[math-fun] This once (briefly) startled Coxeter

Every (circular) cone including an ellipse fixed in 3-space (say, z=0, x^2/a^2 + y^2/b^2 = 1) has its apex on a hyperbola (in this case, y=0, x^2/(a^2-b^2) - z^2/b^2 = 1) thru the foci of the ellipse, and every cone including that hyperbola has its apex on the original ellipse, which, of course, pierces the foci of the the hyperbola. http://gosper.org/conethm.png . Coxeter promptly stomped off to the library and found it in a 1912 book by Salmon. It seems to me that a time-variant formation of low-flying jets could superpose their shockwaves in a moving, destructive hyperbola. --rwg