Recent content by timo1023

The wikipedia article does not reference my specific scenario. I first parametrized all surfaces of revolution, then calculated the first and second fundamental forms, and then used that to find the Gaussian curvature. I simplified it heavily, and got the answer I showed to you. I am nearly 100%...

I appreciate the reply. I have a question that is related to the context of the problem. The original equation that I posted is one that I calculated for the Gaussian curvature of a surface of revolution obtained by revolving the curve \phi (v)[/tex] about the z axis. As previously stated, I...

The only k that I can find which renders it linear is k(\phi )=0; are there others? Are there any existence theorems that would be applicable for this equation? Thanks for the help.

smallphi, I have a strong calculus background, so I am very familiar with integration, however I don't know very much about differential equations. How would integrating the equation give you a 1st order DE? I need to see a simple example of how that would work. Thanks for the response.

Bump (sorry).

Hello, I have the 2nd-order nonlinear ODE below: k(v)=\frac{\phi ''(v)}{\phi (v) (\phi ' ^2 (v) +1)^2} Where k(v) is some function. I would like to investigate for what functions k there can exist solutions on a given interval [a,b]. For example, if k(v)=0, then \phi '' (v)=0 which implies...

Upon further investigation, it seems as though you are right. Here is what I came up with (please forgive my lack of precision in stating x is a positive integer, etc.): \phi (2n)=\left{|}\{x|x\leq 2n-1\}-\{x|x \textrm{ is even}\} - \{i\cdot x | x \textrm{ odd}, x|n, i \textrm{...

Hello, Last year in number theory I discovered something with Euler's Totient Function that I couldn't explain. I asked my professor and he couldn't figure it out either. Here is what I discovered: As a premise, it should be clear that phi(n)==phi(2n) where n is an odd, positive, integer...