Given $\displaystyle \{(u,v) \in R^2|u^2+v^2<1\}$ with $\displaystyle E=G=\frac{4}{(1-u^2-v^2)^2}$ and $\displaystyle F=0$. How do I show that an euclidean circle with center at the origin is a hyperbolic circle?
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Calculate the Gauss curvature on such a circle.
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