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

Because “lines” refers to straight lines. There are no 3d straight lines on a globe, but there are straight lines within the 2d surface of the globe. If you drove a car along a line of latitude you’d have to turn the steering wheel a little bit (unless it’s exactly the equator) — this is easy to see if you consider a line of latitude near one of the poles.

In short, lines of latitude aren’t straight lines within the geometry of a sphere. Straight lines on a sphere are those circles that split the sphere into two parts of equal size — also know as “great circles”. Two different great circles do indeed always intersect.