- Different parameterizations can lead to very different surfaces
- true and I can think of examples
- true but I'm not sure why
- false but I'm not sure why not
- false and I have a reason why not

- The following surfaces were not embedded isometrically via
a C
^{2} mapping
into R^{3}:
- models of hyperbolic geometry
- stereographic projection of the sphere
- flat torus
- all of the above
- none of the above

upper half-plane model conformal, circles and angles

- Gauss curvature
*K* is
- intrinsic
- extrinsic
- a vector
- both a and c
- both b and c

- Gauss-Bonnet relates
- total Gauss curvature in geometry to Euler characteristic in combinatorial topology
- Gauss to Bonnet
- both of the above
- none of the above

- I can intuit the principal normal curvatures at a point on a surface
- agree
- unsure
- need help