Golden Ratio, Phi Ratio


Golden Mean, Golden Section, Divine Proportion






The golden ratio is also called the golden section or golden mean. Other names include extreme and mean ratio, medial section, divine proportion, divine section golden proportion, golden cut, and golden number. 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.

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. Read more ... 




The Golden Ratio in Space





The Golden Ratio in Architecture




Ancient Pueblo Used Golden Ratio to Build the Sun Temple  
Live Science - February 13, 2017

The Great Pyramids in Giza, the Parthenon in Athens and Chichen Itza in Mexico have something in common. Besides attracting hordes of tourists, all of these architectural wonders appear to use the golden ratio. This mathematical number is often written as 1.618, the first few digits of its infinite decimal form. Expressed another way, two quantities - let's call the larger one "a" and the smaller "b" - are in the golden ratio if "a is to b" as "a + b is to a." The result is a composition with aesthetically pleasing proportions. Now, shapes with the golden ratio, as well as other geometric shapes, have been found in another, unexpected site: the Sun Temple at Mesa Verde National Park in Colorado, built by the ancient Pueblo people who lived in what is now the modern-day Southwest; they had no known written language or written number system.




The Golden Ratio in Art


The Vitruvian Man is a drawing created by Leonardo da Vinci circa 1490. It is accompanied by notes based on the work of the architect Vitruvius. The drawing, which is in pen and ink on paper, depicts a male figure in two superimposed positions with his arms and legs apart and simultaneously inscribed in a circle and square. The drawing and text are sometimes called the Canon of Proportions or, less often, Proportions of Man.




The Golden Ratio in Nature






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