A plane is a flat surface with no thickness that extends forever in all directions. It is two-dimensional: length and width, but no height. In Euclidean geometry, the plane is an undefined term, described by axioms. Three non-collinear points determine a unique plane.

Planes contain lines, points, and shapes. Two planes can intersect in a line or be parallel. A line can lie in a plane, intersect it at a point, or be parallel to it. These relationships are studied in solid geometry and linear algebra.

In coordinate geometry, the xy-plane represents all ordered pairs (x, y). The complex plane represents complex numbers. Planes appear in physics as surfaces of constant potential, in computer graphics as rendering surfaces, and in engineering as reference frames. The concept is simple but foundational.

• Flat, two-dimensional, infinite surface
• Determined by three non-collinear points
• Planes intersect in lines or are parallel
• Represented as xy-plane or complex plane