An equation representing a locus L in the n-dimensional Euclidean space. It has the form L:f(x_1, ..., x_n) = 0, where the left-hand side is some expression of the Cartesian coordinates x_1, ..., x_n. The n-tuples of numbers (x_1 ..., x_n) fulfilling the equation are the coordinates of the points of L. For example, the locus of all points in the Euclidean plane lying at distance 1 from the origin is the circle that can be represented using the Cartesian equation x^2 + y^2 - 1 = 0.

affine variety | Cartesian | Cartesian coordinates | Cartesian geometry | coordinate system

René Descartes