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Geometric model of the planar projection of the physical universe
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}
Euclidean_plane
Mathematical model of the physical space
those is the parallel postulate which relates to parallel lines on a Euclidean plane. Although many of Euclid's results had been stated earlier, Euclid
Euclidean_geometry
Isometry of the Euclidean plane
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_plane_isometry
2D surface which extends indefinitely
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
Plane_(mathematics)
Flat surface
In Euclidean geometry, a plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional
Euclidean planes in three-dimensional space
Euclidean_planes_in_three-dimensional_space
Length of a line segment
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
Euclidean_distance
Space in mathematics and theoretical physics
a plane, then it is called a hyperbolic plane. q|U is degenerate. One of the most jarring properties (for a Euclidean intuition) of pseudo-Euclidean vectors
Pseudo-Euclidean_space
Type of non-Euclidean geometry
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
Hyperbolic_geometry
Mathematical space with two coordinates
often called planes (especially the Euclidean plane), or, more generally, surfaces. These include analogs to physical spaces, like flat planes, and curved
Two-dimensional_space
Fundamental space of geometry
commonly called respectively Euclidean lines and Euclidean planes. The qualifier "Euclidean" is used to distinguish Euclidean spaces from other spaces that
Euclidean_space
Type of dynamical system in mathematics
shape in the plane. Classically, this system is defined for the Euclidean plane, but one can also consider the system in the hyperbolic plane or in other
Outer_billiards
Two geometries based on axioms closely related to those specifying Euclidean geometry
geometry, the traditional non-Euclidean geometries. When isotropic quadratic forms are admitted, then there are affine planes associated with the planar
Non-Euclidean_geometry
Compact non-orientable two-dimensional manifold
, is a two-dimensional projective space, similar to the familiar Euclidean plane in many respects but without the concepts of distance, circles, angle
Real_projective_plane
Covering by shapes without overlaps or gaps
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
Tessellation
Upper-half plane model of hyperbolic non-Euclidean geometry
non-Euclidean geometry, the Poincaré half-plane model is a way of representing the hyperbolic plane using points in the familiar Euclidean plane. Specifically
Poincaré_half-plane_model
Curve from a cone intersecting a plane
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
Conic_section
Field of mathematics which studies incidence structures
the study of incidence structures. A geometric structure such as the Euclidean plane is a complicated object that involves concepts such as length, angles
Incidence_geometry
Overview of and topical guide to geometry
sphere geometry Non-Euclidean geometry Noncommutative algebraic geometry Noncommutative geometry Ordered geometry Parabolic geometry Plane geometry Projective
Outline_of_geometry
Geometric concept of a 2D space with "points at infinity" adjoined
mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect
Projective_plane
Abstract mathematical system of two types of objects and a relation between them
between these types of objects. Consider the points and lines of the Euclidean plane as the two types of objects and ignore all the properties of this geometry
Incidence_structure
Geometric model of the physical space
n-dimensional Euclidean space and a Cartesian coordinate system. When n = 3, this space is called the three-dimensional Euclidean space (or simply "Euclidean space"
Three-dimensional_space
Space formed by the ''n''-tuples of real numbers
coordinates of the points of a Euclidean space of dimension n, En (Euclidean line, E; Euclidean plane, E2; Euclidean three-dimensional space, E3) form
Real_coordinate_space
semiregular) of the Euclidean plane, and their dual tilings. There are three regular and eight semiregular tilings in the plane. The semiregular tilings
List of Euclidean uniform tilings
List_of_Euclidean_uniform_tilings
Concept in projective geometry
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
Duality_(projective_geometry)
Mathematical concept
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
Plane_curve
Geometry of the surface of a sphere
tools of spherical trigonometry are in many respects analogous to Euclidean plane geometry and trigonometry, but also have some important differences
Spherical_geometry
Non-Euclidean geometry
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
Elliptic_geometry
Notation for 2-dimensional spherical, euclidean and hyperbolic symmetry groups
groups and wallpaper groups of the Euclidean plane ( E 2 {\displaystyle E^{2}} ), and their analogues on the hyperbolic plane ( H 2 {\displaystyle H^{2}} )
Orbifold_notation
Shortest network connecting points
A Euclidean minimum spanning tree of a finite set of points in the Euclidean plane or higher-dimensional Euclidean space connects the points by a system
Euclidean minimum spanning tree
Euclidean_minimum_spanning_tree
Coordinate system
The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes. The axes
Quadrant_(plane_geometry)
Coordinate system used in projective geometry
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
Homogeneous_coordinates
Isometry group of Euclidean space
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
Euclidean_group
Theorem in set-theoretic geometry
Banach–Tarski paradox. In the Euclidean plane, two figures that are equidecomposable with respect to the group of Euclidean motions are necessarily of the
Banach–Tarski_paradox
Relation used in geometry
Parallel planes are infinite flat planes in the same three-dimensional space that never meet. In three-dimensional Euclidean space, a line and a plane that
Parallel_(geometry)
Vector behavior under coordinate changes
n} matrix, and the matrix transpose has its usual meaning. In the Euclidean plane, the dot product allows for vectors to be identified with covectors
Covariance and contravariance of vectors
Covariance_and_contravariance_of_vectors
Subdivision of the plane into polygons that are all regular
Tilings of the Euclidean plane by convex regular polygons have been widely used since antiquity. The first systematic mathematical treatment was that
Euclidean tilings by convex regular polygons
Euclidean_tilings_by_convex_regular_polygons
Geometry with 7 points and 7 lines
incidences in Euclidean geometry, but they can be given coordinates using the finite field with two elements, GF(2). The standard notation for this plane, as a
Fano_plane
Partition of the Euclidean plane
tesselation or a sectional Dirichlet tesselation, is a partition of the Euclidean plane into polygonal cells defined from a set of circles. The cell for a
Power_diagram
Vertex-transitive tiling of the plane by regular polygons
of the plane by regular polygon faces with the restriction of being vertex-transitive. Uniform tilings can exist in both the Euclidean plane and hyperbolic
Uniform_tiling
Physical quantity that is a vector
magnitude and direction of the main vector. For example, a force on the Euclidean plane has two Cartesian components in SI unit of newtons (describing the
Vector_quantity
Topics referred to by the same term
space called a plane. Euclidean plane geometry, is the most common meaning; it includes Plane analytic geometry Plane synthetic geometry Plane projective
Plane geometry (disambiguation)
Plane_geometry_(disambiguation)
Study of graphs defined by geometric means
geometric properties of geometric graphs, meaning graphs drawn in the Euclidean plane with possibly intersecting straight-line edges, and topological graphs
Geometric_graph_theory
Relation between sides of a right triangle
Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the
Pythagorean_theorem
Directional planes
context of a 1-dimensional orthogonal Cartesian coordinate system on a Euclidean plane, to say that a line is horizontal or vertical, an initial designation
Vertical_and_horizontal
NP-hard problem in combinatorial optimization
path length between A and B in the original graph. For points in the Euclidean plane, the optimal solution to the travelling salesman problem forms a simple
Travelling_salesman_problem
Polygon with 2 sides and 2 vertices
sides (edges) and two vertices. Its construction is degenerate in a Euclidean plane because either the two sides would coincide or one or both would have
Digon
Coordinate system using perpendicular axes
three mutually perpendicular planes. More generally, n Cartesian coordinates specify the point in an n-dimensional Euclidean space for any dimension n.
Cartesian_coordinate_system
coordinates in the hyperbolic plane, that certain graphs including the polyhedral graphs have greedy embeddings in the Euclidean plane, and that unit disk graphs
Greedy_embedding
Undirected unit-distance graph requiring four colors
also be used to prove a result in Euclidean Ramsey theory: if T is any triangle in the plane, and the points of the plane are two-colored black and white
Moser_spindle
Geometric graph with unit edge lengths
distance graph is a graph formed from a collection of points in the Euclidean plane by connecting two points whenever the distance between them is exactly
Unit_distance_graph
Shape with three sides
unique flat plane. More generally, four points in three-dimensional Euclidean space determine a solid figure called tetrahedron. In non-Euclidean geometries
Triangle
Tiling of the hyperbolic plane
no overlaps and no gaps. An example is the familiar tiling of the Euclidean plane by squares, meeting edge-to-edge, as seen for instance in many bathrooms
Binary_tiling
Mathematical concept
In Euclidean geometry, two-dimensional rotations and reflections are two kinds of Euclidean plane isometries which are related to one another. A rotation
Rotations and reflections in two dimensions
Rotations_and_reflections_in_two_dimensions
Equation that does not involve powers or products of variables
Cartesian coordinates of a point of the Euclidean plane. The solutions of a linear equation form a line in the Euclidean plane, and, conversely, every line can
Linear_equation
Index of articles associated with the same name
In geometry, Max Dehn introduced two examples of planes, a semi-Euclidean geometry and a non-Legendrian geometry, that have infinitely many lines parallel
Dehn_plane
Type of plane partition
points { p 1 , … p n } {\displaystyle \{p_{1},\dots p_{n}\}} in the Euclidean plane. In this case, each point p k {\displaystyle p_{k}} has a corresponding
Voronoi_diagram
Group realized geometrically by reflections across the sides of a triangle
Euclidean triangle, a triangle on the sphere, or a hyperbolic triangle. Each triangle group is the symmetry group of a tiling of the Euclidean plane,
Triangle_group
Mathematical expression of circle like slices of sphere
three-dimensional Euclidean space, its circles are the intersections of the sphere with planes, and the great circles are intersections with planes passing through
Spherical_circle
Straight figure with zero width and depth
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
Line_(geometry)
Classic counterexample in topology
topology, a branch of mathematics, the infinite broom is a subset of the Euclidean plane that is used as an example distinguishing various notions of connectedness
Infinite_broom
In geometry, many uniform tilings on sphere, euclidean plane, and hyperbolic plane can be made by Wythoff construction within a fundamental triangle,
List of uniform tilings on the sphere, plane, and hyperbolic plane
List_of_uniform_tilings_on_the_sphere,_plane,_and_hyperbolic_plane
Tree connecting given points by short paths
exact solution of the minimum-diameter spanning tree problem, in the Euclidean plane, can be sped up from O ( n 3 ) {\displaystyle O(n^{3})} to n 17 / 6
Minimum-diameter spanning tree
Minimum-diameter_spanning_tree
Fundamental object of geometry
defined the point as "that which has no part". In the two-dimensional Euclidean plane, a point is represented by an ordered pair (x, y) of numbers, where
Point_(geometry)
Mathematical problem
the Beckman–Quarles theorem, according to which any mapping of the Euclidean plane (or any higher dimensional space) to itself that preserves unit distances
Hadwiger–Nelson_problem
Shape with seven sides
the hyperbolic plane, tilings by regular heptagons are possible. There are also concave heptagon tilings possible in the Euclidean plane. The regular heptagon
Heptagon
Volume space bounded by a sphere
for example, a ball in the Euclidean plane is the same thing as a disk, the planar region bounded by a circle. In Euclidean 3-space, a ball is taken to
Ball_(mathematics)
plane (named after August Ferdinand Möbius) is the Euclidean plane supplemented by a single point at infinity. It is also called the inversive plane because
Möbius_plane
Category of coordinate systems
In the hyperbolic plane, as in the Euclidean plane, each point can be uniquely identified by two real numbers. Several qualitatively different ways of
Coordinate systems for the hyperbolic plane
Coordinate_systems_for_the_hyperbolic_plane
Unstructured (or irregular) grid is a tessellation of a part of the Euclidean plane
unstructured grid or irregular grid is a tessellation of a part of the Euclidean plane or Euclidean space by simple shapes, such as triangles or tetrahedra, in an
Unstructured_grid
Existence of a line through two points
theorem in geometry states that every finite set of points in the Euclidean plane has a line that passes through exactly two of the points or a line
Sylvester–Gallai_theorem
Algorithm used for points in euclidean space
directly to the Euclidean plane, similar algorithms may also be applied to higher-dimensional spaces or to spaces with other non-Euclidean metrics. Lloyd's
Lloyd's_algorithm
Concept in geometry
the case of an affine plane (including the Euclidean plane), there is one ideal point for each pencil of parallel lines of the plane. Adjoining these points
Point_at_infinity
Geometric figure made of 4 points connected by 6 lines
connecting these pairs are called diagonals. For points and lines in the Euclidean plane, the diagonal points cannot lie on a single line, and the diagonals
Complete_quadrangle
Mathematical functions
x^{2}-y^{2}=1} as measured in the Lorentzian plane (not the length of a hyperbolic arc in the Euclidean plane), and twice the area of the corresponding hyperbolic
Inverse_hyperbolic_functions
Theorem in projective geometry
mathematicians "complete" the Euclidean plane by adding points at infinity, following Jean-Victor Poncelet. This results in a projective plane. Desargues's theorem
Desargues's_theorem
Quadrilateral with four right angles
In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular
Rectangle
Line intersecting 2 coplanar lines at 2 points
in the same plane at two distinct points. Transversals play a role in establishing whether two or more other lines in the Euclidean plane are parallel
Transversal_(geometry)
Concept in geometry including line and circle
of constant curvature in the Euclidean plane. The natural setting for generalised circles is the extended plane, a plane along with one point at infinity
Generalised_circle
Unsolved problem in combinatorial geometry
lines. Variations of the problem consider the projective plane rather than the Euclidean plane, and require that the triangles not be crossed by any other
Kobon_triangle_problem
Application of Clifford algebra
cannot both be drawn in familiar Euclidean space. Different authors have termed the plane-based GA part of PGA "Euclidean space" and "Antispace". Conformal
Plane-based_geometric_algebra
Locus of the zeros of a polynomial of degree two
Quadrics in a Euclidean plane have dimension one and are thus plane curves. They are called conic sections, or conics. In three-dimensional Euclidean space,
Quadric
Theorem in projective geometry
projective plane since any two lines meet and no exceptions need to be made for parallel lines. However, the theorem remains valid in the Euclidean plane, with
Pascal's_theorem
Mathematical proof by James Garfield
Garfield's proof of the Pythagorean theorem is an original proof of the Pythagorean theorem discovered by James A. Garfield, the 20th president of the
Garfield's proof of the Pythagorean theorem
Garfield's_proof_of_the_Pythagorean_theorem
Branch of mathematics
geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as
Geometry
Geometric property of a pair of sets of points in Euclidean geometry
In Euclidean geometry, linear separability is a property of two sets of points. This is most easily visualized in two dimensions (the Euclidean plane) by
Linear_separability
Concept in geometry
subtended plane angle remains valid in three-dimensional space (3D), as one vertex and two endpoints (assumed non-collinear) define an Euclidean plane in 3D
Subtended_angle
Study of triangles in other spaces than the Euclidean plane
triangles in the Euclidean plane R 2 {\displaystyle \mathbb {R} ^{2}} . There are a number of ways of defining the ordinary Euclidean geometric trigonometric
Generalized_trigonometry
Circle with radius of one
centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane. In topology, it is often denoted as S1 because it is a one-dimensional
Unit_circle
Study of geometry using a coordinate system
equations for planes, straight lines, and circles, often in two and sometimes three dimensions. Geometrically, one studies the Euclidean plane (two dimensions)
Analytic_geometry
Study of angle-preserving transformations
inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines and that preserves
Inversive_geometry
Geometric object that has length and direction
idea when he established the concept of equipollence. Working in a Euclidean plane, he made equipollent any pair of parallel line segments of the same
Euclidean_vector
Geometric construct
In geometry, a domino tiling of a region in the Euclidean plane is a tessellation of the region by dominoes, shapes formed by the union of two unit squares
Domino_tiling
Mathematical parameter of embeddings
spanners, weighted graphs that approximate the Euclidean distances between a set of points in the Euclidean plane. In this case, the embedded metric S is a
Stretch_factor
region between two parallel lines in the Euclidean plane, or between two parallel planes in three-dimensional Euclidean space or between two hyperplanes in
Slab_(geometry)
Unsolved problem in graph theory
ratio of lengths of Steiner trees and Euclidean minimum spanning trees for the same point sets in the Euclidean plane. It was proposed by Edgar Gilbert and
Gilbert–Pollak_conjecture
Graph of intervisible locations in computational geometry
intervisible locations, typically for a set of points and obstacles in the Euclidean plane. Each node in the graph represents a point location, and each edge
Visibility_graph
Unit-distance-preserving maps are isometries
transformation of the Euclidean plane or a higher-dimensional Euclidean space preserves unit distances, then it preserves all Euclidean distances. Equivalently
Beckman–Quarles_theorem
Two-dimensional geometrical space
projective plane by the removal of different lines may not be isomorphic. Typical examples of affine planes are Euclidean planes, which are affine planes over
Affine_plane
Rational numbers with root 5 added
[\varphi ]} is a Euclidean domain with the absolute value of the norm as its Euclidean function, meaning a version of the Euclidean algorithm can be used
Golden_field
Type of mathematical curve
(or degenerated cubics). A cubic plane curve, or simply a cubic is basically the set of the points in the Euclidean plane whose Cartesian coordinates are
Plane_cubic_curve
travel, tourism, insurance
EUCLIDEAN PLANE
EUCLIDEAN PLANE
Boy/Male
Hindu
The planet, Desirable
Boy/Male
Tamil
Resplendent, The venus planet, Friday, Bright
Girl/Female
Muslim
Planet venus
Boy/Male
Tamil
Mercury planet
Boy/Male
Tamil
Grahin | கà¯à®°à®¾à®¹à¯€à®¨
Of planets
Grahin | கà¯à®°à®¾à®¹à¯€à®¨
Girl/Female
Muslim
Planet venus
Boy/Male
Hindu
Teacher of devas, Jupiter, Guru planet
Boy/Male
Tamil
Sarvagraha | ஸரà¯à®µà®•à¯à®°à®¹à®¾
Nivashinay killer of all evil effects of planets
Sarvagraha | ஸரà¯à®µà®•à¯à®°à®¹à®¾
Boy/Male
Hindu
Teacher of devas, Jupiter, Guru planet
Boy/Male
Hindu
A tree, Name of the planet mars, The son of the earth
Girl/Female
Muslim
Moon of another planet
Boy/Male
Tamil
Grahish | கà¯à®°à®¾à®¹à®¿à®·
Lord of the planets
Grahish | கà¯à®°à®¾à®¹à®¿à®·
Boy/Male
English American
Friend. Famous Bearer: American early rock star who died young in a tragic plane crash.
Boy/Male
Hindu
The planet, Desirable
Girl/Female
Muslim
Name of a planet
Boy/Male
Tamil
The intelligent one, Name of Brihaspati, Planet jupiter, Spiritual preceptor, Epithet of Narayan
Boy/Male
Tamil
A tree, Name of the planet mars, The son of the earth
Girl/Female
Muslim
Beauty, The planet venus
Boy/Male
Hindu
The intelligent one, Name of Brihaspati, Planet jupiter, Spiritual preceptor, Epithet of Narayan
Girl/Female
Tamil
Planet
EUCLIDEAN PLANE
EUCLIDEAN PLANE
EUCLIDEAN PLANE
EUCLIDEAN PLANE
EUCLIDEAN PLANE
EUCLIDEAN PLANE
EUCLIDEAN PLANE
n.
Related to Euclid, or to the geometry of Euclid.
a.
Of or pertaining to planets.
a.
Having the nature of a planet; erratic; revolving; wandering.
a.
Of or pertaining to the planets; as, planetary inhabitants; planetary motions; planetary year.
a.
Caused by planets.
n.
A body resembling a planet; an asteroid.
a.
Under the dominion or influence of a planet.
a.
Pertaining to a planetoid.
a.
Belonging to planets.
n.
One who, or that which, planes; a planing machine; esp., a machine for planing wood or metals.
a.
Alt. of Planet-struck
n.
The surface of constant negative curvature generated by the revolution of a tractrix. This surface corresponds in non-Euclidian space to the sphere in ordinary space. An important property of the surface is that any figure drawn upon it can be displaced in any way without tearing it or altering in size any of its elements.
a.
Consisting of planets; as, a planetary system.
a.
Alt. of Planetical
n.
A little planet.
a.
Affected by the influence of planets; blasted.
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