If all lines on a sphere converge, what happens to latitude lines?

Question

I mean, on an image like this, how do latitude lines not converge? Everywhere i read says that there can be no parallel lines on a sphere. Is this related to the different definition of 'line' in spherical geometry?

Thanks in advance.

Answer 1

All straight lines indeed converge on a sphere. But contrary to longitude lines for example, which are straight lines (great circles) and do converge at the poles, latitude lines are a different kind of line: small circles, meaning they aren't actually straight (great circle) lines (except the Equator).

If you were to walk along a latitude line which isn't the Equator, you would have to turn in order to follow the line. Taking this example to the extreme, imagine you're walking near the North Pole at 89°N. To keep at 89°N and follow the latitude line eastward, you'd have to slowly turn left, essentially circling the pole.

So this special geometry of latitude lines allow them to be parallel to each other, because they aren't great circles or straight lines.