Möbius Transforms

​
The parametric plot shows the transformation of the polar coordinate lines under the Möbius transform
f(z)=
a+bz
1+z
. The point
a
is the image of 0, and
b
is the image if
∞
. Transformation of the complex plane (in polar coordinates) under a Möbius transform can be observed by dragging the two points.

Details

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

References

References for demonstration.

External Links

Möbius Transforms (Wolfram MathWorld)

Permanent Citation

Roman E. Maeder
​
​"Möbius Transforms"​
​http://demonstrations.wolfram.com/MoebiusTransforms/​
​Wolfram Demonstrations Project​
​Published: September 25, 2024