- How many different
geodesics are there between A and B on this 450 degree cone?

- 0
- 1
- 2
- 3
- 4

- What is the equation of a geodesic that an
arbitrary point y(theta,r) satisfies, where d is
and beta is as in the hw sols and following picture:
- theta=r
- r=d sec (theta-beta)
- r=d cos (theta-beta)
- d=r sec (theta-beta)
- arctan(s/d) = n(alpha/2)

- How many times does this geodesic intersect itself?

- 0
- 1
- 2
- 3
- 4

- In general on a cone of small enough cone angle,
a geodesic will self-intersect...
- they will generally not intersect
- at points vertically removed from each other
- at points horizontally removed from each other
- each time its lift crosses the seam of the covering
- infinitely many times

- On a piece of paper, in the covering plane, draw an intersecting
geodesic on a flat torus.

- On a round torus, oriented as follows, the following are geodesics:

- all vertical circles on the donut
- all horizonal circles on the donut
- both of the above
- none of the above

- On a FLAT torus the following are geodesics:
- all vertical circles on the flat donut
- all horizonal circles on the flat donut
- both of the above
- none of the above

- On a round torus, oriented as follows, a geodesic can wrap around the
donut:

- just once
- many times
- both of the above
- none of the above

- S.A. on a torus