The golden ratio is also called the golden section (Latin: sectio aurea) or golden mean. Other names include extreme and mean ratio, medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut, golden number, and mean of Phidias.
In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The figure on the right illustrates the geometric relationship. Expressed algebraically:
where the Greek letter phi represents the golden ratio. Its value is:
At least since the 20th century, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing (see Applications and observations below). Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which can be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has also been used to analyze the proportions of natural objects as well as man-made systems such as financial markets, in some cases based on dubious fits to data.
Other articles related to "ratio, golden ratio, ratios, golden":
... The ratio of the edges of a Kepler triangle are linked to the golden ratio and can be written, or approximately 1 1.272 1.618 ... triangle (see figure) are in geometric progression according to the golden ratio ... Triangles with such ratios are named after the German mathematician and astronomer Johannes Kepler (1571–1630), who first demonstrated that this triangle is ...
... The Golden Ratio" (The Golden Ratio, 2010) "The Sign" (The Sign, 1993) "The Juvenile" (Da Capo, 2002) "Tokyo Girl" (Flowers, Cruel Summer, 1998) "Told My Ma" (The Golden Ratio, 2010) "Travel to Romantis ...
... Examples of disputed observations of the golden ratio include the following Historian John Man states that the pages of the Gutenberg Bible were "based on the golden section shape" ... However, according to Man's own measurements, the ratio of height to width was 1.45 ... shells of mollusks and cephalopods are often claimed to be in the golden ratio ...
... of which illustrate the appearance of the golden ratio in geometric figures ... authors feel there is no actual evidence that Da Vinci used the golden ratio in Vitruvian Man however, Olmos (1991) observes otherwise through geometrical analysis ... and several members of the Amati family) as having similar regulator lines related to the golden ratio ...
... Le Corbusier's faith in the mathematical order of the universe was closely bound to the golden ratio and the Fibonacci series, which he described as "rhyt ... inevitability, the same fine inevitability which causes the tracing out of the Golden Section by children, old men, savages and the learned." Modulor Le ... In addition to the golden ratio, Le Corbusier based the system on human measurements, Fibonacci numbers, and the double unit ...
Famous quotes containing the words ratio and/or golden:
“People are lucky and unlucky not according to what they get absolutely, but according to the ratio between what they get and what they have been led to expect.”
—Samuel Butler (18351902)
“Come live with me, and be my love,
And we will some new pleasures prove
Of golden sands, and crystal brooks,
With silken lines, and silver hooks.”
—John Donne (15721631)