Home > Mathematica, Mathematics > Upon reflection

Upon reflection

The Riemannian spherical representation of the complex plane brings wonderful  insights into complex functions. The above video illustrates complex inversion  (as per Needham), i.e.

h: z\mapsto\frac{1}{z}
This can be decomposed into:

f: z\mapsto \frac{1}{\bar{z}} (inversion)

and

g: z\mapsto\bar{z} (complex conjugation)

i.e.

h =g\circ f

On the sphere, the first operation corresponds to reflection in the plane z=0 and the second operation to reflection in the plane y =0. The composition yields a rotation of 180 degrees around the x (real axis).

The cdf of the video is here.

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Categories: Mathematica, Mathematics
  1. August 13, 2012 at 6:34 pm
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