Cartesianvormiks

Cartesianvormiks is a term used in Dutch-language mathematics to denote expressing a mathematical object in Cartesian form – that is, using coordinates in the Cartesian coordinate system introduced by René Descartes. The Cartesian form emphasizes a representation in terms of the coordinate variables x, y (and z in three dimensions) rather than in parametric, polar, or other forms.

In analytic geometry, many objects are given by equations in Cartesian form. For a straight line, the Cartesian form is Ax + By + C = 0. A circle in the plane is typically written as (x − h)^2 + (y − k)^2 = r^2, while in general form the circle is x^2 + y^2 + Dx + Ey + F = 0. Conic sections are represented by second-degree equations of the type ax^2 + bxy + cy^2 + dx + ey + f = 0. More generally, surfaces in three dimensions have equations in x, y, z, such as a quadratic surface or a plane Ax + By + Cz + D = 0.

A different area where Cartesian form is used is the representation of complex numbers. The Cartesian form of a complex number z = x + iy lists its real and imaginary parts directly as z = x + iy, in contrast to its polar form r(cos θ + i sin θ).

Historically, the Cartesian form is tied to the Cartesian coordinate system; the term is sometimes contrasted with parametric or polar representations, which describe the same object as functions of a parameter or of an angle and radius.

Care should be taken that the term Cartesianvormiks may appear in various Dutch texts with minor variation; it is essentially synonymous with Cartesian form or analytic representation in coordinates.