[math-fun] Heronian octonions?

And finally and even more wildly --- are we eventually going to discover octonions lurking around the corner somewhere in this discussion?

--I doubt it. There is a nice characterization of 2D, 3D, and 4D (and even 5D) rotations using complex #s & quaternions. But there is no such nice characterization using octonions. I think this proof technique is only going to work up to 3D (if there).