Wolfram Demonstrations Project

The parametric plot shows the transformation of the polar coordinate lines under the Möbius transform

. The point

is the image of 0, and

is the image if

. Transformation of the complex plane (in polar coordinates) under a Möbius transform can be observed by dragging the two points.

The code for computing the parameterization is from R. E. Maeder, Computer Science with Mathematica, Oxford: Cambridge University Press, 2000.

Contributed by: Roman E. Maeder

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Möbius Transforms