Analytic geometry (nonfiction)

Diagram of a Cartesian coordinate system on a plane, showing the origin, axes, and the four quadrants, with illustrative points and grid.

In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.

Analytic geometry is widely used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including algebraic, differential, discrete, and computational geometry.

Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and squares, often in two and sometimes in three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space (three dimensions). As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometrical shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. That the algebra of the real numbers can be employed to yield results about the linear continuum of geometry relies on the Cantor–Dedekind axiom.

Fiction cross-reference

• Crimes against mathematical constants
• Forbidden Ratio
• Geometry solvent
• Gnomon algorithm
• Gnotilus
• Mathematics

Nonfiction cross-reference

• Geometry (nonfiction)
• Mathematics (nonfiction)
• Synthetic geometry (nonfiction) - the study of Geometry using the axiomatic method and the tools directly related to them (compass and straightedge) to draw conclusions and solve problems.

External links:

• Analytic Geometry @ Wikipedia