Rectangle

In geometry, a rectangle ( a Orthogon ) a planar quadrilateral whose interior angles are all right angles.

When rectangle is a special case of the parallelogram ( equiangular parallelogram ) and thus also of the trapezoid. A special case of the rectangle is the square in which all sides are of equal length ( equilateral rectangle).

Properties

For each rectangle, the following applies:

• The sum of the angles is 360 °.
• Opposite sides are equal and parallel.
• The two diagonals are equal in length and bisect each other.
• It has a radius and is therefore a cyclic quadrilateral. Circumcenter is the intersection of the diagonals.
• It is axially symmetrical with respect to the mid-perpendicular ( Seitensymmetralen ) of the sides of the rectangle. The two axes of symmetry are therefore perpendicular.
• It is point-symmetric ( symmetric bidentate ) with respect to the diagonal intersection.

Formulary

The formula for the diagonal length is based on the Pythagorean theorem. The radius radius is obtained by halving the diagonal length.

Special rectangles

Golden rectangle

Rectangles with the property called golden rectangles.

→ see also: Golden section Golden rectangle # and Golden Triangle

Perfect rectangle

A rectangle is called perfect, if you can cover it completely and without overlap with squares, where all the squares are different. It is not easy to find such a decomposition. Such a decomposition of a rectangle (32 × 33 ) in nine squares was found in 1925 by Zbigniew Moron. It is composed of squares with side lengths of 1, 4, 7, 8, 9, 10, 14, 15 and 18