Analytic geometry, also called coordinate geometry and earlier referred to as
Cartesian geometry, is the study of geometry using the principles of algebra.
Usually the Cartesian coordinate
system is applied to manipulate equations for
curves, and circles, often in two and
sometimes in three dimensions of measurement.
As taught in school books, analytic geometry can be explained more simply: it
is concerned with defining geometrical shapes in a numerical way, and extracting
numerical information from that representation. The numerical output, however,
might also be a vector or a shape. Some consider that the introduction of
analytic geometry was the beginning of modern mathematics.