Möbius Transformation Acting on S_1
** New! See version 2 here. **
This is a partial, wandering attempt at the problem, "Which Möbius transformations fix the unit circle?" In particular, the applet calculates the images of E, F, and G under T(z)=(Az+B)/(Cz+D).
Move the green points A, B, C, and D freely. You can also move the black points E, F, and G along the unit circle.
To reset the graph, click the icon in the top right corner.
Enjoy!
A result of this approach? The following conditions:
|BC-AD|=|D|^2-|C|^2 and (|D/C|^2-1)AC^2=AD^2-BCD.
One example you can try above is A=(-4,2), B=(-2, -2), C=(2,-2), and D=(4,2).
Tim Cieplowski, January 3, 2010, Created with GeoGebra |