analytic geometry: Quick Facts

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Facts

Also Known As	coordinate geometry

Photos

Diagram showing a double cone intersected by planes at different angles, producing the conic sections: a horizontal plane creates a circle, a tilted plane creates an ellipse, a plane parallel to the cone's side forms a parabola, and a steep plane produces a hyperbola. Each section is labeled, with the axis and apex of the cone indicated.

Cartesian coordinates

Polynomial graphThe figure shows part of the graph of the polynomial equation y = 3x4 − 16x3 + 6x2 + 24x + 1. Note that the same scale need not be used for the x- and y-axis.

A three-dimensional graph of an elliptic paraboloid surface, shaped like an upward-opening bowl, with grid lines and labeled x, y, and z axes. The surface curves upward from the origin, illustrating the equation z = x squared plus y squared.

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Topics

Pappus’s theorem configuration space coordinate system geometry topology Euclidean geometry differential geometry projective geometry non-Euclidean geometry algebraic geometry catastrophe theory Ceva’s theorem length, area, and volume

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Key People

Gaspard Monge, detail of an oil painting by Jean Naigeon, 1811; in the Museum of Fine Arts, Beaune, France.

Gaspard Monge, count de Péluse

French mathematician and public official

Plücker, Julius

Julius Plücker

German mathematician and physicist

August Ferdinand Möbius, detail from an engraving by an unknown artist.

August Ferdinand Möbius

German mathematician and astronomer

Fermat, portrait by Roland Lefèvre; in the Narbonne City Museums, France

Pierre de Fermat

French mathematician

Equations written on blackboard

Numbers and Mathematics

Equations written on blackboard

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