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In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is used, so the Euclidean plane refers to the ...
Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities
Download as PDF; Printable version; ... Euclidean plane geometry (11 C, 96 P) L. Line (geometry) ... Euclidean geometry; List of formulas in elementary geometry; A.
The Elements begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language. [1]
Distance from the origin O to the line E calculated with the Hesse normal form. Normal vector in red, line in green, point O shown in blue. In analytic geometry, the Hesse normal form (named after Otto Hesse) is an equation used to describe a line in the Euclidean plane, a plane in Euclidean space, or a hyperplane in higher dimensions.
A plane segment or planar region (or simply "plane", in lay use) is a planar surface region; it is analogous to a line segment. A bivector is an oriented plane segment, analogous to directed line segments. [a] A face is a plane segment bounding a solid object. [1] A slab is a region bounded by two parallel planes.
Cramer's theorem (algebraic curves) (analytic geometry) Cramér–Wold theorem (measure theory) Critical line theorem (number theory) Crooks fluctuation theorem ; Crossbar theorem (Euclidean plane geometry) Crystallographic restriction theorem (group theory, crystallography) Curtis–Hedlund–Lyndon theorem (cellular automata)
The distance formula on the plane follows from the Pythagorean theorem. In analytic geometry, geometric notions such as distance and angle measure are defined using formulas . These definitions are designed to be consistent with the underlying Euclidean geometry .