1550 Words7 Pages

The Golden Ratio

The Golden Rectangle and Ratio

The Golden Rectangle and Golden Ratio have always existed in the physical universe. Nobody knows exactly when it was first discovered and applied to mankind. Many mathematicians assume that the Golden Rectangle has been discovered and rediscovered multiple times throughout history. This would explain why it is called many different names such as the Golden Mean, divine proportion, or the Golden Section.

The first person who is believed to have used the Golden Ratio is Phidias when he used it to design the statues inside of the Parthenon. This happened between 490 and 430 BC. In the early 300’s BC Plato used the Golden Ratio when he described the five platonic solids which are the tetrahedron, cube, octahedron, dodecahedron, and the icosahedron. Later in the 300’s 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 which had sequential elements that approaches the Golden Ratio asymptotically. Between 1445 and 1517 Luca Pacioli defined the Golden Ratio as the “divine proportion”. Then in between 1550 and 1631 Michael Maestlin published the first known approximation of the inverse golden ratio as a decimal fraction which is 1.61803398875. Very soon afterwards Johannes Kepler proved that the golden ratio is the limit of the ratio of consecutive Fibonacci numbers. Then in between 1842 and 1891 Edouard Lucas named the numerical sequence the Fibonacci sequence. In 1974 Roger Penrose discovered Penrose tiling which is a pattern that is related to the golden ratio both in the ratio of areas of its two rhombic tiles and in their relative frequency within the pattern.

The g...

... middle of paper ...

...n whether or not they were put into the logo on purpose or if it was just by accident to make it more visually appealing. It makes me wonder if there are places in nature that also contain the golden ratio but we just haven’t discovered them yet.

Works Cited

"15 Uncanny Examples of the Golden Ratio in Nature." Io9. N.p., n.d. Web. 10 Mar. 2014.

"Golden Ratio." Golden Ratio. N.p., n.d. Web. 12 Mar. 2014.

"Golden Ratio in Geometry." Golden Ratio in Geometry. N.p., n.d. Web. 11 Mar. 2014.

Livio, Mario. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. New York: Broadway, 2002. Print.

"Logo Design." Phi 1618 The Golden Number RSS. N.p., n.d. Web. 11 Mar. 2014.

"Phi Formula Geometry." Phi 1618 The Golden Number RSS. N.p., n.d. Web. 12 Mar. 2014.

"Theology." Phi 1618 The Golden Number RSS. N.p., n.d. Web. 12 Mar. 2014.

The Golden Rectangle and Ratio

The Golden Rectangle and Golden Ratio have always existed in the physical universe. Nobody knows exactly when it was first discovered and applied to mankind. Many mathematicians assume that the Golden Rectangle has been discovered and rediscovered multiple times throughout history. This would explain why it is called many different names such as the Golden Mean, divine proportion, or the Golden Section.

The first person who is believed to have used the Golden Ratio is Phidias when he used it to design the statues inside of the Parthenon. This happened between 490 and 430 BC. In the early 300’s BC Plato used the Golden Ratio when he described the five platonic solids which are the tetrahedron, cube, octahedron, dodecahedron, and the icosahedron. Later in the 300’s 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 which had sequential elements that approaches the Golden Ratio asymptotically. Between 1445 and 1517 Luca Pacioli defined the Golden Ratio as the “divine proportion”. Then in between 1550 and 1631 Michael Maestlin published the first known approximation of the inverse golden ratio as a decimal fraction which is 1.61803398875. Very soon afterwards Johannes Kepler proved that the golden ratio is the limit of the ratio of consecutive Fibonacci numbers. Then in between 1842 and 1891 Edouard Lucas named the numerical sequence the Fibonacci sequence. In 1974 Roger Penrose discovered Penrose tiling which is a pattern that is related to the golden ratio both in the ratio of areas of its two rhombic tiles and in their relative frequency within the pattern.

The g...

... middle of paper ...

...n whether or not they were put into the logo on purpose or if it was just by accident to make it more visually appealing. It makes me wonder if there are places in nature that also contain the golden ratio but we just haven’t discovered them yet.

Works Cited

"15 Uncanny Examples of the Golden Ratio in Nature." Io9. N.p., n.d. Web. 10 Mar. 2014.

"Golden Ratio." Golden Ratio. N.p., n.d. Web. 12 Mar. 2014.

"Golden Ratio in Geometry." Golden Ratio in Geometry. N.p., n.d. Web. 11 Mar. 2014.

Livio, Mario. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. New York: Broadway, 2002. Print.

"Logo Design." Phi 1618 The Golden Number RSS. N.p., n.d. Web. 11 Mar. 2014.

"Phi Formula Geometry." Phi 1618 The Golden Number RSS. N.p., n.d. Web. 12 Mar. 2014.

"Theology." Phi 1618 The Golden Number RSS. N.p., n.d. Web. 12 Mar. 2014.

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