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[3] [6] John F. Pile, interior design professor and historian, has claimed that Egyptian architects sought the golden proportions without mathematical techniques and that it is common to see the 1.618:1 ratio, along with many other simpler geometrical concepts, in their architectural details, art, and everyday objects found in tombs. In his ...
The golden ratio φ and its negative reciprocal −φ −1 are the two roots of the quadratic polynomial x 2 − x − 1. The golden ratio's negative −φ and reciprocal φ −1 are the two roots of the quadratic polynomial x 2 + x − 1. The golden ratio is also an algebraic number and even an algebraic integer.
The ratio of Seurat's painting/stretcher corresponded to a ratio of 1 to 1.502, ± 0.002 (as opposed to the golden ratio of 1 to 1.618). The compositional axes in the painting correspond to basic mathematical divisions (simple ratios that appear to approximate the golden section).
For example, the height and width of the front of Notre-Dame of Laon have the ratio 8/5 or 1.6, not 1.618. Such Fibonacci ratios quickly become hard to distinguish from the golden ratio. [54] After Pacioli, the golden ratio is more definitely discernible in artworks including Leonardo's Mona Lisa. [55]
The root-3 rectangle is also called sixton, [6] and its short and longer sides are proportionally equivalent to the side and diameter of a hexagon. [7] Since 2 is the square root of 4, the root-4 rectangle has a proportion 1:2, which means that it is equivalent to two squares side-by-side. [7] The root-5 rectangle is related to the golden ratio ...
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 Art of Painting by Jan Vermeer. The term composition means "putting together". It can be thought of as the organization of the elements of art according to the principles of art. Composition can apply to any work of art, from music through writing and into photography, that is arranged using conscious thought.