Partial Solutions to Brainfood #1
These are partial answers so that you can check to see if you are on target.
We expect your actual answers to be "fleshed out" a bit more.
- No, we cannot tell where the image of t=0 is soley by looking at the
curve. For example, the function q(t)=(cos(t+Pi), sin(t+Pi))
has EXACTLY the same image (the unit circle), but the point t=0
is sent to (-1,0) instead of to (1,0).
- The vector c translates the image of the parametrized cicle by c.
- No, you can't determine velocity vectors. The function
r(t)=(cos(2t), sin(2t)) has the unit circle as its image, but
it traces out the circle twice as fast as the function p,
therefore the velocity vectors are twice as long.
- c) The path is a helix.
- Stacking circles that are being linearly translated as they are
stacked results in a "slanted cylinder" as shown below.
Last modified: Wed Oct 23 16:58:48 1996