Rectangle

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Rectangle

In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
, a rectangle is a closed

Closed set

In topology and related branches of mathematics, a closed set is a Set whose complement is open set....
planar quadrilateral

Quadrilateral

In geometry, a quadrilateral is a polygon with four 'sides' or edges and four vertices or corners. Sometimes, the term quadrangle is used, for analogy with triangle, and sometimes tetragon for consistency with pentagon , hexagon and so on....
with four right angle

Right angle

In geometry and trigonometry, a right angle is an angle of 90 degree s, corresponding to a quarter turn . It can be defined; as the angle such that twice that angle amounts to a half turn, or 180?....
s. A rectangle with vertices ABCD would be denoted as .

A rectangle with adjacent sides of length

Length

Length is the long dimension of any object. The length of a thing is the distance between its ends, its linear extent as measured from end to end....
s a and b has area

Area

Area is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. The term surface area refers to the total area of the exposed surface of a 3-dimensional solid, such as the sum of the areas of the exposed sides of a polyhedron....
ab and diagonals of equal length . When a = b the rectangle is a square

Square (geometry)

In Euclidean geometry, a square is a regular polygon with four equal sides and four equal angles . A square with vertices ABCD would be denoted ....
, which is a special case of a rhombus

Rhombus

In geometry, a rhombus , or rhomb is an equilateral polygon parallelogram. In other words, it is a four-sided polygon in which every side has the same length....
. A rhombus is the dual polygon

Dual polygon

In geometry, polygons are associated into pairs called duals, where the Vertex of one correspond to the Edge s of the other.Properties...
of a rectangle. The term oblong is occasionally used to refer to a non-square rectangle.

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Encyclopedia

In geometry

Geometry

Closed set

In topology and related branches of mathematics, a closed set is a Set whose complement is open set....
planar quadrilateral

Quadrilateral

Right angle

Length

Length is the long dimension of any object. The length of a thing is the distance between its ends, its linear extent as measured from end to end....
s a and b has area

Area

Square (geometry)

In Euclidean geometry, a square is a regular polygon with four equal sides and four equal angles . A square with vertices ABCD would be denoted ....
, which is a special case of a rhombus

Rhombus

Dual polygon

Parallelogram

In geometry, a parallelogram is a quadrilateral with two sets of parallel sides. The opposite or facing sides of a parallelogram are of equal length, and the opposite angles of a parallelogram are of equal size....
, which has two pairs of parallel opposite sides. A parallelogram, and hence also a rectangle, is a special case of a trapezium (known as a trapezoid

Trapezoid

In geometry, a trapezoid or trapezium is a quadrilateral with twoparallel sides. The term “trapezoid” is used in North America, while the term “trapezium” is prevalent in Britain....
in North America), which has at least one pair of parallel opposite sides.

Two rectangles, neither of which will fit inside the other, are said to be incomparable

Comparability

In mathematics, two elements x and y of a set partial order by a relation = are said to be comparable if and only if x = y or y = x, or in terms of the strict version of the partial order, if and only if x < y or y < x or y = x....
.

The generalization of a rectangle for higher dimensions is an orthotope or hyperrectangle

Hyperrectangle

In geometry, an orthotope is the generalization of a rectangle for higher dimensions, formally defined as the Cartesian product of interval s....
. A three-dimensional orthotope is also called a cuboid

Cuboid

In geometry, a cuboid is a solid figure bounded by six faces, forming a convex polyhedron. There are two competing and incompatible definitions of a cuboid in the mathematical literature....
, rectangular parallelepiped

Parallelepiped

In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms. It is to a parallelogram as a cube is to a square : Euclidean geometry supports all four notions but affine geometry admits only parallelograms and parallelepipeds....
, right rectangular prism

Prism (geometry)

In geometry, an n-sided prism is a polyhedron made of an n-sided polygon base, a Translation copy, and n faces joining corresponding sides....
, or informally a rectangular box.

A rectangle tiled

Tessellation

A tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of the parts of the plane or of other surfaces....
by equal squares clearly has commensurable

Commensurability (mathematics)

In mathematics, two non-zero real numbers a and b are said to be commensurable iff a/b is a rational number....
sides; that is, their ratio is a rational number

Rational number

In mathematics, a rational number is a number which can be expressed as a quotient of two integers. Non-integer rational numbers are usually written as the vulgar fraction , where b is not 0 ....
(see diagram). Less obvious is the fact that a rectangle has commensurable sides if and only if it is tilable by a finite number of unequal squares. The same is true if the tiles are unequal isosceles right triangles

Triangle

A triangle is one of the basic shapes of geometry: a polygon with three corners or wikt:vertex and three sides or edges which are line segments....
.

A rectangle partitioned into a finite number of similar

Similarity (geometry)

Two geometrical objects are called similar if they both have the same shape. Equivalently and more precisely, one is congruence to the result of a uniform Scaling of the other....
tiles is called a perfect rectangle if no two tiles are the same size. The tiles may be squares, rectangles, or right triangles. If two such tiles are the same size, the tiled rectangle is an imperfect rectangle.

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With interactive animation
with interactive animation

Rectangle

See also

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