Corbyn gave the presentation on his project for curves. This bit about treating the framing as a rigid body and studying the rotational motion as a physicist does is neat. So, we learned about the concept of areal velocity and saw the Darboux vector. By the way, Gaston Darboux was an important French geometer.
Then we talked a little about effective LaTeX.
Then I shared a little bit about Gauss, the father of modern differential geometry (and lots of other bits of mathematics). The neat thing here is to realize that while doing a survey of Hanover, Gauss though about the surface of the land by visualizing its normal lines as picking out points on “the sphere of the heavens”. This is where the Gauss map gets its start. Gaussian curvature is then interpreted as a “local scaling factor of area under the Gauss map.” The bit where we can compute it as the determinant of the shape operator is then a theorem. Either way, this is a cool way to think about surfaces.
Next time, Christine will give a short presentation about Bertrand Curves. And I hope we will talk some more about surfaces. (hint, hint)