study of geometric properties by means of algebraic operations, coordinate geometry
Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of
geometry using the principles of
algebra. 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. Usually the
Cartesian coordinate system is applied to manipulate
equations for planes, lines, 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.
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