wds>I've posted before about knots are really machines and should be analysed as such. This idea turns out not to be new. Here is a paper http://arxiv.org/abs/1002.1723 with computer simulations of knots trying to find the "tightest" form of each knot type. You can see movies of the tightening process for many knots & links here: http://www.jasoncantarella.com/movs/ Many questions suggest themselves... -- Warren D. Smith "Because their strut sets break into a particularly simple form (see pages 36 and 37), these knots may be better candidates for an explicit solution than seemingly simpler knots such as the trefoil." http://www.jasoncantarella.com/movs/3_1ac.mov (note the glitch at 8 o'clock.) Back in the day, IBM hired me to write a demo of Mathematica 1.0(?) for their RT workstation rollout. I produced a fairly tight trefoil as a helix on a torus. WRI wanted the image for a poster, but IBM refused. WRI reverse-engineered the image, but kludgily. They sent me one nicely embroidered on a T-shirt. Just rendering *any* trefoil was a big deal in those days. Are there still no explicitly solved tightenings of it (or any other true knot)? I expect the trefoil to get sorted fairly soon. A crude program of mine came up with 17 and 13 as the minimal "lengths" of the trefoil, and the subarc of the trefoil that could not spontaneously "untie itself". Evidently, I used tube diameter where the convention seems to be radius. Fred> The player spontaneously jumps back in time (Apple iMac / OS10.9.1 / Safari). Anyone else have this problem? I'd email him, if I could decipher his address! < WFL This happened for a while on my MAC, but dragging the player progress indicator seems to force it to finish downloading, and play smoothly. --rwg