- #1

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## Main Question or Discussion Point

1. Homework Statement

Is the gaussian curvature at a point on the surface

[tex]

\frac{1}{(x^2+y^2+1)^2}?[/tex]

2. Homework Equations

shape operator: [tex]

S(\textbf{x})=-D_\textbf{x}\hat{\textbf{n}}=\frac{\partial (n_x, n_y)}{\partial (x,y)}[/tex]

Gaussian Curvature = [tex]

|S(\textbf{x})|[/tex]

[tex]

\hat{\textbf{n}}=\frac{\nabla g}{\|\nabla g\|}[/tex]

3. The Attempt at a Solution

I basically plugged stuff into the above equations. I'm not sure if they're all correct.

Is the gaussian curvature at a point on the surface

[tex]

\frac{1}{(x^2+y^2+1)^2}?[/tex]

2. Homework Equations

shape operator: [tex]

S(\textbf{x})=-D_\textbf{x}\hat{\textbf{n}}=\frac{\partial (n_x, n_y)}{\partial (x,y)}[/tex]

Gaussian Curvature = [tex]

|S(\textbf{x})|[/tex]

[tex]

\hat{\textbf{n}}=\frac{\nabla g}{\|\nabla g\|}[/tex]

3. The Attempt at a Solution

I basically plugged stuff into the above equations. I'm not sure if they're all correct.