I want to prove that the shapes are isometric. How to prove?
There is no info except for the picture. First of all I need to write surface patches. Please can someone help me?
The definition of isometry: let $S_1$ and $S_2$ be two regular surfaces. Let $f: S_1 \to S_2$ be diffeomorphism. $f$ is isometry if the length of $\gamma$ in $S_1$ must be equal to the length of $f\circ \gamma$ in $S_2$ for any curve $\gamma$ in $S_1$. i.e $L_{S_1}(\gamma )= L_{S_2}(f \circ \gamma )$