How can we imagine ‘straight lines’ on a sphere? Any ‘line’ drawn on the surface of the sphere appears to be ‘curved’. We must come up with some definition of ‘straight-line’ that allows ‘curving’.

This is actually simpler than it sounds. Let’s declare the shortest path between two points on the surface of a sphere to be the ‘straight’ segment connecting them. Admittedly it does not appear straight.

Note that we do not go inside the sphere. We want to stay on it’s skin.

In the following video, we discuss more on this notion of ‘straight-line’.