Supplementary mathematics/Analytic geometry

Analytical geometry (also vector geometry) is a branch of geometry that provides algebraic tools (mainly from linear algebra) to solve geometric problems. In many cases, it makes it possible to solve geometric problems purely by calculation, without using the visual aid.

On the other hand, geometry that justifies its propositions on an axiomatic basis without reference to a number system is called synthetic geometry.

The methods of analytical geometry are used in all natural sciences, but above all in physics, such as in the description of planetary orbits. Originally, analytical geometry dealt only with questions of planar and spatial (Euclidean) geometry. In the general sense, however, analytic geometry describes affine spaces of any dimension over any body.