Friday math movie: Moebius Transformations Revealed

1 Dec 2007 · Posted in Computers & Internet, Math movies, Mathematics 

This is cool.

According to this Wikipedia article, a Möbius (or in anglicised form, ‘Moebius’) Transformation is the result of performing…

a stereographic projection from a plane to a sphere, rotating and moving that sphere to a new arbitrary location and orientation, and performing a stereographic projection back to the plane.

The mathematics involves matrices, determinants, transformational geometry (translation, rotation, dilation), complex numbers, group theory, conic sections (parabola, ellipse, etc) and iterations.

Apart from all that, it is a nice visual piece with an appropriate soundtrack (a piano solo that I used to play, from Schumann’s Kinderscenen, Op. 15, I) . The movie has been accessed almost a million times on YouTube.

Enjoy.

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Comments

3 Responses to “Friday math movie: Moebius Transformations Revealed”

  1. maria on December 2nd, 2007 4:26 am

    It is beautiful! And the music too.

  2. th on December 5th, 2007 8:12 pm

    Thanks for this video. It;s amazingly beautiful.
    I have enjoyed your links and vast information on Math. I have learnt a lot.
    Keep it up!

  3. zac on December 5th, 2007 8:16 pm

    Hi Maria and “th” – I’m glad that you enjoyed this math movie. It certainly presses a few buttons in us (artistic, mathematical, musical).

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