The idea of studying geometry by algebraic method has developed into another branch of geometry after the appearance of analytic geometry, which is algebraic geometry. The research objects of algebraic geometry are algebraic curves of plane, algebraic curves of space and algebraic surfaces. The rise of algebraic geometry is mainly due to solving general polynomial equations, and the space formed by the solutions of such equations, the so-called algebraic clusters, has been studied. The starting point of analytic geometry is to introduce a coordinate system to represent the position of a point. Similarly, coordinates can also be introduced into any type of algebraic cluster. Therefore, the coordinate method has become a powerful tool to study algebraic geometry.

Analytic geometry includes two parts: plane analytic geometry and solid analytic geometry. Plane analytic geometry establishes the one-to-one correspondence between points and real number pairs, and the one-to-one correspondence between curves and equations through plane rectangular coordinate system, and studies geometric problems by algebraic method or geometric method. /kloc-since the 0/7th century, due to the development of navigation, astronomy, mechanics, military affairs and production, as well as the rapid development of elementary geometry and elementary algebra, analytical geometry has been established and widely used in various branches of mathematics. Before analytic geometry was founded, geometry and algebra were two independent branches. The establishment of analytic geometry has truly realized the combination of geometric method and algebraic method for the first time, and unified shape and number, which is a major breakthrough in the history of mathematical development. Descartes is the first decisive step in the development of variable mathematics, and the establishment of analytic geometry has played an inestimable role in the birth of calculus.