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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 quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.
A more flexible definition of shape takes into consideration the fact that realistic shapes are often deformable, e.g. a person in different postures, a tree bending in the wind or a hand with different finger positions. One way of modeling non-rigid movements is by homeomorphisms. Roughly speaking, a homeomorphism is a continuous stretching ...
The simplest rectilinear polygon is an axis-aligned rectangle - a rectangle with 2 sides parallel to the x axis and 2 sides parallel to the y axis. See also: Minimum bounding rectangle . A golygon is a rectilinear polygon whose side lengths in sequence are consecutive integers.
When the rectangle is not a square, its right-triangular half is scalene. Every triangle whose base is the diameter of a circle and whose apex lies on the circle is a right triangle, with the right angle at the apex and the hypotenuse as the base; conversely, the circumcircle of any right triangle has the hypotenuse as its diameter.
A rectangle is a quadrilateral with four right angles. A square has four right angles, in addition to equal-length sides. The Pythagorean theorem states how to determine when a triangle is a right triangle .
In geometry, a golden rectangle is a rectangle with side lengths in golden ratio +:, or :, with approximately equal to 1.618 or 89/55. Golden rectangles exhibit a special form of self-similarity : if a square is added to the long side, or removed from the short side, the result is a golden rectangle as well.
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The dual polygon of a rhombus is a rectangle: [12] A rhombus has all sides equal, while a rectangle has all angles equal. A rhombus has opposite angles equal, while a rectangle has opposite sides equal. A rhombus has an inscribed circle, while a rectangle has a circumcircle.