Parametric curves | Multivariable calculus | Khan Academy 

Wait is this Grant Sanderson (3blue1brown)? That's awesome! LOL

Grant, thanks for making these Multivariable Calculus videos. They're terrific.

really incredible skill with graphing but the volume keeps changing levels video to video

is this 3blue1brown?

If grant was my professor I’d never skip lecture!

Khan academy, will you soon start teaching abstract/pure mathematics? Its hard to find easy resources online for these subjects

ITS GRANT!!!

Awesome method of teaching. Terrific work.

Such a soothing voice

Grant, thank you. What I am even more interested in is how do you draw these cool graphics.

I was using t= 2(n)/pi that generate exact same graph instead of using 0

You made the world a better place to live in...this might lead to find a new world to live in....

Calling them "pi-halves" is so cute!

At 5:43, shouldn't t=1 still be in the first quadrant? After the origin, the first time it crosses the y=axis is at t=pi/2,isn't it?

شكرا

thank you so much

It's easier than what it sounds

Cool spiral! 😊

thank you so much!

Marvellous💯

The plot of t*cos(t), t*sin(t) is equivalent as if you drew a circle with a compass whose legs are being constantly stretched.

Vocie of 3blue1brown

the best source

parameter is just kind of a fancy word for input

Can this explain the shape of galaxies?

What is the function that draws the same graph??

Hey! That's 3Blue!Brown!! 😁

Which tool are you using to draw these parametric functions?

wrg, no problx about that, can do anyx

What is the second function?

what software do you use to plot these? Excel or something else?

pls someone should help me out with this assignment Calculate the frenet apparatus for the parameterized curves alpha(t) = (3t-t³,3t²,3t+t³)

is it just a coincidence that this looked like the golden spiral?

How pi/2 is 1.7?

There's a type of parametric curve everyone has missed. graph a slice of a circle no bigger than a semicircle then change one of the radius lengths. Now progress the one radius length to the other radius length in the simplest linear way you should find that for any triangle every side has a corresponding curve. In 3D this also works for curved surfaces on the faces of any tetrahedron. Not only that but you can change how the one radius progresses to the other radius and this even works in 3D if you want to say add bumpiness or roughness to a human face or want to flatten the curvature a bit to represent well the face of wall. Not only this but the surface setting on the triangle can also represent coloring of the surface. In terms of video compression this technique can allow for a very upscalable image be the curvature of smaller detail not as advanced you could also save a lot on data size of the video stream.

hi

dear sir on which axis 't' value has to take?

How π/2 is 1.7?????

Can we say that F(t)=F[x(t),y(t)] in a two dimensional cartesian system?

3 brown 1 blue voice?

Holy crap you sound so different! I'm on my phone so I can't see the date...but if I had to guess, this video is >10 years old

I dont have Ocd, but come on man! Take an extra second to draw something more like a circle! What even is that! D,: that's on the same level as taking a bite of a KitKat without breaking them apart first, it's so Antisatisfying to look at

Why is cos(0) = 0 in this? my life makes no sense .....

Is there a reason you call it "parametric function" instead of path/curve? From my experience thats not only the denomination always used in maths but also sounds a lot more intuitive and less intimidating. Maybe its just this way in my classes though but the only time I ever heard "parametric function" was in my programming lessons. Edit: Ok now I feel stupid. THe domain of curves and paths are just intervalls aren'T they? I guess parametric functions can have a domain in the whole real numbers?