1. According to the reading, one of the greatest achievments of the theory of surfaces was:

a) analytic geometry

b) Gauss-Bonnet theorem

c) classificiation of surfaces

d) discovering surfaces that stretch the imagination

e) none of the above

2. How long have surfaces been studied?

a) In a very short time period during Gauss' lifetime

b) From at least the Greeks until the 1800s

c) From at least the Greeks until the 1900s

d) From at least the Greeks until now

e) none of the above

3. What does the Gaussian curvature measure?

a) the deviance of a curve on the surface from being a geodesic.

b) the deviance of the surface from being a plane at each point.

c) the deviance of the surface from being a round earth at each point.

d) how curvy Gauss' ear was

e) none of the above

4. For curves we learned that curvature and torsion determine the curve up to rigid motion. What are the corresponding features that determine a surface up to rigid motion?

a) two parameters curvature and torsion

b) one parameter, the Gaussian curvature

c) six coefficients of parametric equations called the first and second fundamental forms, local invariants that are functions of arc length

d) eleven dimensions from string theory

e) need an infinite amount of information to obtain a surface

5. Is is possible to win an Academy Award (Oscars) for working on surfaces?

a) yes, definitely

b) yes, but unlikely

c) no

6. According to the reading, surfaces can be represented using

1) the revolutions that form some of them

2) analysis

3) algebra

4) geometry

5) polygon meshes

6) physical models and sculptures

7) computer animations

8) soap bubbles

a) all of the above

b) 3, 4, 6, 7 (ie all but 1, 2, 5 and 8)

1. b

2. d

3. b (a is geodesic curvature)

4. c

5. a

6. a