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.
See the 3 Comments below.