ANALYTIC
GEOMETRY
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.
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