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One Point Six. Uno Punto Seis. Uno Punto Sei. Un Point Six. 
Essay.
Ensayo. Saggio. Essai. The deoxyribose nucleic acid molecule, the program for all life, is based on the Divine Proportion, one point six. It measures twenty one ängstroms long by thirty four ängstroms wide for each full cycle of its double helix spiral. Twenty one & thirty four are numbers in the Fibonacci series & their ratio, 1.6190476 closely approximates Phi, 1.6180339. So, no matter which way you look at it, even in its smallest element, DNA & life is constructed using this mystical ratio. Essay Continued Ensayo Continuó Saggio Continuato Essai Continué ∨
Throughout history the ratio for length to width of rectangles of 1.6180 has been considered the most pleasing to the eye. Whilst this proportion has always existed in mathematics & in the physical universe, it is unknown exactly when it was first discovered & applied by mankind. Early uses in architecture date to the ancient Egyptians & Greeks. The Great Pyramid of Giza built around 2560 BC is one of the earliest examples that utilises the proportion. The Ahmes papyrus of Egypt gives an account of the construction using numbers according to a 'sacred ratio'. Another civilization that used the ratio or, as they called it, the Golden Section, were the Greeks. In the world of mathematics, the numeric value is called 'Phi', named after the Grecian sculptor & mathematician, Phidias. One of the most famous landmarks in Athens, the Parthenon hides many golden rectangles within its construction. The mathematician Pythagoras was especially interested in the Golden Section & proved that it was the basis for the proportions of the human figure. One's upper leg can often be found to be Phi times ones lower leg. Indeed, it has been argued that what we perceive as beauty in a person is determined largely by the closeness of their physical structure to the Golden Section. This ratio can be used to explain the physical dimensions of many life forms & not only the human body. Plato expressed some views on natural science & cosmology in about 360 BC in his writing of 'Timaeus', he considered the Golden Section to be the most binding of all mathematical relationships & the key to the physics of the cosmos.
Many who lived after Phidias, Pythagoras & Plato have also used this proportion. After the Greek empire fell, many of the studies of the Golden Section disappeared. It is reasonable to assume that it has perhaps been discovered & rediscovered throughout history, which explains why it goes under several names. Leonardo Pisaro, often called Fibonacci, an Italian born in 1175 AD, discovered the unusual properties of the numerical series that is now called The Fibonacci Sequence. The sequence is a simple numerical series that is the foundation for an incredible mathematical relationship behind Phi. Starting with 0, 1, 1, each new number in the series is simply the sum of the two before it. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, et cetera. The ratio of each successive pair of numbers in the series approximates Phi, one point six. It's not certain that Fibonacci even realised its connection to Phi & the Golden Mean. During the Renaissance there was a new born interest in mathematics & art. Certain artists used the Golden Mean extensively in their paintings & sculptures to achieve balance & beauty. Luca Pacioli, a mathematician, wrote a book called De Divina Proportione in 1509. It contains drawings made by Leonardo da Vinci of the Five Platonic Solids. Leonardo da Vinci first called it the Sectio Aurea & used it to define all the fundamental proportions in his painting of The Last Supper. From the dimensions of the table at which Christ & the Disciples sat to the proportions of the walls & windows in the background, the ratio is apparent. Leonardo da Vinci like Pythagoras before him was interested in the relationship the ratio had to the human form. He did an entire exploration of the human body & the ratios of the lengths of various body parts. Indeed, your own hand shows Phi & The Fibonacci Sequence. Each section of your index finger, from the tip to the base of the wrist is larger than the preceding one by about the ratio of 1.618, you also have two hands, each with five digits & your eight fingers are each comprised of three sections; evidence of more Fibonacci numbers. Art has always found inspiration in nature; many of Mozart's sonatas divide into two parts exactly at the Golden Section. Indeed, people such as Le Corbusier & Bartók have deliberately & consciously used the Divine Proportion in their designs. In 1950, the architect Le Corbusier published a book entitled 'Le modulator. Essai sur une mésure harmonique a l'échelle humaine applicable universalement a l'architecture et a la mecanique'. He invented the word Modulator by combining 'modula' & 'or', Latin for ratio & gold respectively. The book was based around his mathematical exploration of architecture & how he arrived at the Golden Ratio. There are many examples of the Divine Proportion to be found throughout the universe, some examples evolved by nature others designed by man. Stradivari was aware of the Golden Ratio & used it to place the Fholes in his famous violins. The ratio was popular with Albrecht Dürer & is also seen in some of the work of Georges Seurat, Salvador Dali & Paul Signac. Indeed the ratio appears in the construction of many typefaces including the popular Helvetica. Maybe the ratio could be the subtle difference between the simple naturalistic beauty of Helvetica & the ugly imitator Arial. The painter Mondrian also believed that mathematics & art were closely connected & many of his works are constructed in accordance of the ratio. So, not only did it lead to such divine visual masterpieces such as Leonardo da Vinci’s Mona Lisa but take a close look at the natural world. The pattern by which seeds are arranged on a seed head is the same as that by which leaves are arranged around a stem, or petals around a flower. This is no mere coincidence, it is natures way of optimizing structures. Rotating by Phi guarantees equal spacing of leaves & seeds, no matter how far from the central starting point you go. Plants naturally grow in such a way as to ensure the maximum possible exposure to light on each individual leaf. Arranging the leaves at Phi per turn addresses the potential problem of the upper leaves overshadowing the lower ones from the life giving sun. This also supplies the plant with the largest possible surface area to catch rain water & direct it down the stem to the roots. A peaceful heartbeat is said to even beat in a Phi rhythm, with the T point of a normal electrocardiogram falling at the Phi point of the heart's rhythmic cycle. Over time there have been many different names created, all to explain the same number. The Greeks knew it as the Golden Section. The Renaissance artists knew it as the Divine Proportion. Other names include the Golden Ratio, the Golden Mean, Phi, the Divine Section, the Golden Cut, the Golden Proportion & Tau. Which ever name you decide to call it, one point six is the common factor. It is the number that connects nature & art with mathematics & science. One point six is the number of beauty. And beauty is underrated. Close Essay Ensayo Cercano Saggio Vicino Essai Étroit ∧ 





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