In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted E 2 {\displaystyle {\textbf {E}}^{2}} or E 2 {\displaystyle \mathbb {E}...

In geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical...

Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements...

commonly called respectively Euclidean lines and Euclidean planes. The qualifier "Euclidean" is used to distinguish Euclidean spaces from other spaces that...

two-dimensional Euclidean space, the definite article is used, so the Euclidean plane refers to the whole space. Several notions of a plane may be defined...

distance from a point to a line, in the Euclidean plane The distance from a point to a plane in three-dimensional Euclidean space The distance between two lines...

In Euclidean geometry, a plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional...

geometry, the traditional non-Euclidean geometries. When the metric requirement is relaxed, then there are affine planes associated with the planar algebras...

mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect...

a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: For any given line R and point P not on R, in the plane containing...

non-Euclidean geometry, the Poincaré half-plane model is a way of representing the hyperbolic plane using points in the familiar Euclidean plane. Specifically...

⁠, is a two-dimensional projective space, similar to the familiar Euclidean plane in many respects but without the concepts of distance, circles, angle...

sphere geometry Non-Euclidean geometry Noncommutative algebraic geometry Noncommutative geometry Ordered geometry Parabolic geometry Plane geometry Projective...

represent physical positions, like an affine plane or complex plane. The most basic example is the flat Euclidean plane, an idealization of a flat surface in...

floors. More formally, a tessellation or tiling is a cover of the Euclidean plane by a countable number of closed sets, called tiles, such that the tiles...

Euclidean plane tilings by convex regular polygons have been widely used since antiquity. The first systematic mathematical treatment was that of Kepler...

Perga's systematic work on their properties. The conic sections in the Euclidean plane have various distinguishing properties, many of which can be used as...

the study of incidence structures. A geometric structure such as the Euclidean plane is a complicated object that involves concepts such as length, angles...

three mutually perpendicular planes. More generally, n Cartesian coordinates specify the point in an n-dimensional Euclidean space for any dimension n....

tools of spherical trigonometry are in many respects analogous to Euclidean plane geometry and trigonometry, but also have some important differences...

In mathematics, a plane curve is a curve in a plane that may be a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases...

and keep a fixed minimum distance. In three-dimensional Euclidean space, a line and a plane that do not share a point are also said to be parallel. However...

geometry has a variety of properties that differ from those of classical Euclidean plane geometry. For example, the sum of the interior angles of any triangle...

In mathematics, a Euclidean group is the group of (Euclidean) isometries of a Euclidean space E n {\displaystyle \mathbb {E} ^{n}} ; that is, the transformations...

of a point. Most commonly, it is the three-dimensional Euclidean space, that is, the Euclidean space of dimension three, which models physical space....

an ancient Greek mathematician. Euclidean space, the two-dimensional plane and three-dimensional space of Euclidean geometry as well as their higher...

geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as...

points in a plane are collinear if and only if any (k–1) pairs of points have the same pairwise slopes. In Euclidean geometry, the Euclidean distance d(a...

into a correlation, the Euclidean plane (which is not a projective plane) needs to be expanded to the extended euclidean plane by adding a line at infinity...

to specify a point in the projective plane. The real projective plane can be thought of as the Euclidean plane with additional points added, which are...