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analytic geometry

n. (context geometry English) a branch of mathematics that investigates properties of figures through the coordinates of their points.

analytic geometry

n. the use of algebra to study geometric properties; operates on symbols defined in a coordinate system [syn: analytical geometry, coordinate geometry]

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 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. The numerical output, however, might also be a vector or a shape. 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.

Usage examples of "analytic geometry".

In analytic geometry we may cross two or three number-lines at right angles to create a multi-dimensional space.

She closed her eyes, and her mind drifted to analytic geometry and the distance formula.

Not to mention analytic geometry, calculus, and computer programming, I thought.

My old Analytic Geometry textbook, still flecked with insulation from the attic, has been sitting on my thigh like a lump of ice.

She did so, and through Cloud's mind raced the appropriate equations of solid analytic geometry.