Geodesy is the study of Earth’s shape and size, and of variations in its gravitational field. A simple way to visualise Riemann’s curved manifold is to think of Earth’s surface. So the shortest route from Dublin to Melbourne is a line passing close to Earth’s centre. The shortest route is then a great circle; its centre is at Earth’s centre, but we travel via an arc along the surface. When we make allowances for the slight flattening of Earth, however, something curious happens: the shortest route is no longer unique.

Source: The Irish Times April 19, 2018 03:56 UTC