DanA> A few years ago I tried to solve for the tightest (smallest constant slope) helical rope about the z-axis in R^3. I.e., the lowest-slope helix about the z-axis such that if each point P of the helix has a flat, closed, perpendicular disk of radius = 1 centered at P that touches the z-axis, the interiors of all such disks are disjoint. This results in a transcendental equation that can only be solved numerically, but it was a fun endeavor and is in some sense the simplest "tightest-knot" type question I can think of. --Dan It might be easier to think in terms of a moving sphere. Was your equation amenable to Lambert-W, or equivalent to Kepler's? (http://www.tweedledum.com/rwg/pizza.html) Did you grab 20 digits and ask http://isc.carma.newcastle.edu.au ? In any event, I'd count this as resoundingly solved. All we need is *any* system of equations admitting routine numerical methods. --rwg