plane

Plane is a term with several related but distinct meanings in mathematics, physics, and everyday use. In geometry, a plane is an idealized flat surface that has length and width but no thickness and extends without bound in all directions. A plane is determined by three non-collinear points or by a point and a normal vector; it can be described algebraically by a linear equation such as ax + by + cz + d = 0. Planes form the basis for many geometric constructions and concepts such as parallelism, intersection, and angles between planes. The coordinate planes, such as the xy-plane, are familiar examples within a higher-dimensional space.

An airplane, or plane, is a powered fixed-wing aircraft designed for air travel. It achieves lift with wings as it moves through the atmosphere, using engines to provide thrust. Modern planes range from small single-engine planes to large commercial airliners, and may employ jet or propeller propulsion. They are equipped with a fuselage, wings, empennage (tail), landing gear, flight controls, and instrumentation, and operate under aerodynamic, propulsion, and navigational principles.

A plane is also a woodworking tool—the hand plane—used to shave and smooth wood surfaces. It consists of a wooden or metal body, a cutting blade (iron), and a mechanism to advance the blade and set its depth, producing a flat, even surface.