# Prove its Gauss curvature K = 1

1. Nov 10, 2014

### Shackleford

1. The problem statement, all variables and given/known data

Assume that the surface has the first fundamental form as

E = G = 4(1+u2+v2)-2

F = 0

2. Relevant equations

K = $\frac{-1}{2\sqrt{EG}}[(\frac{E_v}{\sqrt{EG}})_v + (\frac{G_u}{\sqrt{EG}})_u]$

3. The attempt at a solution

Ev = -16v*(1+u2+v2)-3

Gu = -16u*(1+u2+v2)-3

When I take the partials and find K, I get something messy that doesn't lead me to the conclusion that K = 1.

2. Nov 11, 2014

### RUber

Start by substituting E=G and \sqrt(EG) = |E|.
What did you end up with?

3. Nov 11, 2014

### Shackleford

Thanks for the reply. I found my error a little bit ago. For some reason, I kept using the denominator of E and G AS E and G. -_- It was late, so I'll credit it to sleep deprivation. Heh.