Introduction
Coordinate geometry is also referred as Cartesian geometry or analytical geometry. It is the study of geometry using the principles of algebra. Usually the Cartesian coordinate system is applied to manipulate equations for planes, lines, straight lines, and squares, often in two and sometimes in three dimensions of measurement. The introduction of analytic geometry was the beginning of modern mathematics.
The Greek mathematician Menaechmus solved problems and proved theorems by using a method that had a strong resemblance to the use of coordinates.
Apollonius of Perga, in On Determinate Section dealt with problems in a manner that may be called an analytic geometry of one dimension.
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Apollonius of Perga
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Apollonius of Perga was known as 'The Great Geometer'. He had a very great influence on the development of mathematics;, in particular his famous book Conics introduced terms which are familiar to us today such as parabola, ellipse and hyperbola. His application of reference lines, a diameter and a tangent is essentially no different than our modern use of a coordinate frame.
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The eleventh century Persian mathematician Omar KhayyÃ¡m saw a strong relationship between geometry and algebra, and was moving in the right direction when he helped to close the gap between numerical and geometric algebra with his geometric solution of the general cubic equations.
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Omar KhayyÃ¡m
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Analytic geometry has traditionally been attributed to RenÃ© Descartes who made significant progress with the methods of analytic geometry in 1637. Descartes made one of the greatest advances in geometry by connecting algebra and geometry. A myth is that he was watching a fly on the ceiling when he conceived of locating points on a plane with a pair of numbers. Fermat also discovered coordinate geometry, but it's Descartes' version that we use today.
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RenÃ© Descartes