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analytic geometry   -

branch of geometry in which points are represented with respect to a coordinate system, such as cartesian coordinates. Analytic geometry was introduced by René Descartes in 1637 and was of fundamental importance in the development of the calculus by Sir Isaac Newton and G. W. Leibniz in the late 17th century. Its most common application - the representation of equations involving two or three variables as curves in two or three dimensions or surfaces in three dimensions - allows problems in algebra to be treated geometrically and geometric problems to be treated algebraically. The methods of analytic geometry have been generalized to four or more dimensions and have been combined with other branches of geometry.
1 Dimension: Points || General Quadratic Equations || Circles
2 Dimensions: Points || Directions || Lines || Triangles || Polygons || 
Conic Sections [hyperbolas | parabolas | ellipses | circles]
General Quadratic Equations || 
3 Dimensions:


Points || Directions || Lines || Planes || Triangles || Tetrahedra || 
General Quadratic Equations and Quadric Surfaces || Spheres

1. Gellert, W., S. Gottwald, M. Hellwich, H. Kästner, H. Küstner, eds., K. A. Hirsch
and H. Reichardt, Scientific Advisors, The VNR Concise Encyclopedia of Mathematics,
2nd edition, Van Nostrand Reinhold, New York, NY, 1989, pp. 282-319, 530-547.

2. Zwillinger, Daniel, CRC Standard Mathematical Tables and Formulae,
30th Edition, CRC Press, Boca Raton, FL, 1996, pp. 249-319.

Compiled by Robert L. Ward.

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