I like your second approach. Since the 2-sphere is simply-connected, every map f:S^2 -> T^2 lifts to the universal cover (i.e., lifts to a continuous map F:S^2 -> R^2.) This lift is unique up to the choice of a point in the fiber above f(1,0,0), where I'm assuming (1,0,0) to be the chosen...
Thanks for sharing your updates, Nick. It's totally cool to watch the progress and hear about the learning process. Good luck next term; I hope you keep this thread alive for part 2!
Hi, all,
I have a question about coloring a 3D parametric surface in Mathematica.
Setup:
Take as given a surface M in R^3 and a parameterization of that surface p:[a,b] x [c,d] -> R^3. Let f:M -> R be a function defined on M.
Question:
How can I plot this surface so that points p...
OK, I think I've formulated a better question, one closer to my actual confusion.
In geometric terms, we define a rotation to be an orientation-preserving isometry that fixes some point p. Thus, a rotation is a map with properties.
In everyday terms, however, a rotation is a...
Thanks for the reply.
Since I'm mostly interested in the geometry and mathematics involved, I'm assuming that Earth is spherical. My main concern is the use of one-parameter group actions to model time-dependent rotations. As a mathematician, whose specialties are far afield from physics...
Does anyone know of a good mathematical reference covering the use of one-parameter group actions to model rotations of planets and/or other rigid bodies?
Thanks in advance!