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

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.


Oops! You're not seeing a graph! Check your message bar at the top of the screen; make sure ActiveX controls are enabled.

Else, sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser
(Click here to install Java now)

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