Describing rotation in 3d with a vector

[@neopalm2050]

It's official. Khanacademy has been graced with the presence of a pi creature. Grant has fully joined team Khan.

[@Rocky-me5cw]

π creatures are now on khan academy too. #πFever

[@jvcmarc]

3blue1brown is slowly taking over KhanAcademy

[@cyancoyote7366]

Nothing wrong with that. Sal, if you're reading this, you're awesome as well.

[@frognik79]

Came here (and elsewhere) after watching a Quaternions numberphile video saying you need 4 dimensions to describe 3 dimensional rotation, 1 scalar + 3 vector. The right hand rule + vector magnitude is a really smart idea for getting the scalar inherently.

[@FernandoVinny]

This guy is from 3Blue1Brown

[@janApen]

Fernando Gonzaga yep he talks about it all the time.

[@anujarora0]

Matthew Ripley ikr

[@DavidsKanal]

This guy IS 3Blue1Brown

[@ONS0403]

The pi creature coupled with Grant's voice literally made me think I was watching 3blue1brown videos. I didn't realize this was Khan until the video ended.

[@namitanene3531]

The pi creature looks so cute when its rotating 😣✊

[@zts99]

Great videos. They are wonderful conceptual understandings for the intuition behind the mechanics. Are you the same mind behind 3blue1brown ? voice and style are nearly identical. And if yes, when did you jump on the Khan team ?

[@3blue1brown]

Yup! I came on around October, but up until recently I had been focussing on non-video content.

[@mohammedzerrak5639]

You are the best man , very intuitive and clear

[@dqrksun]

@@3blue1brown Whoa

[@ChatGPT-]

​​@@3blue1brown I was not sure it's you .. until I saw pi creature rotating on the screen 😂🤨🤨 Thankyou you very much for the videos 😊

[@vigneshwarm]

Ah! I can finally see the pi creatures in Khan Academy.

[@stutteringcris468]

Very important for game development!

[@janApen]

I love you! ... I.. I mean I love your math.

[@huyngo1630]

That convention resembles the right hand rule in electromagnetic.

[@Magnawulf]

Is it really possible to describe all rotations in 2D with one number? Aren't you also forgetting about the center of origin of the rotation? That's not convention, it's something that can vary. It doesn't seem possible to map every point to it's rotated image using one number (theta in your case), you would need a two dimensional number like a vector right? Similarly wouldn't you need a 3 dimensional number to talk about rotation in 3d?

[@kangalio]

Rotation around some point = Rotation around center + Moving in a circle

[@descai10]

The position is a 2-dimensional vector, the rotation is a single number.

[@That_One_Guy...]

Center of rotation can be translated into origin then retranslated back after rotation, as for. In 2D rotation you can use 1 angle variable using rotation matrix, so does with 3D rotation (but it's fixed to an axis rotation) . If you want a fluid and flexible rotation in 3D (that can form a sphere and not gonna need center of rotation) you would need what's called Quarternion, it's a 4D number (consisting of 3 imaginary number + 1 real number; no angle variable needed).

[@roygalaasen]

I know Grant has been doing videos with Khan Academy before, and I was sure that I was watching Khan Academy, but when the pi figure appeared spinning around on my screen I had to double check that I hadn’t actually stumbled onto 3b1b channel instead.

[@TheAbdelwahab83]

thanks; but where are next videos???

[@shenelf240]

it is like that curl3D(x,y,z) = (curl2D(yz),curl2D(zx),curl2D(xy))

[@joschistep3442]

1:53 so now it's official. It really doesn't matter.

[@diqnu]

@Khan Academy: I´m confused with one thing: We are able to describe a rotation (spin) by a vector of course. But adding two of them will result in one new single-axis spin representation. Though: This can´t be right: A 1-Hz-spin around the x-axis combined with a 10-Hz-spin around z-axis is definitely not the same as single-axis rotation around (1, 0, 100), is it? So, spin vestors aren´t real vectors in the sense of a vector space? How are multi-axes spins descibed mathematically then?

[@feiwang9892]

ha this π comes from the videos from 3 blue 1 brown =D

[@layer1087]

Surprised to see 3blue1brown here 😍

[@giridharpalvai7516]

Rotation is always up word direction ?

[@giridharpalvai7516]

I am learning cmm machine possible to give rotation and transaction topics information

[@adamroer3908]

Thank you this was really helpful

[@jj8614]

I was 3 min through the video considering its 3blue1brown channel lol

[@harishthethird]

A FREAKING PI CREATUREEEE

[@luvley5323]

The pi creature!

[@aienbalosaienbalos4186]

To use a vector, you are limiting yourself to rotations in 3D, because only then is the normal of the plane of rotation a vector. Furthermore, the rotation is on a plane, why would it's definition involve a vector in a other, unrelated dimension? Which is why, in my opinion, and I think the opinion of most people that have heard of geometric algebra, it makes more sense to define the plane of rotation. To define a plane you would need 2 numbers, leaving the third number for the speed of rotation. In some contexts, an oriented plane with a magnitude is called a bivector. If you are interested, search a quick video about geometric algebra and bivectors.

[@putinstea]

Yo it's my boy 3blu 😄

[@arnavkumar3060]

We use the right hand rule every night.

[@NeostormXLMAX]

Arnav Kumar what if you’re a lefty

[@212_umairathar9]

Liar it is 3D rotation . We are not finding the direction of current

[@ch.ajaysingh]

Poor π creature!

[@randomstuff9960]

Here comes the pi creature...😃😃😃