A great circle is a circle on the surface of a sphere that has the same diameter as the sphere. A great circle is the intersection of a sphere with a plane going through its center. A great circle is the largest circle that can be drawn on a sphere.
Great circles are the "straight lines" (geodesics) of the sphere in non-Euclidean geometry.
The great circle on the spherical surface is the path with the smallest curvature, and hence the shortest path between two points on the surface. The distance between any two points on a sphere is known as the great circle distance. When intercontinental airline routes are drawn on a flat map (for instance, the Mercator projection), they often look curved. This is because they lie on great circles. A route that would look like a straight line on the map would actually be longer.