Today we discussed two exercises from Shifrin. Corbyn did 1.2.11, which was a patient and careful computation. Mark did 1.2.8, which showed that a curve which has all of its normal lines through a fixed point must be a planar circle. This used all three of the “big tricks” from classical differential geometry. In order.
We then discussed project ideas. I figured that you might want some help choosing appropriate projects, so I did this:
| Name | Project |
|---|---|
| Emily | Tangent Spherical Image |
| Christine | Bertrand Mates |
| Gustavo | Pedal Curves |
| Corbyn | The Darboux Vector |
| Jesse M | Cauchy-Crofton formula and applications |
| Jesse T | The Locus of Centers |
| Mark | Curves on quadric surfaces |
| Sladana | The Bishop Framing |
| TJ | The Four Vertex theorem and its converse |
We still haven’t talked about Shifrin 1.2 # 7, 9 and Struik 1.6 # 2-4. Please prep those for next time.