![]() ![]() Some people believe that the Ancient Egyptians used Golden Ratio to build pyramids. Golden Ratio has been in used in human art and design for many hundreds of years. It can be found in the shapes of hurricanes, elephant tusks, Rose petals and even in the formation of galaxies. A Cosmic constant that is also termed as the “Divine Proportion”. We can witness one common mathematical pattern in all natural creations the “Golden Ratio”. Blessed are those who are intellectually curious about the discovery of the Universe.Īs we gaze upon the creations in the universe, the plants, the humans, the stars and the galaxies in the Universe. We just start experiencing the life without a start. Neither have we remembered our life from day one. Nobody fills any form to choose where they should be born. Since this is a novel in the world of mathematics, its applications were also altered and thus revealed new concepts and theories, including ideas for the transformation of Rolynian space and chaos theory.Making Graphics Using Golden Ratio and Fibonacci Sequence Using the initial concept for R-space which is a Rolynian space in the 3rd degree, describes the three compacting circles were firstly solved and the results were modified to conclude the manner of R-space in the nth degree. Its theories revealed astonishing results such that the term irrational systems were used to explain the chaos of each circle, characteristic of matrix derived from the radius-factor, existence of pi conjecture, properties, and proving. These processes and formulas reveal an in-depth and comprehensive characteristic of pi, the behavior of R-space that is dependent on the number of circles compacting, reinvented concepts and applications of golden ratio, and of course, novel theories in accordance of compaction that twist the fundamental views to the established nature of the golden ratio, pi, and the Fibonacci sequence. GOLDENRATIO IN CIRCLE SERIESThe development of the compacting circles is a novel nature and so a novel series of processes and set of mathematical formulas and analyses were used to identify the R-space both in 2D and 3D. Here, the compaction and its mathematical results are said to be golden, or divine, when the golden ratio was used to strictly characterize the results and theories of the compaction. This method was also applied in solving the values of all the interior angles of the formed polygon. By listing its radius-factor and performing the Gauss-Jordan elimination method, the values for each radius of compacting circles was solved. Throughout the process, the intriguing nature of golden ration and pi are comprehensively explained. ![]() The R-space is a Rolynian space which defines an area created by the compaction of circles, with sharp points, and p-space is the remaining area inside the polygon which was considered and achieved as an area sector of the circles. This polygon, if behaves in the golden ratio will be considered a golden polygon or a divine polygon. The definition of compaction is, the circles draw a polygon using the radiuses of the circles, and the area of this polygon is the sum of the R-space and p-space. In this research, we used the golden ratio to limit the properties of compaction and thus the result behaves to the golden ratio. The existence of the golden ratio fascinates the nature through its pattern. ![]()
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