Eli5:In non-euclidean geometry (for my example a globe).Lines of longitude are parallel @ the equator but meet @ the poles. Lines of latitude (let’s take tropic cancer, equator & tropic Capricorn)also 3 lines are parallel, also on a curved plain, but this time don’t converge.What am I missing out?

Question

Eli5:In non-euclidean geometry (for my example a globe).Lines of longitude are parallel @ the equator but meet @ the poles. Lines of latitude (let’s take tropic cancer, equator & tropic Capricorn)also 3 lines are parallel, also on a curved plain, but this time don’t converge.What am I missing out?

In: Mathematics

Answer 1

A “line” in spherical geometry are the [great circles](https://en.wikipedia.org/wiki/Great_circle) – what you get when you intersect a plane through the center of the sphere. They give us things like the shortest distance between two points, which is what regular lines do in Euclidean geometry.

The only ~~longitude~~ latitude line that’s *actually* a “line” in the sense of spherical geometry is the equator. All the other latitudes should be thought of as curves rather than lines. This is why they don’t intersect, which is what any two pairs of lines in spherical geometry do. You should see their non-intersection as being just as relevant as [these two parabolas not intersecting](https://www.desmos.com/calculator/x57ji80vhq).