Mathematical laws mainly solve the contradiction between the earth's curved surface and the map plane. Map projection, map scale and map orientation constitute the mathematical rules of map.
The ellipsoid of the earth is an inextensible surface, and the map is usually a continuous two-dimensional plane. If the sphere is forcibly unfolded, cracks or folds will inevitably appear. Therefore, some mathematical laws must be established on the sphere and plane to solve this problem.
The method of converting points on the ellipsoid of the earth into points on the map plane is called map projection. Map projection solves the mathematical transformation from sphere to plane, and becomes one of the theoretical foundations of modern cartography.
Characteristics of maps
1. Testability generated by special mathematical rules. Special mathematical rules include map projection, map scale and map direction.
2. Use map language to express the intuition generated by things. All kinds of complex natural and human things represented on the map are realized by map language. Map language includes map symbols and map annotations.
3. Overview generated after implementation of cartographic generalization.
4. Maps must follow certain mathematical laws.