Analytic geometry

Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry, is the study of geometry using the principles of algebra to manipulate planes, lines, curves, and circles, often in two and sometimes three dimensions of measurement on a coordinate plane, usually the Cartesian coordinate system. Some observers note that the introduction of analytic geometry was the beginning of modern mathematics.

René Descartes introduced the foundation for the methods of analytic geometry in 1637 in the appendix titled GEOMETRY of the titled Discourse on the Method of Rightly Conducting the Reason in the Search for Truth in the Sciences, commonly referred to as Discourse on Method. This work, written in his native language, French, and its philosophical principles, provided the foundation for the calculus later introducted by Sir Isaac Newton and Gottfried Wilhelm Leibniz, independent of each other.

Analytical Geometry, as tought in school books, is about defining geometrical shapes in a numerical way and extracting (basically) numerical information out of it. The numerical output, however, might also be a Vector or a Shape.

Important themes of analytical geometry are:

• Vector Space
• Definition of the Plane
• Distance problems
• The Dot product to get the angle of two vectors
• The Cross product to get a perpendicular vector of two known vectors

(and also their spatial volume)

• intersection problems

Many of these problems involve linear algebra.