Describing rotation in 3d with a vector

Тәжірибелік нұсқаулар және стиль

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Learn how a three-dimensional vector can be used to describe three-dimensional rotation. This is important for understanding three-dimensional curl.

Пікірлер: 45

  • @neopalm2050
    @neopalm20506 жыл бұрын

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

  • @Rocky-me5cw
    @Rocky-me5cw6 жыл бұрын

    π creatures are now on khan academy too. #πFever

  • @jvcmarc
    @jvcmarc6 жыл бұрын

    3blue1brown is slowly taking over KhanAcademy

  • @cyancoyote7366

    @cyancoyote7366

    6 жыл бұрын

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

  • @frognik79
    @frognik796 жыл бұрын

    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.

  • @vigneshwarm
    @vigneshwarm5 жыл бұрын

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

  • @ONS0403
    @ONS04035 жыл бұрын

    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.

  • @FernandoVinny
    @FernandoVinny7 жыл бұрын

    This guy is from 3Blue1Brown

  • @janApen

    @janApen

    6 жыл бұрын

    Fernando Gonzaga yep he talks about it all the time.

  • @anujarora0

    @anujarora0

    6 жыл бұрын

    Matthew Ripley ikr

  • @DavidsKanal

    @DavidsKanal

    6 жыл бұрын

    This guy IS 3Blue1Brown

  • @janApen
    @janApen6 жыл бұрын

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

  • @adamroer3908
    @adamroer39085 жыл бұрын

    Thank you this was really helpful

  • @zts99
    @zts998 жыл бұрын

    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

    @3blue1brown

    8 жыл бұрын

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

  • @mohammedzerrak5639

    @mohammedzerrak5639

    6 жыл бұрын

    You are the best man , very intuitive and clear

  • @dqrksun

    @dqrksun

    2 жыл бұрын

    @@3blue1brown Whoa

  • @ChatGPT-

    @ChatGPT-

    4 ай бұрын

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

  • @namitanene3531
    @namitanene35313 жыл бұрын

    The pi creature looks so cute when its rotating 😣✊

  • @stutteringcris468
    @stutteringcris4682 жыл бұрын

    Very important for game development!

  • @huyngo1630
    @huyngo16306 жыл бұрын

    That convention resembles the right hand rule in electromagnetic.

  • @soeinspast4096
    @soeinspast40962 жыл бұрын

    Woah its Grant Sanderson!!

  • @diqnu
    @diqnu3 жыл бұрын

    @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?

  • @giridharpalvai7516
    @giridharpalvai75164 жыл бұрын

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

  • @roygalaasen
    @roygalaasen4 жыл бұрын

    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
    @TheAbdelwahab836 жыл бұрын

    thanks; but where are next videos???

  • @shenelf240
    @shenelf2404 жыл бұрын

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

  • @giridharpalvai7516
    @giridharpalvai75164 жыл бұрын

    Rotation is always up word direction ?

  • @Magnawulf
    @Magnawulf6 жыл бұрын

    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

    @kangalio

    6 жыл бұрын

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

  • @descai10

    @descai10

    6 жыл бұрын

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

  • @That_One_Guy...

    @That_One_Guy...

    4 жыл бұрын

    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).

  • @feiwang9892
    @feiwang98926 жыл бұрын

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

  • @joschistep3442
    @joschistep3442 Жыл бұрын

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

  • @layer1087
    @layer1087 Жыл бұрын

    Surprised to see 3blue1brown here 😍

  • @harishthethird
    @harishthethird4 жыл бұрын

    A FREAKING PI CREATUREEEE

  • @putinstea
    @putinstea Жыл бұрын

    Yo it's my boy 3blu 😄

  • @luvley5323
    @luvley53234 жыл бұрын

    The pi creature!

  • @jj8614
    @jj86146 жыл бұрын

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

  • @ch.ajaysingh
    @ch.ajaysingh5 жыл бұрын

    Poor π creature!

  • @aienbalosaienbalos4186
    @aienbalosaienbalos41863 жыл бұрын

    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.

  • @randomstuff9960
    @randomstuff99603 жыл бұрын

    Here comes the pi creature...😃😃😃

  • @arnavkumar3060
    @arnavkumar30605 жыл бұрын

    We use the right hand rule every night.

  • @NeostormXLMAX

    @NeostormXLMAX

    5 жыл бұрын

    Arnav Kumar what if you’re a lefty

  • @212_umairathar9

    @212_umairathar9

    5 жыл бұрын

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

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