Many problems in navigation can be best viewed and solved as problems in analytical geometry. We only need to understand the geometry of two ‘navigable’ surfaces; the sphere and the ellipsoid of revolution. The ellipsoidal model is generated by revolving an ellipse about its minor axis and this model is used as a global model for the surface of the Earth. The eccentricity of the meridian ellipse is small (≈0·082) so we sometimes refer to this surface as a ‘spheroid’ since the surface is still ‘sphere-like’. The physical Earth is, in fact, referred to as a ‘geoid’ whose surface is that which approximates global mean sea level. The mathematical representation of the geoid is not trivial and the ellipsoid of revolution is an extremely good approximation to it.