# Friday math movie: Moebius Transformations Revealed

By Murray Bourne, 01 Dec 2007

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.

### 3 Comments on “Friday math movie: Moebius Transformations Revealed”

1. maria says:

It is beautiful! And the music too.

2. th says:

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. Murray says:

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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