I've been telling people that the ovoid hole in the Arnold puzzle is a disappointingly nondescript image of an ellipse under a homographic transformation, but on prodding from Veit, found a surprisingly simple form, a/((b*i+c)*(i*sin(t)+d*cos(t)-1/4)+1), where a, b, c, and d are classified under the technology export act. But it occurred to me that my rattleback (a solid plastic lifesize statue of a dead banana slug, with the puzzling ability to spin only counterclockwise on a flat surface)
It rectifies time! I.e., the time-reversal of the rotation is unphysical.
might be a segment of a torus, which takes seven points to determine. And maybe even the Arnold cavity is a toric section. Alas, it isn't, but it is so close that the laser program would describe the exact same polygon, so I could claim it *is* a toric section. ("I planned it all along.") Unfortunately, the "minor" radius is nearly twice the major, so it's an ATRESIC (spindle) TORUS and needs a RESUSCITATOR. --rwg
As mentioned here a few years ago, and also in http://mathworld.wolfram.com/CassiniOvals.html, Cassini's ovals *are* toric sections. Pic: http://www.tweedledum.com/rwg/cassini.html . --rwg SECTIONED TORUS DEUTEROTONICS