Find the gaussian and the mean curvatures of

Now, I know that I have to parametrize this equation first, but I'm not sure how I should do it, please help.

Printable View

- April 19th 2008, 08:34 PMtttcomraderFind curvatures
Find the gaussian and the mean curvatures of

Now, I know that I have to parametrize this equation first, but I'm not sure how I should do it, please help. - April 26th 2008, 01:47 PMTwistedOne151
Isn't this a hyperboloid of two sheets? Are we interested in only one of the sheets, or both? As for parametrizing, consider cylindrical coordinates: that is, we can parametrize the upper sheet as

with parameters (note that u and v correspond to r and θ of cylindrical coordinates).

--Kevin C. - April 26th 2008, 02:01 PMTwistedOne151Addition
A moment of additional thought made me realize that the parametrization is simpler with hyperbolic functions: the upper sheet can be done as:

with as before.

--Kevin C.