Jon Ziegler points out some nice stuff @ http://johncarlosbaez.wordpress.com/2013/12/03/rolling-hypocycloids ,<http://johncarlosbaez.wordpress.com/2013/12/03/rolling-hypocycloids> to which I add Julian's http://gosper.org/sidereal.gif (the numerals record full rotations) and http://gosper.org/tri-penta.gif , showing how the quadricuspid hypocycloid is a trisectrix and the epicycloid is a pentasectrix. The former construction produces all three angular solutions, plus five other angles for which we've never found a purpose. The epicycloid produces all five solutions plus three "superfluons". Both animations are supplanted by Manipulators in http://gosper.org/tri-pentasect.cdf , which includes the source code and some explanatory text. It might be instructive to roll hypocycloids on epicycloids, and vice versa. --rwg <http://johncarlosbaez.wordpress.com/2013/12/03/rolling-hypocycloids>