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A root-phi rectangle divides into a pair of Kepler triangles (right triangles with edge lengths in geometric progression). The root-φ rectangle is a dynamic rectangle but not a root rectangle. Its diagonal equals φ times the length of the shorter side. If a root-φ rectangle is divided by a diagonal, the result is two congruent Kepler triangles.
The size of a screen is usually described by the length of its diagonal, which is the distance between opposite corners, typically measured in inches. It is also sometimes called the physical image size to distinguish it from the "logical image size," which describes a screen's display resolution and is measured in pixels .
Date/Time Thumbnail Dimensions User Comment; current: 14:02, 23 November 2008: 600 × 600 (1 KB): Hohum {{Information |Description={{en|1=Showing that the diagonal measurement of a rectangle is the same as the diameter of a circumscribed circle.}} |Source=Own work by uploader |Author=Hohum |Date=November 2008 |Permission= |other_versions= }}
If the diagram is further subdivided by perpendicular lines through U and V, the lengths of the diagonal and its subsections can be expressed as trigonometric functions of arguments 72 and 36 degrees, the angles of the golden triangle: Diagonal segments of the golden rectangle measure nested pentagons. The ratio AU:SV is φ 2.
The area, height and width of displays with identical diagonal measurements vary dependent on aspect ratio. On two-dimensional display devices such as computer monitors the display size or viewable image size is the actual amount of screen space that is available to display a picture , video or working space, without obstruction from the bezel ...
It is the ratio of a regular pentagon's diagonal to its side and thus appears in the construction of the dodecahedron and icosahedron. [7] A golden rectangle—that is, a rectangle with an aspect ratio of —may be cut into a square and a smaller rectangle with the same aspect ratio.
A magic square is an arrangement of numbers in a square grid so that the sum of the numbers along every row, column, and diagonal is the same. Similarly, one may define a magic cube to be an arrangement of numbers in a cubical grid so that the sum of the numbers on the four space diagonals must be the same as the sum of the numbers in each row, each column, and each pillar.
A crossed rectangle is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals [4] (therefore only two sides are parallel). It is a special case of an antiparallelogram , and its angles are not right angles and not all equal, though opposite angles are equal.