Golden Ratio

Custom Student Mr. Teacher ENG 1001-04 25 September 2016

Golden Ratio

The Golden Ratio which is also referred to as golden mean, golden section or divine proportion is a number frequently encountered when calculating ratios of distances particularly in simple geometric figures like pentagram, dodecahedron, pentagon and pentagram. It is an irrational constant in mathematics which is given an approximate value of 1. 6180339887 and is symbolized by the Greek letter phi or in other words , or sometimes .

Most of the greatest mathematicians in the ancient Greece, Euclid and Pythagoras along with Leonard of Pisa who was medieval Italian Mathematician together with Johannes Kepler, Renaissance astronomer and the present day scientific individuals like Roger Penrose, Oxford Physicist have spent a lot time in studying this ratio along with its properties (Weisstein, 2010). The Ancient Greek mathematicians initially studied the Golden Ratio simply because it frequently appeared in geometry. The Greeks have always attributed the discovery of this ratio to Pythagoras along with his followers.

The Golden Ratio was first used by Martin Ohm in his 2nd edition book Die Reine Elementar-Mathematik in 1835. The fascination of this concept is not confined to mathematicians but also artists, musicians, biologists, mystics, architects, historians and psychologist have debated and pondered the basis of its appeal and ubiquity. Prof. Michael Maestlin wrote the first approximation of the Golden Ratio in 1597 and stated it to be about 0. 6180340. It is fair to declare that the Golden Ratio have brought inspiration to most thinkers of various disciplines than any other number has done in the history of mathematics (Weisstein, 2010).

The Golden Ratio in Art Just as the Golden Ratio is used in the beauty and design of nature, it can also be applied in achieving balance and beauty in the design of art. This is just a tool for composition although it is not a rule. Leonardo Da Vinci, used the Golden Ratio intensively in designing and in many of his paintings, he featured the Golden Ratio which he called the “divine proportion”. This he did after his exploration of the human body by engaging in the ratios of the lengths of different body parts.

His illustration of the polyhedra on the divine proportion, and his perspective concerning the body proportions portraying the Golden Ratio has led to the speculation by some scholars that he used Golden Ratio in painting. This speculation has been seen in his Mona Lisa painting where it employs Golden Ratio proportion. The Sacrament of the Last Supper, which is a painting by Salvador Dali explicitly, illustrates the application of the Golden Ratio. The canvas’ dimension is that of the golden rectangle and what dominates the composition is the large dodecahedron which has its edges in Golden Ratio and swings above and behind Jesus.

Other paintings speculated to symbolize the Golden Ratio are Holy Family by Micahelangelo, Crucifixion by Raphael, Self-portrait by Rembrandt, Golden Section Plate by Fletcher Cox and Bathers by Seurat (Obara 2010). The Golden Ratio in Architecture The Ancient Egyptians became the first individuals to apply mathematics in art. It is obvious that they did this by ascribing magical properties of the Golden Ratio and henceforth using that in designing their great pyramids. Some studies regarding the Parthenon and Acropolis offer a conclusion that most of its proportions give an estimated value of Golden Ratio.

The facade of the Parthenon along with the elements of its facade are suspected to be circumscribed in terms of golden rectangles. The fact that the proportions of the classical buildings or rather their elements are according to the Golden Ratio clearly explain that the architects who designed them were conscious of the Golden Ratio and applied it in their designs. On the other hand, it is possible that the architects applied their special sense of good proportion and as a result their proportions gave approximate of the Golden Ratio (Obara 2010).

According to a geometrical analysis carried out by Boussora and Mazouz concerning to the Great Mosque of Kairoua, it is evident that there was consistent utilization of the Golden Ratio in its design. The Golden Ratio is applied in the overall proportion of the plan along with the dimensioning of the court, the prayer space and the minaret. Mazouz and Boussora further scrutinized earlier archaeological theories concerning the mosque and demonstrated the Golden Ratio in the geometric constructions through the application of the constructions on the plan so as to test their hypothesis(The Golden Number).

Le Coubusier explicitly applied the Golden Ratio specifically in his Moduaor system which he saw as a continuation of the traditions of the work of Battista Alberti, Leonardo da Vinci’s “Vitruvian Man” and others who applied the human body proportions to improve the function and appearance of architecture. Mario Botta, a Swiss architect based most of his designs on figures of geometry. Some of the private houses which he designed in Switzerland consist of cylinders, squares, cubes and circles.

In Origlio, Mario has designed a house with the proportion of the Golden Ratio between the side sections and the central section of the house. In a recent book by Jason Elliot, it has been contemplated that the Golden Ratio was utilized in designing the Lotfollah mosque and Naqsh-e Jahan Square. The Golden Ratio was also used in designing the Notre Dame in Paris in 1250 (The Golden Number). Conclusion The idea of translating beauty into a simple number, the Golden Ratio is quite disturbing.

It is true that beauty is not something that is so substantial in something like a lifeless number but rather something we all have to make personal choices regarding it. Basing on the rule of thirds that is used in photography, for a photo to emerge appealing and balanced, the image must be made to abide by the grid that is divided into thirds. The number of comments that a person receives directly correlates with the beauty found in his/her image. Though, there are other factors that affect how people view a person or something, good comments are given depending on how the image appeals the eyes.

For attractive people like Angelina Jolie and Brad Pitt, the skeleton of Golden Ratio almost fit perfectly on them. However, when the skeleton was put on a picture of an individual who looked a bit unattractive, the skeleton did not fit. I am not suggesting that beauty should be translated into being lifeless and cold because of it being defined inform of numbers. However, I think that the paintings and houses that used the proportions of the Golden Ratio look appealing and beautiful. In my opinion therefore, physical beauty can be measured by Golden Ratio.


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  • University/College: University of Chicago

  • Type of paper: Thesis/Dissertation Chapter

  • Date: 25 September 2016

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