Wasn't v created from u by lazy Roman stonecutters? Mens et Manvs -- William Barton Rogers (Ovr Fovnder). No matter what font you are using for math, I think it would be a good idea to avoid mixing u and v closely. There are so many other good pairings to choose from. -Hilarie Lost cause! Integration by parts. Do you prefer "e^u du/dx, takes the place of normal sex, ..." ? Trisectrix: I've mentioned Julian's lovely http://gosper.org/tripenta.gif here before, but in off-list conversation added: The angle being "sected" is between the x axis (not shown) and the short green rotor, whose length is 1/4. The angle's three trisectors are the cyan radii of the lesser moving circle (radius 3/4), determined by its intersection with the (unit radius) astroid (= quadricuspid hypocycloid). There are five additional intersections (magenta) whose significance we've never determined. The (quadricuspid) epicycloid is a pentasectrix when intersected with the moving circle of radius 5/4. The five legitimate pentasectors are dark blue, with three mysterious bogons in red. If you have a theory for the red or magenta bogons, Neil, Julian, & I are all ears. Also I once posed here: Given its three girths, what are the semiaxes of an ellipsoid? No closed forms? I could only find (three) series solutions (for each semiaxis). At least they converge rapidly. --rwg