As an assignment I have been asked to write an essay on an aspect related to differential geometry. My lecturer has proposed topics such as architecture, navigation and computer graphics. I personally find these boring. I would like to talk about something interesting in relation to physics and the universe. Could anyone provide some particularly interesting suggestions? The reason I am posting this question is because I believe there is someone who knows something great that I could write about! These are the concepts that have been taught:
- Conic sections
- Special Parametric Curves (Cycloid etc)
- Arc length
- Curvature
- Osculating circles
- Evolutes
- Envelopes
- Total curvature
- Parametric curves
- Parametric surfaces
- Serret-Frenet Equations
- Osculating planes
- Area of surfaces in 3D
- Shape operator
- First fundamental form
- Second fundamental form
- Gaussian, mean, and principal curvature
- Umbilical points
- Minimal surfaces
- Geodesics and geodesic curvature
- Theorema Egregium
- Gauss-Bonnet Theorem
I will tick the answer that I find most interesting. Links are not necessary but are appreciated.
Thank you in advanced for your help!
While other people will recommend relativity, let's take the road less travelled by: bubbles.
If you are looking for particularly interesting physics, then soap bubbles are the way to go. Not only do they relate to minimal surfaces and mean curvature, but they're out-of-the-box. Plus, who doesn't want to have an excuse to write the word "bubble" all over a math essay?