Is there a name for the shortest path on a sphere?

The shortest path between two points on a flat surface or in space follows a straight line, and we therefore say that the path itself is a “line segment” (because segment means “a piece of”). But on a sphere like the Earth, the shortest path is curved, not straight, because it is a portion of a great circle. So what do we call it? The answer is that it is called a geodesic. In fact, the term geodesic can be used to describe the shortest path between two points on any surface, whether it is a sphere, a plane, or something else. For example, if you draw the shortest path between two points on a lamp shade, it will be curved in a different way from the shortest path on a sphere, but the path is still called a geodesic.