What topic should I base a non-Euclidean geometry paper on?

[NihalRi]

Homework Statement

A short paper 12-16 pages I'm also fairly new to this topic

Homework Equations

The Attempt at a Solution

I tried to ecplain it's application using the Robertson walker mrttuc but it ended upmlooking too much like a physics psper:/

 

[DuckAmuck]

General Relativity, or if you want to keep it simple, flight paths.

Flight paths use non-euclidean geometry, since the Earth is a sphere. The shortest distance between 2 points is not a line, it's a circle segment.