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All elementary functions can be extended to the complex plane. Such definitions agree with the real definitions on the x-axis and constitute an analytic continuation.

For a function with 2 degrees of freedom, the 2-dimensional phase space that is accessible to the function or object is called its phase plane.

Through any point in the plane, there is at most one straight line parallel to a given straight line. This axiom is equivalent to the parallel postulate.

The point-slope form of a line through the point (x_1,y_1) with slope m in the Cartesian plane is given by y-y_1=m(x-x_1).

The projective plane crossing number of a graph is the minimal number of crossings with which the graph can be drawn on the real projective plane. A graph with projective ...

Increasing a plane figure's linear dimensions by a scale factor s increases the perimeter p^'->sp and the area A^'->s^2A.

A "curve" (i.e., a continuous map of a one-dimensional interval) into a two-dimensional area (a plane-filling function) or a three-dimensional volume.

A spatial point process is a point process which models data that is localized at a discrete set of locations in space or, more specifically, on a plane.

A three-dimensional knot spun about a plane in four dimensions. Unlike suspended knots, spun knots are smoothly embedded at the poles.

The asymptotic series of the Airy function Ai(z) (and other similar functions) has a different form in different sectors of the complex plane.