/sci/ - Science & Math

>>9020052
The fundamental property of a straight line in a Euclidean space is that it's the shortest curve connecting two points. This observation is used to generalize the notion of "straight line" on a curved surface. Such curves are called geodesics and they are the unique curves minimizing distances between pairs of points. (the actual definition is very different but this is the intuitive explanation). If you take a sphere for example, you can convince yourself that the geodesics are precisely great circles - intersections of the sphere with planes passing through the origin. Or equivalently circles with center at the center of the sphere. And of course, any two distinct great circles intersect at two antipodal points - this is what you call that they "converge". Also, latitudes are NOT "lines" in this context. They are just arbitrary curves on a sphere without any special property. They are not geodesics.