So our instructor wants us to write a 3 page report on some fact in Differential Geometry relating to curves or surfaces. It can be a theorem, a fact or some special case.
The only restriction is that I cannot write about things we did in class. We are using a book called Elementary Differential Geoemetry by Andrew Presley. We've covered pretty much all of the book.
This includes main theorems like Gauss Bonnet, Theorema Egregium, Gaussian/Mean curvatures, Euler's Theorem, Geodesic, Gauss Map, the First/Second Fundamentals, just scratched on the surface of Minimal surfaces.
After googling some topics, I was overwhelmed due to the shocking level of mathematics involved and have thus no where else to look. So if anyone could suggest some topics for me, it would be awesome. Preferably keep it to the level of someone who only have had a course in calculus of severable variables and linear algebra. But if the restrictions are too much, you may assume that the student have had a course in Real Analysis.