Abstract
The cartographer, faced with the problem of mapping one surface on another surface or on a plane, may select one of two alternative methods if he wishes his representation to be mathematically accurate. He may represent his surface conformally so that the angles between any lines on the surface are equal to the angles between the corresponding lines on the nap, or he may choose to leave the areas undistorted. Only in the case of a few exceptional surfaces is it possible to have both angles between lines and areas go over into the map without change. In most of our ordinary maps both angles and areas are distorted, the cartographer's purpose being to strike a happy medium. An interesting account of the history of mapping can be found in the Encyclopedia Britanica under Maps.