
GaussBonnet help
We found out how to figure out GaussBonnet for spherical geometry in our class, which was using the sum from 1 to n of (alpha + beta + gamma)  pi and turning this into 2piX(x).
We are supposed to try to find GaussBonnet for hyperbolic and Euclidean. I think I can get it for hyperbolic, it seems very similar to spherical. However, Euclidean he said to work backwards? I'm confused with this, it seems like it is trickier and I don't know where to start.

Applying the GaussBonnet theorem for Euclidean space is much more simple than its nonzerical counterparts. Consider a triangle with angles $\displaystyle a, b, c$.
We know the Gaussian curvature is zero, so all we have to do is sum the jumps of the tangent at each vortex, which ofcourse is $\displaystyle \pia+\pib+\pi  c=3\piabc$. So we end up with $\displaystyle 2\pi(3\piabc)=0$ or $\displaystyle a+b+c=\pi$, a result old Euclid would agree with.