, but again, it didn’t preserve the original shape of the graphs, so I understand why you didn’t continue to use them. To me it’s just a different ‘dimension’ or ‘medium’ in which you can animate them.
Man, this looks like so much fun to mess with Is this the basis of standard graphical manipulations with images and stuff? 9:38 I think you can kinda see the points on the curve where things rotate around 11:00 also that looks like a halftone gradient! That's kinda useful after all!!!
This reminds me so much of my high school mucking about on Turbo Pascal! I messed around with a turtle algorithm, using Trig (waaaayy before I knew what they were!) to draw pseudo-random walks
I'm unsure if someone's already said this, but you can make your list even easier! By setting a variable a=10, for example, you can then create a sequence n=[0...a-1] that will automatically fill in the integers in between. Then you can say L=pi*n/a and it will make L exactly the same as shown in your video, except with less typing. Plus, you can modify the number of copies with a slider or animation!
The beginning of the first episode was like, yay, spinning graphs, as i always wanted :3! And its actually fairly easy But this has gone rogue quite fast, specially at the end, back to feeling stupid i guest…😅 Anyways, very good videos, really liked the humor in between the clear explanation, and the colours really helped to get what each part do
Btw I use this constantly, and currently working on a theory to make a well defined way to find the inverse of a function as the inverse of a function is just that function mirrored around x, so if I wanted to, I could use this to do this for anything in a well defined way
Can't believe you're only at 6k subs. Then again, you started uploading just a month ago. Keep it up man I am learning so much ! Your videos are so entertaining !
at 1:45, an alternate way of obtaining second sine way would be to use the equations- y=sinx x=siny and then make the subsitution although it makes sense to use your method as it is a more generalized method to obtain any n number of sine ways
In desmos if you open the wrench menu there's a button to switch from radians mode to degrees mode - but they don't support gradians (400 gradians make a full turn) yet.
Is it possible to get function notation to still work when undergoing these rotational transformations? Like, if you wanted to put a point (a,f(a)) moving along on your parabola as it spins, can you do that?
8:43 Not true actually. If you have enough x and y coordinates of any curve you want to make, you can approximately parametrize it using the discrete fourier transform. Any curve you can think of can be written as a superposition of sines and cosines, it's just a matter of finding the right coefficients and using enough terms. If you don't have an image or image data of the curve ahead of time you could always draw the curve you want or generate it in some other way, then collect the x and y data needed. I know this because I made a Mathematica notebook that could do this a while ago for some research I was doing.
Yoooo. I don't understand the majority of what's happening (I'm in Algebra 1 at the moment), but I'm just ecstatic to find out you CAN do this kinda stuff! Awesome!
So what? Just learn everything else from the Internet! I don't want to brag but just to tell that it's possible, I learned calculus and linear algebra from 3b1b in 7th grade, so don't feel limited!
@@tahamuhammad1814 Cool! As for why I don't understand: I don't know how SIN and COS work. I also am confused by theta θ. If I wanted to, I could probably understand this, look up math tutorials and such, but I'm mostly just here for the show.
You probably know this, but you can change desmos graphs into degrees instead of radians. Just click the settings tab in the top right corner. Looks like a wrench. Love the videos btw!
Radians superor tho
@@pedrosso0 Radians better, degrees simpler
@@hesterclapp9717 I disagree. It's simpler to write 2pi than 360 degrees
@@jimi02468 don’t forget the small r!
@@gabenugget114 the r is for perimeter, not angle
Phenomenal job on your presentation both visually and verbally, RedBeanie! I hope your channel begins to thrive from now.
I’m so excited to see the 3d rotations don’t leave us hanging !!
3d is just 2d but 1 extra dimenion
@@Skittleplays891 I know this, but I'm curious about how you can project a 3d rotation on the 2d plane, that's what was talked about at the end of the vid
@@aymanadyel3515 3d Projection
Incredible work. Love when creators SHOW THEIR WORK. So much fun to follow. Cannot wait until you do your 3rd video with projections from a third dimension.
A bit difficult to do projection from a third dimension while operating on a 2D plane.
I adore learning about these fun math problems. Showing graphs and math as something less abstract (based on simple principles) helps tremendously in understanding them. From part 1 equations slowly grow more complex but you did amazing job at showing the stages and reason behind them eliminating any confusion.
you better make part 3, im not very into math but im super into your teaching methods, school needs to have more teachers like you!
@hifty7779 they added part 3
Hey man, I just have to say that the best thing about your videos is how you made a simple question that anyone could have asked in school. Then you went through and solved it in an easy to follow way. Keep it up, I’m sure many others will love it as it is.
Just discovered your channel today, via part 1 in this series. Love your way of presenting these ideas, you make it sound like we're discovering this together! From this first impression, your channel is criminally underappreciated, keep up the good work!
Using a browser extension that (among other things) allows me to transpose the audio, I figured out that you use a transposition of "+3" (out of 12, of course), so 3 half-steps, in order to set your voice pitch in post.
Thank you, your videos are understandable and this is a pure pleasure to watch it. Keep going like that. We can see the quality and know that the work behind each video is massive. Your channel is 30 days old and this is one of the best that I have ever seen.
Thank you again.
One of your french fans.
Holy crap, this is worth watching just to learn Desmos features you never got around to hearing about.
can’t wait for part 3‼️Glad you got a sponsor from Desmos
It is nice to see 3-figure channels appear on the home page.
This is absolutely wonderful! Surprisingly easy to follow even with my sleepy brain! Thank you so much for this I love it so much
I am so excited for part 3!!!!!!! You clearly put so much work in these videos and I appreciate that. All the best!
I definitely would love to see you make a series of these types of desmos graphs. Its amazing
Just discovered your channel! Really underrated, I'm subbing
This actually makes a really good introduction to some basic linear algebra
it's actually introduction to computer graphics. next this guy will show us opengl
At 5:30, the equations are applying the transformations incorrectly. They should be:
(x, y) : start
(x + a, y + b) : move the graph away from (a, b)
(xcos(θ) - ysin(θ) + a, xsin(θ) + ycos(θ) + b) : rotate about the origin
((x - a)cos(θ) - (y - b)sin(θ) + a, (x - a)sin(θ) + (y - b)cos(θ) + b) : move back towards (a, b)
On a related note, if you want the windmill at 7:02 to keep its shape, you should be using:
(x - cos(θ))sin(θ + L) + (y - sin(θ))cos(θ + L) + 0.37 = 1/5 sin(5((x - cos(θ))cos(θ + L) - (y - sin(θ))sin(θ + L) + 2.64))
Or better yet, to rotate it at a different speed than it orbits the origin:
(x - cos(θ))sin(3θ + L) + (y - sin(θ))cos(3θ + L) + 0.37 = 1/5 sin(5((x - cos(θ))cos(3θ + L) - (y - sin(θ))sin(3θ + L) + 2.64))
Thanks to part 1 of this series i was finally able to find the reason why the graph x^2 - y^2 = 2 is the same as 1/x rotated clock-wise by 45 degrees
You literally just rotate 1/x by 1/4pi and you indeed get x^2 - y^2 = 2
Very cool.
love the way you think and explain stuff
11/10
would be consumed by swirling effervescence again
I wrote a complex number lib, and you can just multiply the function in parametric form by (cos θ, sin θ). Works like a charm.
Love the video, this sort of stuff is exactly what I used to think about in my math classes, just trying to rotate a graph because I feel like it’s possible, and trying different things out to see if I can.
I know the ‘t’ equations aren’t suitable for animating the graph in the way you were trying to show, but I didn’t think they were any less interesting than when you don’t use it to draw the graph, it’s just a different way to animate the graph by changing the lines themselves. If you could calculate the right coefficients for t then I’m sure you could use it in some interesting ways. I already thought the ones you showed were quite cool-looking, but again, it didn’t preserve the original shape of the graphs, so I understand why you didn’t continue to use them. To me it’s just a different ‘dimension’ or ‘medium’ in which you can animate them.
Man, this looks like so much fun to mess with
Is this the basis of standard graphical manipulations with images and stuff?
9:38 I think you can kinda see the points on the curve where things rotate around
11:00 also that looks like a halftone gradient! That's kinda useful after all!!!
okay one more comment. just because I really want the algorithm to pick this up, or whatever YT does behind these scenes. This needs to be seen!!!!
You weren't lying. You saved the best until last and it was all very very good stuff.
This reminds me so much of my high school mucking about on Turbo Pascal!
I messed around with a turtle algorithm, using Trig (waaaayy before I knew what they were!) to draw pseudo-random walks
Part 42: Running Doom in Desmos
I'm unsure if someone's already said this, but you can make your list even easier!
By setting a variable a=10, for example, you can then create a sequence n=[0...a-1] that will automatically fill in the integers in between. Then you can say L=pi*n/a and it will make L exactly the same as shown in your video, except with less typing. Plus, you can modify the number of copies with a slider or animation!
or you could use the variable of a to make a list of the radians with the 0 to a list by using “for i” making it become
[i pi/a for i = [0…a-1]]
using that as L
That first windmill be lookin kinda sus tho
i was just looking for this
That’s just the Hindu peace symbol
the rotations of the parametric equation when you added in t again looked *very* similar to 3d rotation, same with the sin wave that became a tangent.
Desmos is the GOAT
2:03 me after failing art school
edit: 2:51 this can’t be a coincidence anymore
Bro i was concerned asf
@@swagoverload1343 nah cause how do you accidentally make the swastika and the black sun in the span of a minute
While I watched this video the time changed from "11 moths ago" to a "1 year ago"
Congratulations!
I can't describe how happy I am to have come across this channel
9:36 "t' is like a 3d object rotating on a 2d plane
thx for sharing, i was just wondering about this like yesterday lol
The beginning of the first episode was like, yay, spinning graphs, as i always wanted :3! And its actually fairly easy
But this has gone rogue quite fast, specially at the end, back to feeling stupid i guest…😅
Anyways, very good videos, really liked the humor in between the clear explanation, and the colours really helped to get what each part do
Btw I use this constantly, and currently working on a theory to make a well defined way to find the inverse of a function as the inverse of a function is just that function mirrored around x, so if I wanted to, I could use this to do this for anything in a well defined way
This is so cool! Underrated!!!
This is so new and so well presented! Very high quality my dude!
loll the Don't Hug Me I'm Scared reference
Can't believe you're only at 6k subs. Then again, you started uploading just a month ago. Keep it up man I am learning so much ! Your videos are so entertaining !
Damn I kinda like the toxic y - x tho
looking fire af bro
at 1:45, an alternate way of obtaining second sine way would be to use the equations-
y=sinx
x=siny and then make the subsitution
although it makes sense to use your method as it is a more generalized method to obtain any n number of sine ways
1:25 thats not a windmill, thats a sinestika
This is awesome, I'm loving this series and the rest of your stuff. Excited for part 3, subbed, keep it up
Amazing video. Can't wait to see the 3d rotations!
That windmill looking kind of sus 👀
He really deserves 100k likes
Subscribed! You explain things exactly how I would imagine them honestly it makes me happy lol
We all love desmos!!!!!
informative and intuitive content keep it up .
MAN WE NEED THAT 3D PROJECTION METHOD PLEASE 🙏🙏
For some reason if u spin 4 linear graphs the 4th one disappears at pi dividers (0, pi, 2pi…)
It does still rotate with the rotation depending on T - it's just rotating in different dimensions
Your videos are great, I'd be surprised if you don't hit 100k soon :)
Where is part 3?! Where is part 3?! 😱😱
Nah that windmill be looking kinda sus 🤨
Haha yeah
if you use the new 3d feature and replace theta with z it makes a cool helix out of any graph
Wow nice video, everything is so well explained and it looks so nice
10:26 this is DEFINITELY some kind of 3d rotation. isn't it??
It seems like it man
yes, but 8t's projecting to 2d
YESSS
My man needs more subs. This is amazing
cu in the next video! Great Job!!!
If you stare in the center of the ten sin wave windmill for a while everything starts wiggling, you made an optical illusion.
Ahh, i never knew you could do that with desmos lists!!
UPDATE!
Desmos has a z-axis.
Very cool video, I’m glad I got recommended this!
I kinda love the never use t again song😂
Dude this is really cool, please make enother one of the viseos
Very interesting
Desmos does a z axis now, which is cool
What a cliff hanger
Love the DHMIS reference :)
If this channel blows up, I was one of your first 100 subs.
In desmos if you open the wrench menu there's a button to switch from radians mode to degrees mode - but they don't support gradians (400 gradians make a full turn) yet.
4:11 just for your own sanity you can abstract it even more by doing L = pi/n * [0...n-1] and then adding a slider for n
Ngl using t was also pretty cool
If I only knew about this one year ago😮😮😮
So cool
very good video
🎶Now let's all agree, to never use t again🎶
Very nice! Now I challenge you to move and rotate it through 3D space
at least for the tan lines it looks like a 3d projection in 2d and its just a spinning 3d shape
Is it possible to get function notation to still work when undergoing these rotational transformations? Like, if you wanted to put a point (a,f(a)) moving along on your parabola as it spins, can you do that?
THE ADDING T THING IS LIKE A 3D ROTATION IN 2D
11:00 I don't know about you but that looks very cool
Excellent stuff
GENIUS
Keep up the great work
You're a funny guy 😆. Hope you get many subs
You gained a subscriber
8:43 Not true actually. If you have enough x and y coordinates of any curve you want to make, you can approximately parametrize it using the discrete fourier transform. Any curve you can think of can be written as a superposition of sines and cosines, it's just a matter of finding the right coefficients and using enough terms. If you don't have an image or image data of the curve ahead of time you could always draw the curve you want or generate it in some other way, then collect the x and y data needed. I know this because I made a Mathematica notebook that could do this a while ago for some research I was doing.
that ist something that is really activating my ADHD brain
Nice dhmis reference
16:33 there is now a 3d desmos app, and 3d made in desmos
this is so trippy
bro the windmill looks like something else 💀1:25
Yoooo. I don't understand the majority of what's happening (I'm in Algebra 1 at the moment), but I'm just ecstatic to find out you CAN do this kinda stuff! Awesome!
So what? Just learn everything else from the Internet! I don't want to brag but just to tell that it's possible, I learned calculus and linear algebra from 3b1b in 7th grade, so don't feel limited!
BTW, everything in these two videos was super simple. What did you not understand? I don't want to be rude, just curious.
@@tahamuhammad1814 Cool! As for why I don't understand: I don't know how SIN and COS work. I also am confused by theta θ. If I wanted to, I could probably understand this, look up math tutorials and such, but I'm mostly just here for the show.
@@zelda1420they're just ratios. sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent
That is amasing!