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In
Euclidean plane geometry Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the '' Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axio ...
, a rectangle is a
quadrilateral In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''latus'', meaning "side". It is also called a tetragon, ...
with four
right angle In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles. Th ...
s. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a
parallelogram In Euclidean geometry, a parallelogram is a simple (non- self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of eq ...
containing a right angle. A rectangle with four sides of equal length is a ''
square In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90- degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length a ...
''. The term " oblong" is occasionally used to refer to a non-
square In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90- degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length a ...
rectangle. A rectangle with vertices ''ABCD'' would be denoted as . The word rectangle comes from the
Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...
''rectangulus'', which is a combination of ''rectus'' (as an adjective, right, proper) and ''angulus'' (
angle In Euclidean 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. Angles formed by two rays lie in the plane that contains the rays. Angles ...
). A
crossed rectangle In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containin ...
is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals (therefore only two sides are parallel). It is a special case of an
antiparallelogram In geometry, an antiparallelogram is a type of self-crossing quadrilateral. Like a parallelogram, an antiparallelogram has two opposite pairs of equal-length sides, but these pairs of sides are not in general parallel. Instead, sides in the ...
, and its angles are not right angles and not all equal, though opposite angles are equal. Other geometries, such as
spherical A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the ce ...
,
elliptic In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in ...
, and
hyperbolic Hyperbolic is an adjective describing something that resembles or pertains to a hyperbola (a curve), to hyperbole (an overstatement or exaggeration), or to hyperbolic geometry. The following phenomena are described as ''hyperbolic'' because they ...
, have so-called rectangles with opposite sides equal in length and equal angles that are not right angles. Rectangles are involved in many
tiling Tiling may refer to: *The physical act of laying tiles * Tessellations Computing *The compiler optimization of loop tiling *Tiled rendering, the process of subdividing an image by regular grid *Tiling window manager People *Heinrich Sylvester T ...
problems, such as tiling the plane by rectangles or tiling a rectangle by
polygon In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed '' polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two ...
s.


Characterizations

A
convex Convex or convexity may refer to: Science and technology * Convex lens, in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytop ...
quadrilateral In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''latus'', meaning "side". It is also called a tetragon, ...
is a rectangle
if and only if In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false. The connective is bic ...
it is any one of the following: * a
parallelogram In Euclidean geometry, a parallelogram is a simple (non- self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of eq ...
with at least one
right angle In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles. Th ...
* a parallelogram with
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. Informally, any sloping line is called diagonal. The word ''diagonal'' derives from the ancient Greek δ� ...
s of equal length * a parallelogram ''ABCD'' where
triangle A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non- colline ...
s ''ABD'' and ''DCA'' are
congruent Congruence may refer to: Mathematics * Congruence (geometry), being the same size and shape * Congruence or congruence relation, in abstract algebra, an equivalence relation on an algebraic structure that is compatible with the structure * In mod ...
* an equiangular quadrilateral * a quadrilateral with four right angles * a quadrilateral where the two diagonals are equal in length and bisect each other * a convex quadrilateral with successive sides ''a'', ''b'', ''c'', ''d'' whose area is \tfrac(a+c)(b+d). * a convex quadrilateral with successive sides ''a'', ''b'', ''c'', ''d'' whose area is \tfrac \sqrt.


Classification


Traditional hierarchy

A rectangle is a special case of a
parallelogram In Euclidean geometry, a parallelogram is a simple (non- self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of eq ...
in which each pair of adjacent sides is
perpendicular In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the '' perpendicular symbol'', ⟂. It c ...
. A parallelogram is a special case of a trapezium (known as a
trapezoid A quadrilateral with at least one pair of parallel sides is called a trapezoid () in American and Canadian English. In British and other forms of English, it is called a trapezium (). A trapezoid is necessarily a convex quadrilateral in Eu ...
in North America) in which ''both'' pairs of opposite sides are
parallel Parallel is a geometric term of location which may refer to: Computing * Parallel algorithm * Parallel computing * Parallel metaheuristic * Parallel (software), a UNIX utility for running programs in parallel * Parallel Sysplex, a cluster o ...
and equal in
length Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the Inte ...
. A trapezium is a
convex Convex or convexity may refer to: Science and technology * Convex lens, in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytop ...
quadrilateral In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''latus'', meaning "side". It is also called a tetragon, ...
which has at least one pair of
parallel Parallel is a geometric term of location which may refer to: Computing * Parallel algorithm * Parallel computing * Parallel metaheuristic * Parallel (software), a UNIX utility for running programs in parallel * Parallel Sysplex, a cluster o ...
opposite sides. A convex quadrilateral is *
Simple Simple or SIMPLE may refer to: *Simplicity, the state or quality of being simple Arts and entertainment * ''Simple'' (album), by Andy Yorke, 2008, and its title track * "Simple" (Florida Georgia Line song), 2018 * "Simple", a song by Johnn ...
: The boundary does not cross itself. *
Star-shaped In geometry, a set S in the Euclidean space \R^n is called a star domain (or star-convex set, star-shaped set or radially convex set) if there exists an s_0 \in S such that for all s \in S, the line segment from s_0 to s lies in S. This defin ...
: The whole interior is visible from a single point, without crossing any edge.


Alternative hierarchy

De Villiers defines a rectangle more generally as any quadrilateral with axes of symmetry through each pair of opposite sides. This definition includes both right-angled rectangles and crossed rectangles. Each has an axis of symmetry parallel to and equidistant from a pair of opposite sides, and another which is the
perpendicular In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the '' perpendicular symbol'', ⟂. It c ...
bisector of those sides, but, in the case of the crossed rectangle, the first
axis An axis (plural ''axes'') is an imaginary line around which an object rotates or is symmetrical. Axis may also refer to: Mathematics * Axis of rotation: see rotation around a fixed axis * Axis (mathematics), a designator for a Cartesian-coordinat ...
is not an axis of
symmetry Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...
for either side that it bisects. Quadrilaterals with two axes of symmetry, each through a pair of opposite sides, belong to the larger class of quadrilaterals with at least one axis of symmetry through a pair of opposite sides. These quadrilaterals comprise isosceles trapezia and crossed isosceles trapezia (crossed quadrilaterals with the same
vertex arrangement In geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes. For example, a ''square vertex arrangement'' is understood to mean four points in a plane, equa ...
as isosceles trapezia).


Properties


Symmetry

A rectangle is
cyclic Cycle, cycles, or cyclic may refer to: Anthropology and social sciences * Cyclic history, a theory of history * Cyclical theory, a theory of American political history associated with Arthur Schlesinger, Sr. * Social cycle, various cycles in so ...
: all
corner Corner may refer to: People *Corner (surname) * House of Cornaro, a noble Venetian family (''Corner'' in Venetian dialect) Places *Corner, Alabama, a community in the United States *Corner Inlet, Victoria, Australia *Corner River, a tributary of ...
s lie on a single
circle A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is cons ...
. It is equiangular: all its corner
angle In Euclidean 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. Angles formed by two rays lie in the plane that contains the rays. Angles ...
s are equal (each of 90 degrees). It is isogonal or
vertex-transitive In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure. This implies that each vertex is surrounded by the same kinds of fa ...
: all corners lie within the same
symmetry orbit In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism ...
. It has two
line Line most often refers to: * Line (geometry), object with zero thickness and curvature that stretches to infinity * Telephone line, a single-user circuit on a telephone communication system Line, lines, The Line, or LINE may also refer to: Art ...
s of
reflectional symmetry In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D th ...
and
rotational symmetry Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which ...
of order 2 (through 180°).


Rectangle-rhombus duality

The
dual polygon In geometry, polygons are associated into pairs called duals, where the vertices of one correspond to the edges of the other. Properties Regular polygons are self-dual. The dual of an isogonal (vertex-transitive) polygon is an isotoxal (ed ...
of a rectangle is a
rhombus In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The ...
, as shown in the table below. * The figure formed by joining, in order, the midpoints of the sides of a rectangle is a
rhombus In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The ...
and vice versa.


Miscellaneous

A rectangle is a
rectilinear polygon A rectilinear polygon is a polygon all of whose sides meet at right angles. Thus the interior angle at each vertex is either 90° or 270°. Rectilinear polygons are a special case of isothetic polygons. In many cases another definition is ...
: its sides meet at right angles. A rectangle in the plane can be defined by five independent
degrees of freedom Degrees of freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a thermodynamic system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or ...
consisting, for example, of three for position (comprising two of
translation Translation is the communication of the meaning of a source-language text by means of an equivalent target-language text. The English language draws a terminological distinction (which does not exist in every language) between ''transla ...
and one of
rotation Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...
), one for shape ( aspect ratio), and one for overall size (area). Two rectangles, neither of which will fit inside the other, are said to be incomparable.


Formulae

If a rectangle has length \ell and width w * it has
area Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while '' surface area'' refers to the area of an op ...
A = \ell w\,, * it has
perimeter A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several pr ...
P = 2\ell + 2w = 2(\ell + w)\,, * each diagonal has length d=\sqrt, * and when \ell = w\,, the rectangle is a
square In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90- degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length a ...
.


Theorems

The isoperimetric theorem for rectangles states that among all rectangles of a given
perimeter A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several pr ...
, the square has the largest
area Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while '' surface area'' refers to the area of an op ...
. The midpoints of the sides of any
quadrilateral In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''latus'', meaning "side". It is also called a tetragon, ...
with
perpendicular In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the '' perpendicular symbol'', ⟂. It c ...
diagonals 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. Informally, any sloping line is called diagonal. The word ''diagonal'' derives from the ancient Greek δ ...
form a rectangle. A
parallelogram In Euclidean geometry, a parallelogram is a simple (non- self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of eq ...
with equal
diagonals 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. Informally, any sloping line is called diagonal. The word ''diagonal'' derives from the ancient Greek δ ...
is a rectangle. The
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. Triangulating an arbitrary cyclic quadrilateral by its diagonals yields four overlapping tr ...
states that the incentres of the four triangles determined by the vertices of a cyclic quadrilateral taken three at a time form a rectangle. The
British flag theorem In Euclidean geometry, the British flag theorem says that if a point ''P'' is chosen inside a rectangle ''ABCD'' then the sum of the squares of the Euclidean distances from ''P'' to two opposite corners of the rectangle equals the sum to the oth ...
states that with vertices denoted ''A'', ''B'', ''C'', and ''D'', for any point ''P'' on the same plane of a rectangle: :\displaystyle (AP)^2 + (CP)^2 = (BP)^2 + (DP)^2. For every convex body ''C'' in the plane, we can inscribe a rectangle ''r'' in ''C'' such that a homothetic copy ''R'' of ''r'' is circumscribed about ''C'' and the positive homothety ratio is at most 2 and 0.5 \text(R) \leq \text(C) \leq 2 \text(r).


Crossed rectangles

A ''crossed'' ''quadrilateral'' (self-intersecting) consists of two opposite sides of a non-self-intersecting quadrilateral along with the two diagonals. Similarly, a crossed rectangle is a ''crossed quadrilateral'' which consists of two opposite sides of a rectangle along with the two diagonals. It has the same
vertex arrangement In geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes. For example, a ''square vertex arrangement'' is understood to mean four points in a plane, equa ...
as the rectangle. It appears as two identical triangles with a common vertex, but the geometric intersection is not considered a vertex. A ''crossed quadrilateral'' is sometimes likened to a
bow tie The bow tie is a type of necktie. A modern bow tie is tied using a common shoelace knot, which is also called the bow knot for that reason. It consists of a ribbon of fabric tied around the collar of a shirt in a symmetrical manner so that t ...
or
butterfly Butterflies are insects in the macrolepidopteran clade Rhopalocera from the order Lepidoptera, which also includes moths. Adult butterflies have large, often brightly coloured wings, and conspicuous, fluttering flight. The group compris ...
, sometimes called an "angular eight". A
three-dimensional Three-dimensional space (also: 3D space, 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). This is the inform ...
rectangular
wire Overhead power cabling. The conductor consists of seven strands of steel (centre, high tensile strength), surrounded by four outer layers of aluminium (high conductivity). Sample diameter 40 mm A wire is a flexible strand of metal. Wire is co ...
frame that is twisted can take the shape of a bow tie. The interior of a ''crossed rectangle'' can have a polygon density of ±1 in each triangle, dependent upon the winding orientation as clockwise or counterclockwise. A ''crossed rectangle'' may be considered equiangular if right and left turns are allowed. As with any ''crossed quadrilateral'', the sum of its interior angles is 720°, allowing for internal angles to appear on the outside and exceed 180°. A rectangle and a crossed rectangle are quadrilaterals with the following properties in common: * Opposite sides are equal in length. * The two diagonals are equal in length. * It has two lines of reflectional symmetry and rotational symmetry of order 2 (through 180°).


Other rectangles

In
spherical geometry 300px, A sphere with a spherical triangle on it. Spherical geometry is the geometry of the two-dimensional surface of a sphere. In this context the word "sphere" refers only to the 2-dimensional surface and other terms like "ball" or "solid sp ...
, a spherical rectangle is a figure whose four edges are
great circle In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point. Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geome ...
arcs which meet at equal angles greater than 90°. Opposite arcs are equal in length. The surface of a sphere in Euclidean solid geometry is a non-Euclidean surface in the sense of elliptic geometry. Spherical geometry is the simplest form of elliptic geometry. In
elliptic geometry Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines ...
, an elliptic rectangle is a figure in the elliptic plane whose four edges are elliptic arcs which meet at equal angles greater than 90°. Opposite arcs are equal in length. In
hyperbolic geometry In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For any given line ''R'' and point ''P ...
, a hyperbolic rectangle is a figure in the hyperbolic plane whose four edges are hyperbolic arcs which meet at equal angles less than 90°. Opposite arcs are equal in length.


Tessellations

The rectangle is used in many periodic
tessellation A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of ...
patterns, in
brickwork Brickwork is masonry produced by a bricklayer, using bricks and mortar. Typically, rows of bricks called ''courses'' are laid on top of one another to build up a structure such as a brick wall. Bricks may be differentiated from blocks by si ...
, for example, these tilings:


Squared, perfect, and other tiled rectangles

A rectangle tiled by squares, rectangles, or triangles is said to be a "squared", "rectangled", or "triangulated" (or "triangled") rectangle respectively. The tiled rectangle is ''perfect'' if the tiles are similar and finite in number and no two tiles are the same size. If two such tiles are the same size, the tiling is ''imperfect''. In a perfect (or imperfect) triangled rectangle the triangles must be
right triangle A right triangle (American English) or right-angled triangle ( British), or more formally an orthogonal triangle, formerly called a rectangled triangle ( grc, ὀρθόσγωνία, lit=upright angle), is a triangle in which one angle is a right a ...
s. A database of all known perfect rectangles, perfect squares and related shapes can be found a
squaring.net
The lowest number of squares need for a perfect tiling of a rectangle is 9 and the lowest number needed for a perfect tilling a square is 21, found in 1978 by computer search. A rectangle has commensurable sides if and only if it is tileable by a finite number of unequal squares. The same is true if the tiles are unequal isosceles right triangles. The tilings of rectangles by other tiles which have attracted the most attention are those by congruent non-rectangular
polyomino A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling. Polyominoes have been used in pop ...
es, allowing all rotations and reflections. There are also tilings by congruent polyaboloes.


Unicode

U+25AC ▬ BLACK RECTANGLE U+25AD ▭ WHITE RECTANGLE U+25AE ▮ BLACK VERTICAL RECTANGLE U+25AF ▯ WHITE VERTICAL RECTANGLE


See also

*
Cuboid In geometry, a cuboid is a hexahedron, a six-faced solid. Its faces are quadrilaterals. Cuboid means "like a cube", in the sense that by adjusting the length of the edges or the angles between edges and faces a cuboid can be transformed into a c ...
*
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. Golden rectangles exhibit a special form of self-similarity ...
*
Hyperrectangle In geometry, an orthotopeCoxeter, 1973 (also called a hyperrectangle or a box) is the generalization of a rectangle to higher dimensions. A necessary and sufficient condition is that it is congruent to the Cartesian product of intervals. If al ...
* Superellipse (includes a rectangle with rounded corners)


References


External links

*
Definition and properties of a rectangle
with interactive animation.

with interactive animation. {{Authority control Types of quadrilaterals Elementary shapes