Möbius transformations

This applet lets you draw points, lines, and circles, and see what happens to them under Möbius transformations. It is possible to use this applet to find the answers to most of the homework questions in Sections 7.2 and 7.3.

A Möbius transformation (also called a fractional linear transformation, projective linear transformation, or a bilinear transformation by some authors) is any map of the form w = (az+b)/(cz+d), where a,b,c,d are complex numbers. For technical reasons we exclude the case when ad-bc = 0 (for instance, the map w = (3z+6)/(z+2) is not a Möbius transform).

The applet is not as complicated as it first appears! A tutorial is given below.

Thanks to Hauke Reddmann for some suggestions.


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