I think calling them sections sounds more professional and fancy-like.
I don't understand being passionate about Geometry, but I respect you for it! I think such subjects (STEM) really need more instructors who are passionate about them. It's how you reach hearts, and encourage young minds to go for it!
Golden, we called them "periods" when I was in school too. Of course, I have no idea what the teachers called them! And that was... more than a few years ago.