ABSTRACT
‘Map projections' is also called ‘mathematical cartography.' It principally studies the theories and methods of building the basic mathematics for maps. This research object is the result of the characteristic contradiction between the non-developable earth's surface and the map plane. As we know, the earth has a natural surface that is complicated. For the purpose of measurement and calculation on the earth's surface, the earth should be replaced by an ellipsoid or sphere that approximates the earth's natural body in overall shape. This is because an ellipsoid and a sphere can be expressed by a simple mathematical equation. In geometry such an ellipsoid or sphere is also known to be a non-developable surface. But it is necessary to expand part of or the entire terrestrial ellipsoidal (or spherical) surface onto a plane surface according to some required specification for map use. To expand the non-developable earth's surface into a plane forms the characteristic contradiction of map science.
