What is Straight on a Sphere?
a.) Imagine yourself to be a bug crawling around on a sphere. (This bug can neither fly nor burrow into the sphere). Thr bug's universe is just the surface; it never leaves it. What is "straight" for this bug? What will the bug see or experience as straight? How can you convince yourself of this? Use the properties of striaghtness.
b.) Show (that is, convince yourslef, and give an argument to convince others) that the great circles on a sphere are straight with repsect to the sphere, and that no other circles on the sphere are straight with repsect to the spehere.
Any thoughts that can be helpful?