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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.
Contributed by: Roman E. Maeder (March 2011)
Open content licensed under CC BY-NC-SA
The code for computing the parameterization is from R. E. Maeder, Computer Science with Mathematica, Oxford: Cambridge University Press, 2000.
Wolfram Demonstrations Project
Published: March 7 2011