In woodworking, planing is the activity of using a wood plane to smooth a flat surface of a piece of wood.
In music theory, planing is where chords move in parallel motion, thereby eliminating any feeling of harmonic progression.
The above terms can vary in meaning, particularly comparing usage of the first two terms in the US and in Europe.
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In mathematics, a plane is a fundamental two-dimensional object.
The topological plane, or its equivalent the open disc, is the basic topological neighbourhood used to construct surfaces (or 2-manifolds) classified in low-dimensional topology.
The topological plane is the natural context for the branch of graph theory that deals with planar graphs, and results such as the four color theorem.
It is easy to check that it obeys the rules required of projective planes: any pair of distinct great circles meet at a pair of antipodal points, and any two distinct pairs of antipodal points lie on a single great circle.
In this representation of the Fano plane, the seven points are shown as small blobs, and the seven lines are shown as six line segments and a circle.
The definition of projective plane by incidence properties is something special to two dimensions: in general projective space is defined via linear algebra.
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