A mapping that projects a sphere onto a plane in such a way that all great circles of the sphere are represented by straight lines. This involves mapping points of the sphere onto a tangent plane by constructing rays from the centre of the sphere through all surface points, with the rays finishing on the tangent plane. The construction means that it is only possible to project less than half a sphere onto a plane of finite extent. The gnomonic projection has been attributed to the ancient Greek philosopher Thales.

There are applications of the gnomonic projection to several branches of physical science, including astronomy and X-ray crystallography, as well as to navigation and photography. It is particularly useful in seismology because seismic waves follow great circles of the earth to a very good approximation. See also stereographic projection.