There are
two animations available for downloading. One generates the hypocycloid
with the ratio of one circle to the other an integer, and the other animation
has this ratio set to a rational number. Each of these animations is available
as a QuickTime (.mov) file for Macintosh systems and also as a Video for
Windows (.avi) file for DOS/Windows platforms.
Download Macintosh versions of the animations.
Download DOS/Windows versions of the animations.
If you prefer, you can download the Mathematica 4.0 notebook Kakeya.nb in which you can set the radii of each circle and observe the different curves that are generated. It is interesting to conjecture what happens when the ratio of the radius of one circle to the radius of the other circle is (a) an integer, (b) rational, or (c) irrational.