Assuming that the radius vector should always be normal to the tangent of the circumference, am I right to assume that if the surface curvature is such that rho=constant, the ratio will be exactly the same (Pi)? Otherwise, it's obviously no longer a constant.
Does the randomness allow for numbers to be generated twice? If not, it should be exactly the same as trying to enumerate the set of integers, which is infinite. If it does, on the other hand, it just makes things worse as the probability of a particular integer to be generated is even smaller.
I wasn't quoting the links, just that sentence; my personal experience of women in science is that they are sometimes biased against women, including themselves :)
I'm not sure I managed to get the message across. What I'm trying to say is that I have observed exactly what the OP is describing: many of my female colleagues do feel like the males are more capable/smarter (which is obviously nonsense).
This is what I'm talking about. Most men I know don't...
I'm in my fourth and final year of grad school in applied mathematics and software engineering. I have met and worked with many people, so here are my observations for my particular societal group of a few dozen people in science. I make no claim that these things are true in general, but they...
I'm a little confused about Pf and P0. If I understood correctly, where I now read P0, it should be Pf? If so, P0 is probably the initial condition you will use to solve your equation. Your final equation is pretty easy to solve (unless I'm missing something), considering it's full of constants...
Indeed, there is great interconnection between real and complex analysis. In fact, there is a rigorous method to calculate real integrals using complex analysis (using Cauchy's residue theorem).
What exactly is your question? Is it how to solve the system of equations? Have you tried plugging your system into a numerical solver? It is highly non-linear so I don't see much hope in deriving a closed form solution.
Xmmmm but shouldn't there be an ideal inner to outer radius ratio and angular momentum combination for which it doesn't collapse on itself? So to speak if you had a cosmic mold to create the planet and just put it there and spin it, it would stay there.
P.S. It would probably need to be smaller...
It's not spherical coords but maybe this video can help you out if you haven't watched it already (the drawing starts at about 4.00):
http://www.youtube.com/watch?NR=1&v=AKPZkHvqTao&feature=endscreen
Although in physics, 4th dimension is usually regarded to be 'time'. Therefore, your representation would be the cube's shape and position as time passes (so, a bunch of different plots of cubes).