the shortest course between two points on the surface of a sphere. It lies in a plane that intersects the sphere's centre and was known by mathematicians before the time of Columbus. Until the 19th century ships generally sailed along rhumb lines, which made use of prevailing winds and fixed compass headings. The development of steamships in the 19th century allowed complete independence from the winds, removing the major uncertainty for sailors trying to follow a geometrically prescribed route.

Great circle routes, which require constantly changing headings, are most useful beyond the equatorial regions and for distances greater than several hundred miles. Long-distance air traffic uses great circle routes routinely, saving time and fuel. Navigational radio signals also follow great circle paths.

Great circle routes are usually plotted on charts based on the gnomonic projection, on which great circles appear as straight lines.