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

Lines of longitude are all exactly equal in length and are “great circles” – the longest possible line you can draw on a sphere. Every great circle will intersect every other great circle in two places. The only line of latitude that is a great circle is the equator. All other longitudinal lines are shorter. You can have an infinite number of non-intersecting circles on a sqare, provided you have at most one great circle.