I was badly mistaken on both counts: a) because I didn't read the problem carefully. b) because I just plugged the equation given by Ed into the somewhat buggy Mac Grapher utility, *and* I didn't look at the equation carefully. Obviously the cubic equation does have (x,y) <—> (y,x) symmetry. Duh^2. I knew the Grapher utility has a lot of bugs, which I've been nagging Apple to fix for over 10 years. (They're still bundling the identical version with new Macs. And yeah, there's that thing about a person who does the same behavior over and over but expects something different to happen.) But I had no idea the Grapher utility was *that* buggy! This is really a terrible piece of garbage. —Dan
On May 18, 2016, at 4:03 PM, James Propp <jamespropp@gmail.com> wrote:
a) I don't understand why, with the problem having the symmetry of the square, the curves seem to have only (x,y) <—> (y,x) symmetry
and
b) that doesn't seem to be the right equation of the cubic curve that I see, both because it lacks (x,y) <—> (y,x) symmetry, and its shape doesn't seem right.