Affine polygons: This applet extends Napoleon's theorem from a triangle to a generalized n-gon. I have not proved that the theorem implied is true. (I have also not implied that the true theorem is proved.)

Midpoint Porism: These applets demonstrate a new (to me) porism involving the midpoints of inscribed polygons. I have proved that the porism holds for triangles, and quadrilaterals, but not for higher order polygons.

I'd like to hear by email if you know about these in the literature or can prove something new. Enjoy.

Stars: This applet draws stars with different numbers of vertices and spacing.

Tiling Transformer This applet allows you to modify tilings to create other tilings.

Celtic Knots This applet lets you create celtic knot designs.

I would like to thank The Vestibules for their funny song "Bulbous Bouffant." This seemed like a song that needed to have a math version since so many students get stuck on math vocabulary. Here is my version: Obtuse Angle.

And of course there is a walking fire warrior and antisocial wizard designed by my son Matthew Berglund.