Research Question

Have the Golden Ratio and Fibonacci Sequence been observed in nature and history and can they be applied to various works and projects to add value and enhance the product/results? 

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Art

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 The Golden Ratio And Fibonacci Sequence In Art And Architecture  Although humans are blessed with the gift of nature, we tend to enjoy aesthetically pleasing order and symmetry. According to evidence, humans are likely to detect symmetry in as little as 0.05 of a second! It is evident that humans do not only like seeing symmetry and Divine Proportion, but also working to create and display it. It can be seen in art and architecture.   In paintings, portraits and drawings, artists like following it.  Vitruvian Man (Leonardo Da Vinci)  The Great Wave (Katsushika Hokusai)   The Last Supper (Leonardo Da Vinci) Mona Lisa (Leonardo da Vinci) Rembrandt's Self Portrait Mondrian, Tableau 1. For example, the Vitruvian Man exhibits a pentagonal symmetry, and the square side to circle radius ratio is the golden ratio. The dimensions of the table and the proportions of the wall and background in Da Vinci's "The Last Supper" display an attempt of following the gold...
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Topic: The Golden Ratio

 The Golden Ratio The golden ratio is described as a ratio between two numbers that equals approximately 1.618. It is also referred to as the golden number, golden proportion or the divine proportion.  The Greek letter  " φ" (phi) is used to denote the golden ratio.  It is often associated with the Fibonacci sequence, which is a naturally occurring series of numbers, in which each number is added to the last. Although the golden ratio is vastly viewed as a mathematical ratio, it can be found anywhere. In the creation of every balanced thing around us, r anging from nature and architecture , to paintings and music, it plays a part. It is often applied advertently to create an organic and aesthetically pleasing composition.  
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Music

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  Mathematical harmony has, over the years, been used deliberately and unknowingly in musical composition. Mathematician Gottfried Leibnez wrote that "music is the pleasure the human mind experiences from counting without being aware that it is counting." Italian composer and lutenist, Vincenzo Galelie also wrote a discourse on string theory, which states that "the universe is constructed by tiny vibrating particles", which are assumed to be even smaller than subatomic particles, and these interact with each other by twisting, folding and vibrating. They create phenomena like electromagnetism and gravity. This string theory may also be linked to sound and hence music.   Composers often rely on the golden ratio and Fibonacci sequence to enhance their compositions, and construct balanced, melodic, dynamic movements and rhythms. Claude Debussy's music, for example, use the golden ratio, prominently the "dramatic" climax of "Cloches a travers les feui...
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