Plane (geometry)

A plane is a flat, two-dimensional space extending without bound. Any two points in a plane determine a unique line, and any three noncollinear points determine a unique plane.

Euclidean geometry: A geometry based on Euclid’s postulates, including the parallel postulate. The plane is the central setting for ordinary Euclidean geometry.
Cartesian coordinate system: A system that locates points using coordinates measured from intersecting axes. Two coordinates specify every point in a plane once axes are chosen.
Hyperbolic geometry: A non-Euclidean geometry in which infinitely many lines through a point can avoid a given line. It replaces the Euclidean plane’s parallel postulate with a different rule.
Plane of symmetry: A plane that divides a three-dimensional object into mirror-image halves. It uses a plane to describe reflectional symmetry in solid figures.
Point (geometry): An idealized location with no dimensions. Points locate positions in a plane without occupying area.
Equation of a plane: An algebraic relation whose solutions are exactly the points on a plane. A plane in three-dimensional coordinates is commonly written ax + by + cz = d.
Elliptic geometry: A non-Euclidean geometry in which every pair of lines intersects. Its geometry has no parallel lines, unlike the Euclidean plane.
Cross section: A two-dimensional shape formed by cutting a three-dimensional object with a plane. A plane specifies the cut that produces a solid’s cross section.
Line (geometry): A straight, one-dimensional set of points extending without bound in both directions. Any two distinct points in a plane determine exactly one line.
Normal vector: A vector perpendicular to a line, curve, or surface at a specified location. A plane’s normal vector determines its orientation and helps specify its equation.

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