- Homework 9 is returned
- Problem 1:
- period is $4\pi$; length of the curve is 9.42943. If you don't have period right, you won't get this!
- You know it's not $2\pi$-periodic when it requires about $4\pi$ length of values to find the horizontal and vertical slopes....
- Problem 2:
- hyperbola(s)
- parabola (half!): $x \gt 3$
- These are conic sections (celestial paths/orbits):
(slices of a cone). Notice that the circle and parabola are actually degenerate cases (we say "non-generic"). They are very precarious: the slightest perturbation (bump) throws them into something else:
- For the circle, it's an ellipse;
- but the parabola is between two worlds: an ellipse if
pushed one way, and hyperbolas if pushed the other!
Notice that straight lines and points are other degenerate cases.
- Problem 1:
- A few more bits about Sect. 10.4: Polar coordinates (pdf, pdf summary)
In particular, we want to talk about lengths of polar curves, and orange peeling....
- Then it's on into 3 dimensions (and beyond!): Sect. 12.1: 3D coordinate systems (pdf, pdf summary)