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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 .
A dynamic rectangle is a right-angled, four-sided figure (a rectangle) with dynamic symmetry which, in this case, means that aspect ratio (width divided by height) is a distinguished value in dynamic symmetry, a proportioning system and natural design methodology described in Jay Hambidge's books.
The rectangles chosen as "best" by the largest number of participants and as "worst" by the fewest participants had a ratio of 0.62 (21:34). [20] This ratio is known as the "golden section" (or golden ratio) and referred to the ratio of a rectangle's width to length that is most appealing to the eye. Carl Stumpf was a participant in this study.
Art historian Daniel Robbins argued that in addition to referencing the mathematical golden section, the term associated with the Salon Cubists also refers to the name of the earlier Bandeaux d'Or group, with which Albert Gleizes and other former members of the Abbaye de Créteil had been deeply involved.
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.
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.
A realization of the Borromean rings by three mutually perpendicular golden rectangles can be found within a regular icosahedron by connecting three opposite pairs of its edges. [2] Every three unknotted polygons in Euclidean space may be combined, after a suitable scaling transformation, to form the Borromean rings.