Wonderful Mobius Transformation Video

Via The Art of Problem-Solving, a great video on Mobius transformations. I never really got how the inversion transformation fit in with the others before seeing this!

0 thoughts on “Wonderful Mobius Transformation Video

  1. Xanthir, FCD

    That’s awesome, Mark! It’s really interesting how geometry all fits together.
    I wonder if the sphere analogy was intended originally, or if it was merely realized later that the Mobius transformations correspond to simple movements on a sphere?

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  2. Crow

    Wonderful. This is one of the best pieces of mathematical educational material I’ve ever seen. But more than that, this is one of those “isn’t the universe we live in cool” moments for me. When you can combine education with that kind of wonder and delight, you’ve really got something good.
    Huge kudos to the authors.

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  3. Vlad Shcherbina

    Overwhelming! I feel burning interest to complex analysis after your movie. A great moment of enlightment (both literally and allegorically). Thanks.

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  4. CCP

    I don’t know from math, but this was really beautiful on a purely visual level. Too bad about the sedate piano accompaniment…those colors seem more suited to an Anthem of the Sun-era Grateful Dead soundtrack, man.

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  5. Stephen Wells

    Two minutes ago I didn’t even know what a Mobius transformation was. Seeing that inversion in the plane corresponds to rotating the projective sphere- that was truly enlightening. Does this generalise to higher dimensions?- e.g. can I think of an inversion in 3-D space as corresponding to rotation of a projective hypersphere?

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  6. Jonathan Lubin

    Very nice indeed. Some years ago, I tried to do similar things for the Hyperbolic Plane, but while I came up short, these guys succeeded brilliantly. The Schumann was good accompaniment, but I too would have preferred something a little jumpier. Maybe Feltsman doing a fugue from the WTC.

    Reply

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