What is "gnomonic projection"

Gnomonic \Gno*mon"ic\, Gnomonical \Gno*mon"ic*al\, a. [L. gnomonicus, Gr. ?: cf. F. gnomonique. See Gnomon.] Of or pertaining to the gnomon, or the art of dialing.

Gnomonic projection, a projection of the circles of the sphere, in which the point of sight is taken at the center of the sphere, and the principal plane is tangent to the surface of the sphere. ``The gnomonic projection derives its name from the connection between the methods of describing it and those for the construction of a gnomon or dial.''
--Cyc. of Arts & Sciences.

n. (context cartography English) A mapping projection in which all great circle paths (on a sphere the shortest path between points) are shown as straight lines.

A gnomonic map projection displays all great circles as straight lines, resulting in any straight line segment on a gnomonic map showing a geodesic, the shortest route between the segment's two endpoints. This is achieved by casting surface points of the sphere onto a tangent plane, each landing where a ray from the center of the sphere passes through the point on the surface and then on to the plane. No distortion occurs at the tangent point, but distortion increases rapidly away from it. Less than half of the sphere can be projected onto a finite map. Consequently, a rectilinear photographic lens, which is based on the gnomonic principle, cannot image more than 180 degrees.