Möbius Transformations

Time for a little math/geometry lesson. The following is an awesome video graphically representing Möbius transformations, first simply by themselves (which might make them appear difficult and not worth your time), but then they are shown as simple three-dimensional stereographic projections over the Reimann sphere.

As you may or may not know, one of Rene Descartes' greatest contributions to mathematics is the synthesis of algebra and geometry into analytic geometry (and the subsequent cartesian coordinate plane); similarly, Reimann's greatest contribution to math was probably the merging of projective geometry and complex number theory into what is now known as Reimannian Geometry, which set the stage for the possibility of Einstein's general theory of relativity.

I'm not really sure why they are called möbius transformations, but the name reminded me of a möbius strip, so I'll be making an entry on a couple of awesome geometric/topological objects soon. You won't want to miss that... it'll be your chance to do a little hands-on experimenting with infinity... how awesome would that be?
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