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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.
Many works of art are claimed to have been designed using the golden ratio. However, many of these claims are disputed, or refuted by measurement. [1] The golden ratio, an irrational number, is approximately 1.618; it is often denoted by the Greek letter φ .
Hambidge distinguishes these from rectangles with rational proportions, which he terms static rectangles. [3] According to him, root-2, 3, 4 and 5 rectangles are often found in Gothic and Classical Greek and Roman art, objects and architecture, while rectangles with aspect ratios greater than root-5 are seldom found in human designs. [4]
Paintings such as the Mona Lisa and various sculptures such as the Venus de Milo contain several golden rectangles. The use of the golden rectangle is found in modern architecture, such as the United Nations building in New York City. Modern painters have also rediscovered the magic of the golden rectangles. The Spirit shows Donald how the ...
Stacking golden rectangles produces golden rectangles anew, and removing or adding squares from golden rectangles leaves rectangles still proportioned in ratio. They can be generated by golden spirals , through successive Fibonacci and Lucas number-sized squares and quarter circles.
Rabatment of the rectangle is a compositional technique used as an aid for the placement of objects or the division of space within a rectangular frame, or as an aid for the study of art. Every rectangle contains two implied squares, each consisting of a short side of the rectangle, an equal length along each longer side, and an imaginary ...
Large rectangles and circles in varying shades of blue from light to dark are illustrated with detail in black and white line showing aquatic motifs such as swirling water, foam and fish. [48] Piper's large west window is the principal decorative element, and the only visible glazing, in Richard Twentyman's modernist church, built 1965–67. [48]
Three mutually perpendicular golden ratio rectangles, with edges connecting their corners, form a regular icosahedron. Another way to construct it is by putting two points on each surface of a cube. In each face, draw a segment line between the midpoints of two opposite edges and locate two points with the golden ratio distance from each midpoint.
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