Geometrical Substantiation of Phi, the Golden Ratio and the Baroque of Nature, Architecture, Design and Engineering

Abstract

Golden Proportion or Golden Ratio is usually denoted by the Greek letter<i> </i>Phi <i>(φ)</i>, in lower case,<i> </i>which represents an irrational number, 1.6180339887 approximately. 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. 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. 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. The properties of Golden Section can be instituted in the pattern of mathematical series and geometrical patterns. 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. Geometrical substantiation of the equation of Phi, based on the classical geometric relations, is also explicated in this study. Golden Ratio and its chronicle, concept of Golden Mean and its relations with the geometry, various dynamic rectangles and their intimacy with <i>Phi</i>, Golden Ratio in the beauty of nature, <i>Phi</i> ratio in the design, architecture and engineering are also presented in this study in a panoptical manner.