Above: the path of a ship sailing from Cayenne to Lisbon. This is a screenshot from my program *Geodysseus* which plots courses over various map projections. Whilst the Earth is a not a perfect sphere, assume that it is for the purposes of this argument. If you think about the course of a ship, you will realise that it never sails in a straight line; instead it travels in “arcs” on the surface of the sea. The shortest arc between two points on a sphere is the one least bent – or the arc with the greatest radius – which must be the radius of the sphere itself.

The red arc AB is called a “geodesic line” and is part of a “great circle” that encompasses the sphere. A great circle always has the same radius, center and circumference as the sphere itself. One such great circle on a globe is the equator; others are the lines of longitude. Any great circle will always divide the sphere exactly in half. Geodesy is the science concerned with determining the exact position of geographical points and the shape and size of the earth. (From the Greek *Geodaisia*; *Geo* [Earth] + *daiein* [to divide] ). Geodesic design is the science concerned with determining the exact position and size of struts on a particular envelope. This envelope is usually spherical, but it may be ellipsoidal or egg-shaped.