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

The lines of longitude are all circles of the same size, rotated slightly so they only cross at the poles. They are only parallel at the equator because at all other points they are getting closer as they converge.

The lines of latitude are concentric circles; different sizes next to one another. That means they don’t overlap.