![]() The Fibonacci Series was discovered, around 1200 AD, by Leonardo Fibonacci (1170-1250 AD) who was an Italian born mathematician. He also proved the links of this number with the construction of a pentagram. Afterwards the use of the term, Mean, appeared as Golden Mean to represent the ratio. ![]() In Elements, Euclid (325-265 BC) represented a line by dividing at the 0.6180399 point as the extreme and mean ratio. Plato (427-347 BC), in his views and understanding on natural science and cosmology presented in his Timaeus, one of his well-known dialogues, considered the golden section to be the most binding of all mathematical relationships and the key to the physics of the cosmos. ![]() Phidias, a Greek sculptor and mathematician (490-430 BC), studied Phi and applied this ratio in designing the sculptures of the Parthenon. The Greeks based the design of the Parthenon (example of Doric architecture, the main temple of the goddess Athena built more than 400 years BC) on this proportion. It appears that the primitive Egyptian engineers may have used both Pi ( π) and Phi ( φ) in the structural design of the Great Pyramids. ![]() It is unknown exactly when the idea was first discovered and applied by mankind. In the medieval age and during the Renaissance, the ubiquity of ‘ φ’ in mathematics aroused the involvement of many mathematicians. In the early days of the 19 th century it was suggested that the Greek letter ‘ φ’ ( Phi), the initial letters of Phidias’s name, should be adopted to designate the golden ratio. According to the great German mathematician Johannes Kepler (Decem– November 15, 1630), geometry has two great treasures, theorem of Pythagoras and the division of a line into extreme and mean ratio. The proportion known as the Golden Mean has always existed in mathematics and in the physical universe and it has been of interest to mathematicians, physicists, philosophers, architects, artists and even musicians since antiquity. The natural proportioning system provides the foundation of the work of many artists and designers. which is the result of dividing a segment into two segments (A + B) such that A/B = (A+B)/A = 1. The ‘ φ’ also called as the divine proportion, golden section, golden cut, golden ratio, golden mean etc. The designs are approximated by a rectangle shaped such that the ratio of its length and height is equal to the ‘Golden Ratio,’ φ = (1 + 5 1/2 )/2 = 1. Instauration The interrelation between proportion and good looks has made a lot of discussion in science because of the accidental occurrence of the shapes in various designs of objects like books, paintings, edifices and so on. Golden Ratio and its chronicle, concept of Golden Mean and its relations with the geometry, various dynamic rectangles and their intimacy with Phi, Golden Ratio in the beauty of nature, Phi ratio in the design, architecture and engineering are also presented in this study in a panoptical manner.ġ. Geometrical substantiation of the equation of Phi, based on the classical geometric relations, is also explicated in this study. This paper seeks to represent a panoptic view of the miraculous Golden Proportion and its relation with the nature, globe, universe, arts, design, mathematics and science. The properties of Golden Section can be instituted in the pattern of mathematical series and geometrical patterns. The Golden Proportion is considered as the most pleasing to human visual sensation and not limited to aesthetic beauty but also be found its existence in natural world through the body proportions of living beings, the growth patterns of many plants, insects and also in the model of enigmatic universe. Renaissance architects, artists and designers also studied on this interesting topic, documented and employed the Golden section proportions in eminent works of artefacts, sculptures, paintings and architectures. Because of its unique and mystifying properties, many researchers and mathematicians have been studied about the Golden Ratio which is also known as Golden Section. Golden Proportion or Golden Ratio is usually denoted by the Greek letter Phi (φ), in lower case, which represents an irrational number, 1.6180339887 approximately.
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