This app would be pretty straightforward to implement, say in Java. But you don't want two planes --- one suffices, the mouse dragging z while f(z) is displayed in a different colour. It might be worth displaying the previous history of each point as a curve, optionally wipeable. Nice project for an undergrad graphics course maybe? WFL On 8/30/14, James Propp <jamespropp@gmail.com> wrote:

Viewing David Eisenbud's Numberphile video http://www.numberphile.com/videos/fundamental_theorem_of_algebra.html makes me wonder if anyone's created a better animation of this proof (note that the animation in the video treats the image of a circle centered at 0 under a polynomial map of degree n as just a circle, rather than a funky curve with winding number n).

For that matter, it'd be neat to have an app that shows two copies of the complex plane: you get to move z around in one plane, which causes f(z) to move around appropriately in the other plane, and your goal is to move f(z) toward 0 by moving z as needed. Does such an app exist?

Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun