For the Ovaloid where |P - F1| + k|P - F2| = c... I think it's the "simplest," even though it has fourth powers in its equation. But, you know, scare quotes. I have a hard time believing it never received interest before. The questions below are phrased as if it were a new thing. Has anyone thought of a workable mechanical construction to plot it, analogous to the string around two pins? I have been designing things with levers and pulleys and holes through the paper with no success. I think maybe a pantograph is called for... Has anyone thought of an interesting optical property, analogous to the ones ellipses and parabolas have? Maybe something about materials with different refractive indices, or coupling between two parallel eggs with different speeds of sound. Or, a dog jumps swims from island to shore with the frisbee, drops off the frisbee, and then swims faster (no frisbee drag) to the second island-- and it takes the same time no matter what point on the shore he swims to. When k = -1 it's a hyperbola. Do other negative numbers give mismatched-pair hyperbola-oids? Do they go asymptotic to straight lines, asymptotic to something else, or what? What is it a cross-section of? Does it correspond to an orbit in a strange force field? If so, is there an analog of the equal-area rule? If you make pictures before I do, I wouldn't mind if you posted them somewhere on the web. --Steve ovaltine levation olive-tan velation violante not-alive vital-one elan-vito toenail-V a-violent intel-ova naive-lot ovate-nil ion-valet ten-viola ain't-love evil-NATO