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# Rectangle

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. [1]

78 relations: Angle, Antiparallelogram, Area, Bisection, Bow tie, Brickwork, British flag theorem, Butterfly, Circle, Circumscribed circle, Commensurability (mathematics), Comparability, Congruence (geometry), Convex polygon, Crelle's Journal, Cuboid, Degree (angle), Degrees of freedom (mechanics), Density (polytope), Diagonal, Dihedral group, Dual polygon, Duke Mathematical Journal, Edge (geometry), Elliptic geometry, Equality (mathematics), Equiangular polygon, Euclidean geometry, Golden rectangle, Great circle, Group action, Herringbone pattern, Homothetic transformation, Hyperbolic geometry, Hyperrectangle, If and only if, Inscribed figure, Internal and external angles, Isogonal figure, Isoperimetric inequality, Isosceles trapezoid, Japanese theorem for cyclic quadrilaterals, Journal of Combinatorial Theory, Latin, Length, Line (geometry), List of self-intersecting polygons, Parallel (geometry), Parallelogram, Perimeter, ... Expand index (28 more) »

## Angle

In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

## Antiparallelogram

In geometry, an antiparallelogram is a quadrilateral having, like a parallelogram, two opposite pairs of equal-length sides, but in which the sides of one pair cross each other.

## Area

Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.

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## Bisection

In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector.

## Bow tie

The bow tie is a type of traditional necktie.

## Brickwork

Brickwork is masonry produced by a bricklayer, using bricks and mortar.

## British flag theorem

In Euclidean geometry, the British flag theorem says that if a point P is chosen inside rectangle ABCD then the sum of the squared Euclidean distances from P to two opposite corners of the rectangle equals the sum to the other two opposite corners.

## Butterfly

Butterflies are insects in the macrolepidopteran clade Rhopalocera from the order Lepidoptera, which also includes moths.

## Circle

A circle is a simple closed shape.

## Circumscribed circle

In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon.

## Commensurability (mathematics)

In mathematics, two non-zero real numbers a and b are said to be commensurable if their ratio is a rational number; otherwise a and b are called incommensurable.

## Comparability

In mathematics, any two elements x and y of a set P that is partially ordered by a binary relation ≤ are comparable when either x ≤ y or y ≤ x. If it is not the case that x and y are comparable, then they are called incomparable.

## Congruence (geometry)

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

## Convex polygon

A convex polygon is a simple polygon (not self-intersecting) in which no line segment between two points on the boundary ever goes outside the polygon.

## Crelle's Journal

Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).

## Cuboid

In geometry, a cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube.

## Degree (angle)

A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360 degrees.

## Degrees of freedom (mechanics)

In physics, the degree of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration.

## Density (polytope)

In geometry, the density of a polytope represents the number of windings of a polytope, particularly a uniform or regular polytope, around its center.

## Diagonal

In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge.

## Dihedral group

In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.

## Dual polygon

In geometry, polygons are associated into pairs called duals, where the vertices of one correspond to the edges of the other.

## Duke Mathematical Journal

Duke Mathematical Journal is a peer-reviewed mathematics journal published by Duke University Press.

## Edge (geometry)

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.

## Elliptic geometry

Elliptic geometry is a geometry in which Euclid's parallel postulate does not hold.

## Equality (mathematics)

In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.

## Equiangular polygon

In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal.

## Euclidean geometry

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

## Golden rectangle

In geometry, a golden rectangle is a rectangle whose side lengths are in the golden ratio, 1: \tfrac, which is 1:\varphi (the Greek letter phi), where \varphi is approximately 1.618.

## Great circle

A great circle, also known as an orthodrome, of a sphere is the intersection of the sphere and a plane that passes through the center point of the sphere.

## Group action

In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.

## Herringbone pattern

The herringbone pattern is an arrangement of rectangles used for floor tilings and road pavement, so named for a fancied resemblance to the bones of a fish such as a herring.

## Homothetic transformation

In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and a nonzero number λ called its ratio, which sends in other words it fixes S, and sends any M to another point N such that the segment SN is on the same line as SM, but scaled by a factor λ. In Euclidean geometry homotheties are the similarities that fix a point and either preserve (if) or reverse (if) the direction of all vectors.

## Hyperbolic geometry

In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.

## Hyperrectangle

In geometry, an n-orthotopeCoxeter, 1973 (also called a hyperrectangle or a box) is the generalization of a rectangle for higher dimensions, formally defined as the Cartesian product of intervals.

## If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

## Inscribed figure

An inscribed triangle of a circle In geometry, an inscribed planar shape or solid is one that is enclosed by and "fits snugly" inside another geometric shape or solid.

## Internal and external angles

In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint.

## Isogonal figure

In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.

## Isoperimetric inequality

In mathematics, the isoperimetric inequality is a geometric inequality involving the surface area of a set and its volume.

## Isosceles trapezoid

In Euclidean geometry, an isosceles trapezoid (isosceles trapezium in British English) is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides.

## Japanese theorem for cyclic quadrilaterals

In geometry, the Japanese theorem states that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle.

## Journal of Combinatorial Theory

The Journal of Combinatorial Theory, Series A and Series B, are mathematical journals specializing in combinatorics and related areas.

## Latin

Latin (Latin: lingua latīna) is a classical language belonging to the Italic branch of the Indo-European languages.

## Length

In geometric measurements, length is the most extended dimension of an object.

## Line (geometry)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

## List of self-intersecting polygons

Self-intersecting polygons, crossed polygons, or self-crossing polygons are polygons some of whose edges cross each other.

## Parallel (geometry)

In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel.

## Parallelogram

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.

## Perimeter

A perimeter is a path that surrounds a two-dimensional shape.

## Perpendicular

In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees).

## Polyabolo

In recreational mathematics, a polyabolo (also known as a polytan) is a shape formed by gluing isosceles right triangles edge-to-edge, making a polyform with the isosceles right triangle as the base form.

## Polygon

In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.

## Polyomino

A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge.

In Euclidean plane geometry, a quadrilateral is a polygon with four edges (or sides) and four vertices or corners.

## Rectilinear polygon

A rectilinear polygon is a polygon all of whose edge intersections are at right angles.

## Reflection symmetry

Reflection symmetry, line symmetry, mirror symmetry, mirror-image symmetry, is symmetry with respect to reflection.

## Rhombus

In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a simple (non-self-intersecting) quadrilateral whose four sides all have the same length.

## Right angle

In geometry and trigonometry, a right angle is an angle of exactly 90° (degrees), corresponding to a quarter turn.

## Right triangle

A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle).

## Rotation

A rotation is a circular movement of an object around a center (or point) of rotation.

## Rotational symmetry

Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn.

## Similarity (geometry)

Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other.

## Simple polygon

In geometry a simple polygon is a flat shape consisting of straight, non-intersecting line segments or "sides" that are joined pair-wise to form a closed path.

## Space frame

In architecture and structural engineering, a space frame or space structure is a rigid, lightweight, truss-like structure constructed from interlocking struts in a geometric pattern.

## Spherical geometry

Spherical geometry is the geometry of the two-dimensional surface of a sphere.

## Square

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.

## Star-shaped polygon

A star-shaped polygon is a polygonal region in the plane that is a star domain, that is, a polygon that contains a point from which the entire polygon boundary is visible.

## Superellipse

A superellipse, also known as a Lamé curve after Gabriel Lamé, is a closed curve resembling the ellipse, retaining the geometric features of semi-major axis and semi-minor axis, and symmetry about them, but a different overall shape.

## Symmetry

Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance.

## Tessellation

A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.

## Three-dimensional space

Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).

## Translation (geometry)

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or a space by the same distance in a given direction.

## Trapezoid

In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezoid in American and Canadian English but as a trapezium in English outside North America.

## Triangle

A triangle is a polygon with three edges and three vertices.

## Vertex (geometry)

In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.

## Vertex arrangement

In geometry, a vertex arrangement is a set of points in space described by their relative positions.

## Wire

A wire is a single, usually cylindrical, flexible strand or rod of metal.

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## References

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