The golden sectionThe rectangle and the golden sectionThe golden rectangle and the golden section have always existed in the physical universe. No one knows exactly when it was first discovered and applied to humanity. Many mathematicians assume that the golden rectangle has been discovered and rediscovered several times throughout history. This would explain why it is called by many different names such as Golden Ratio, Divine Proportion or Golden Ratio. The first person believed to have used the golden ratio is Phidias when he used it to design the statues inside the Parthenon. . This happened between 490 and 430 BC. In the early 300s BC, Plato used the golden ratio when he described the five Platonic solids which are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. Later in 300 Euclid gave the first written definition of the golden ratio which is an extreme and mean ratio. Then between 1170 and 1250 Fibonacci discovered a numerical series that had sequential elements that asymptotically approached the golden ratio. Between 1445 and 1517 Luca Pacioli defined the golden section as the "divine proportion". Then between 1550 and 1631 Michael Maestlin published the first known approximation of the inverse golden ratio as a decimal fraction which is 1.61803398875. Shortly thereafter, John Kepler demonstrated that the golden ratio is the limit of the ratio between consecutive Fibonacci numbers. Then between 1842 and 1891 Edouard Lucas called the numerical sequence the Fibonacci sequence. In 1974 Roger Penrose discovered Penrose tiling which is a pattern related to the golden ratio both in the ratio between the areas of its two rhombic tiles and in their relative frequency within the pattern. The g...... center of the paper. ...and whether or not they were included in the logo on purpose or if it was just by accident to make it more visually appealing. I wonder if there are places in nature that also contain the golden ratio but we haven't discovered them yet. Works Cited "15 Mysterious Examples of the Golden Ratio in Nature." Io9. Np, nd Web. March 10, 2014. “Golden Ratio.” Golden section. Np, nd Web. March 12, 2014. “Golden Ratio in Geometry.” Golden section in geometry. Np, nd Web. 11 March 2014. Livio, Mario. The Golden Ratio: The Story of Phi, the Most Amazing Number in the World. New York: Broadway, 2002. Print."Logo Design." Phi 1618 The Golden Number RSS. Np, nd Web. March 11, 2014. “Geometry of the Phi Formula.” Phi 1618 The Golden Number RSS. Np, nd Web. March 12, 2014."Theology." Phi 1618 The Golden Number RSS. Np, nd Web. March 12. 2014.