What defines a great circle?

A great circle is defined as the shortest distance between any two points on the surface of a sphere, such as the Earth. This concept is crucial in navigation and aviation, as it represents the path that minimizes travel distance across the globe, making it the most efficient route between destinations. Great circles can be visualized as the intersection of a sphere with a plane that passes through the center of the sphere, resulting in the largest possible circle that can be drawn on the sphere's surface.

In the context of navigation, understanding great circles assists navigators in plotting courses that save time and fuel, as opposed to following a loxodromic curve, which crosses lines of latitude at the same angle but does not offer the same efficiency in distance traveled. While a curved line on a Mercator chart or the concept of the smallest circle drawn on the sphere may relate to different geometric figures or mapping projections, they do not encapsulate the essential characteristic of a great circle as the most direct route between two points.