He further developed relations between the abscissas and the corresponding ordinates that are equivalent to rhetorical equations (expressed in words) of curves. His application of reference lines, a diameter and a tangent is essentially no different from our modern use of a coordinate frame, where the distances measured along the diameter from the point of tangency are the abscissas, and the segments parallel to the tangent and intercepted between the axis and the curve are the ordinates. Apollonius in the Conics further developed a method that is so similar to analytic geometry that his work is sometimes thought to have anticipated the work of Descartes by some 1800 years. Īpollonius of Perga, in On Determinate Section, dealt with problems in a manner that may be called an analytic geometry of one dimension with the question of finding points on a line that were in a ratio to the others. The Greek mathematician Menaechmus solved problems and proved theorems by using a method that had a strong resemblance to the use of coordinates and it has sometimes been maintained that he had introduced analytic geometry. 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. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometric shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and circles, often in two and sometimes three dimensions. It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry. This contrasts with synthetic geometry.Īnalytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.
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