Analytic geometry

Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry, is the study of geometry using the principles of algebra. Usually the Cartesian coordinate system is applied to manipulate equations for planes, lines, curves, and circles, often in two and sometimes in three dimensions of measurement. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining geometrical shapes in a numerical way, and extracting numerical information from that representation. The numerical output, however, might also be a vector or a shape. Some consider that the introduction of analytic geometry was the beginning of modern mathematics.

Important themes of analytical geometry

• vector space
• definition of the plane
• distance problems
• the dot product, to get the angle of two vectors
• the cross product, to get a perpendicular vector of two known vectors (and also their spatial volume)
• intersection problems

Many of these problems involve linear algebra.

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