jonathanrogness
jonathanrogness
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Moebius Transformations Revealed
A short film depicting the beauty of Moebius Transformations in mathematics. The movie shows how moving to a higher dimension can make the transformations easier to understand.
The full version is available at www.ima.umn.edu/~arnold/moebius/
The background music (from Schumann's Kinderszenen, Op. 15, I) is performed by Donald Betts and available at www.musopen.com.
Переглядів: 2 141 210

Відео

КОМЕНТАРІ

  • @manfredbogner9799
    @manfredbogner9799 Місяць тому

    Sehr gut

  • @josephdays07
    @josephdays07 2 місяці тому

    Wow I am very impressive with your job. I have developed the same graph with Trigonometric Partitions Equations. ua-cam.com/video/Xd8V9ST1RDg/v-deo.htmlsi=gISfQb2K2XuIMiSi

  • @masela01
    @masela01 4 місяці тому

    morbious transformations (really sweet visualization though)

  • @sabaztrevolviouz1702
    @sabaztrevolviouz1702 4 місяці тому

    I don't know but is this related? A Line has 2 point on its edge A Square has 4 line on its edge A Cube has 6 square on its edge . . And A Tesseract has 8 Cube on its edge?

  • @kchromaticpiano
    @kchromaticpiano Рік тому

    Wow, this is so cool!

  • @nova-nj7ge
    @nova-nj7ge Рік тому

    I dont know whats going on but if this was done with an equation ima just say it ur a genius

  • @phmfthacim
    @phmfthacim Рік тому

    So beautiful, thank you, this video changed my life years ago when I first saw it!

  • @xue8364
    @xue8364 Рік тому

    hello from 2023

  • @mastershooter64
    @mastershooter64 Рік тому

    I think this was the video Terrance Tao was talking about in that talk.

  • @ElliottBrownWX
    @ElliottBrownWX 2 роки тому

    Morbius transformations

  • @stephanieshepherd3704
    @stephanieshepherd3704 2 роки тому

    This has been one of my favorite videos for so long that it is like an old friend. Great choice of music. Schumann Kinderszenen opus 15 number 1 beautifully played by the late Donald Betts.

  • @KarlLew001
    @KarlLew001 2 роки тому

    Wow! Thanks! I'm here from researching the Z-Transform. I needed a concrete visual and THIS is it. THanks!

  • @CHAS1422
    @CHAS1422 3 роки тому

    Casper the friendly ghost is a Moebius 1:02

  • @ДенисНовиков-з8и
    @ДенисНовиков-з8и 3 роки тому

    Кто от Ульянова - ставьте лукас!

  • @brendawilliams8062
    @brendawilliams8062 3 роки тому

    Thankyou

  • @harriehausenman8623
    @harriehausenman8623 3 роки тому

    Legendary!

  • @pyrole
    @pyrole 4 роки тому

    I want to pay you money for taking time to build this animation Seriously, I felt spell bound...Thanks so much

  • @Rodric380
    @Rodric380 4 роки тому

    This is beautiful indeed

  • @teslaonly2136
    @teslaonly2136 4 роки тому

    I am here because of this paper: Data augmentation with Mobius transformations

  • @DeeHarvey
    @DeeHarvey 5 років тому

    I love having my mind blown so gently.

  • @jamesgriebler
    @jamesgriebler 5 років тому

    The greatest video I've seen on mobius transformations

  • @adriannowak485
    @adriannowak485 5 років тому

    What software can be used to do that?

  • @imranq9241
    @imranq9241 5 років тому

    Anyone here from Terence Taos talk?

  • @davidfuller1061
    @davidfuller1061 5 років тому

    hbar / ((27pi) / 13) = 1.61624007e-35 m^2 kg / s photos.app.goo.gl/3KXBCDiV2ECJ2wkr9 photos.app.goo.gl/L2cKcqhLpGntNdjE8 photos.app.goo.gl/pUgd18b2S5ZksnB79 ((27pi) / 13) / c = 2.17645445e-8 kg exactly ((27pi) / 13) * c = 1.9560997e+9 joules exactly (27pi) / 13 = 6.52484628053 momentum exactly

  • @bordershader
    @bordershader 5 років тому

    I wonder what Bernhard Riemann would say about this, if he could see this video? I bet his mind would be blown. Back in his day I bet all mathematicians had to imagine and visualise, rather than having a handy animation to do the visualising for them. That's quite mindblowing, really. I mean, maths is hard enough for me to get my head around, let alone having to imagine it all rather than see it. Pairing this with the Schumann is inspired, by the way.

  • @raylin4635
    @raylin4635 5 років тому

    Wow... Purdy colors😱

  • @QuiteDan
    @QuiteDan 6 років тому

    Alright gang let's see who the Moebius Menace really is! *takes off mask* GASP! Old man Sphere Projection!

  • @EyeoftheAbyss
    @EyeoftheAbyss 6 років тому

    In HD: ua-cam.com/video/0z1fIsUNhO4/v-deo.html

  • @kockarthur7976
    @kockarthur7976 6 років тому

    A rotation of the Riemann sphere about a horizontal axis does not represent an inversion of the complex plane. It represents an inversion and a rotation (combined). The true sphere representation of an inversion corresponds to reaching through the sphere, pinching the other side, and pulling it through, i.e. literally turning it inside out (inverting it). In the case where the inversion swaps zero and infinity, one would reach directly through the diameter of the sphere, and hence the transformation is equivalent to mirroring across a horizontal plane.

  • @llewgibson
    @llewgibson 6 років тому

    I found your video mate, really love the content. Subbed straight away, We should connect!

  • @ffhashimi
    @ffhashimi 6 років тому

    Another proof that a picture worth a thousand words, Great job

  • @basharatmalik3005
    @basharatmalik3005 7 років тому

    beauti

  • @brenoakiy
    @brenoakiy 7 років тому

    jump scare at the end

  • @pronounjow
    @pronounjow 7 років тому

    But what happens when you move part of the sphere below the plane? Right-side up and upside-down?

  • @theo1395
    @theo1395 7 років тому

    This is very clear. Thank you !

  • @tonymaric
    @tonymaric 7 років тому

    What pulchritude.

  • @bordershader
    @bordershader 7 років тому

    I've come back to this vid over and over across the years. There's something about it that gives me great peace and satisfaction.

  • @KekzZor
    @KekzZor 7 років тому

    Meier brought me here!

  • @Se-pk8lg
    @Se-pk8lg 7 років тому

    Amazingly simple and beautiful!

  • @ccitza
    @ccitza 8 років тому

    most stunning video ever seen on youtube

  • @talss56
    @talss56 8 років тому

    Marvelous.

  • @이재환-t2d
    @이재환-t2d 8 років тому

    Wow, this video sure is a good demonstration of the Moebius Transformations. But I think there would be a problem if the figure on the sphere is not a lattice shape when explaining inversion. I did a quick calculation and I came to the conclusion that it would be a true inversion for any kind of figure on the sphere if the sphere and the figure on it is mirrored by a z=r plane(where r is the radius of the sphere) This certainly can not be accomplished by just rotating the sphere

    • @holopaste
      @holopaste 6 років тому

      aren't Mobius transformations orientation-preserving?

  • @wedmunds
    @wedmunds 8 років тому

    Came here from Apophysis.

  • @proxima_fish
    @proxima_fish 8 років тому

    Anyone here from MathPath?

  • @MrWillvee
    @MrWillvee 8 років тому

    This is so great!! What software did you use to animate this :)

  • @OrionoftheStar
    @OrionoftheStar 9 років тому

    Then, put a hypersphere above THAT sphere!

    • @jesusnthedaisychain
      @jesusnthedaisychain 8 років тому

      You are a madman and I will have no part of this insanity!

    • @noahwilliams8996
      @noahwilliams8996 7 років тому

      I intend to fund your research into this! :O

  • @ayhankaraoglanlar5346
    @ayhankaraoglanlar5346 9 років тому

    ...

  • @ethanpavelsky2571
    @ethanpavelsky2571 9 років тому

    omg i just did archive and saw this on youtube when it was 1st made

  • @tranceasylum7537
    @tranceasylum7537 10 років тому

    ...No comments...\o/...<3...

  • @Phi1eap
    @Phi1eap 10 років тому

    Hello, I would like to make similar animation on my own, but instead of sphere, place different shaped object. I'm not trained in Blender or similar soft. Could someone give me a hint how to easily made something like that (if easily is possible)? Maybe share softwere name, or even project where I could just replace the object?

    • @yakoudbz
      @yakoudbz 9 років тому

      If you have a little experience in programming, use something like shadertoy.com It's a site that display the webgl result of the fragment shader you created. a fragment shader is simply a program that is executed for each pixel of the screen in this case. The xy coordinate of the pixel are given by gl_FragCoord. you can manipulate all that to give the right color to your pixel