SLD
Contributor
So, just playing around with a graphics program, and using spherical coordinates, phi, rho and r. I graphed this equatio:
here is the result:
Rather odd looking fu cation. The bumpiness is due to the limits of the program, but clearly part of the domain of this function is indeed a smooth manifold. But it doesn’t look like all of it is. Is there a mathematical way to determine whether it is Everywhere?
You can obviously differentiate it with respect to phi and rho. But just visually it doesn’t look like it’s a smooth manifold everywhere.
I’ve created a few other odd ones that I’m not sure about either.
here is the result:
Rather odd looking fu cation. The bumpiness is due to the limits of the program, but clearly part of the domain of this function is indeed a smooth manifold. But it doesn’t look like all of it is. Is there a mathematical way to determine whether it is Everywhere?
You can obviously differentiate it with respect to phi and rho. But just visually it doesn’t look like it’s a smooth manifold everywhere.
I’ve created a few other odd ones that I’m not sure about either.