Golden Ratio in Le Corbusier's Architecture: A Mathematical Perspective - Essay Sample

Introduction

This paper explains how the golden ratio and Fibonacci sequence ensued alongside its application in contemporary architecture. Le Corbusier, the founder of present architecture and the chief of the International Style employed the Golden ratio in his design with a key basis on mathematics and science. He was not interested in achieving architectural beauty but rather used it in his Modulorsystem for the degree of architectural proportion. Le Corbusier supported the structure on the individual dimension, Fibonacci values, and the dual part. These measurements were based on the Fibonacci numbers principle where the sum of two values made the next sequence value.

Is your time best spent reading someone else’s essay? Get a 100% original essay FROM A CERTIFIED WRITER!

Save 25%

Several names have been used to refer to the term golden ratio. These include Phi, Golden Mean, Golden Proportion as well as the Divine Proportion. The Great Pyramid of Giza, of 2560 BC exhibits the initial application of the golden ratio. Every base side of the pyramid is 756 feet long and 481 feet high. That gives a ratio of 1.57 of its base to the altitude. Euclid indicated that splitting a line at the 0.62position shows a division in the average percentage. This gave rise to the name Golden Mean.

A Greek philosopher by the name Plato later came up with the Golden Ratio. He stated that division of a line into two unequal parts such that the two parts are inter-related results to a special proportional correlation. In 1509 Luca Pacioli wrote a book on proportion, The Divine Proportion. Currently, mathematicians engage the use of the first letter of the Greek Philidias who applied the golden ration in his art.

Master Fibonacci, a businessman, saw the beauty in the calculation and considered it in the form of art. He found the Hindu-Arabic numeric to be quite pleasant since their use creates balanced, systematic and comparable measurements. His business role made him consider the order to be beautiful; just like the ordinary humans who like the artistic allure of order and symmetry. Research indicates that "humans can sense symmetry within about 0.05 of a second. This stimulus duration is too short for eye movements to be completed." Don Ruggles, an architect stated that "the human symmetry processing is a universal, hard-wired action of the brain." The Fibonacci sequence enables one to realize the elements of beauty.

Special number sequence alongside ratios has been applied in several cases like scholarly texts, botany, architecture, and carving. The concept of beauty erupts from an arrangement of essential parts into an orderly, equal, symmetrical and a united exhibition (Czech, Anna, and Justyna Borucka, p1583). Aristotle suggested that, "an alive being and each whole made up the parts, must ... present a definite array in its arrangement of parts" for it to remain beautiful. Plato, the Greek philosopher, on the other hand, proposed that the theory of separation in extreme and average ratio determines the ultimate beauty of an ideal number and percentage.

Vitruvius Pollio, a Roman architect regarded architecture as a whole beauty in its complexity constrict by primary unity. He described architecture to include an arrangement, order, proportion, decor, distribution, and symmetry; an opinion that was seconded by Astronomer Johannes Kepler. Mathematically, the Golden Ratio and the Fibonacci sequence have always been applied to evaluate the arrangement and unity of some art and music items. Objects with noticeable balanced and proportionate ratio comparative to Golden Ratio have proved to be quite pleasant and beautiful (Mohamed, Marina, p267).

Pythagoras states that the most pleasant ratio exists when there is an equal division of a line such that the smaller and the larger parts are proportional. This is what is termed as the Golden Mean, often referred to as the Golden Ratio. A close look at the world's best art, for example, the great pyramid of Khufu applies the Fibonacci/ the Golden ratio design. This reveals the relationship between the Fibonacci numeric and the scope of music and art.

Proportions of consecutive digits in a Fibonacci sequence, where each consequent figure is gotten from the addition of the former two, turn out to be logical estimates of the Golden Mean with upward correctness. The higher the scale of the digits, the greater the Golden Ratio generated. This explains why Fibonacci digits are applied as aspects in any design or construction to evade the complexity of making use of the irrational number (). Engineers and Architects in the past centuries used the Golden Ratio application to bring back the "lost harmony of Pythagoras".

A Greek mathematician named Phidias employed the use of Phi (), in his model of Parthenon statues. Architects before him had earlier used both Phi () and Pi (p) in designing the Great Pyramids. The pyramids perfectly indicate the depth of scientific knowledge through their sizes and forms.

The design of architecture applying the Fibonacci sequence alongside the Golden ratio was common in Renaissance architecture. An example of Santa Maria Cathedral in Florence built-in 1434 indicates the Fibonacci sequence: 55, 84 and 144 including 17 which is the median of 34 alongside 72 which is the semi of 144. This sequence appears in its sails and cell projection. Recently, the obscure Fibonacci sequence was noted in a church in San Nicola in Italy. Centuries had passed before the discovery of rectangular and circular inlay series in one of the lunettes in the church. The arrangement of geometric figures referenced the application of Fibonacci numbers in architecture. According to Professor Armienti, "The first nine figures of the Fibonacci series, 1, 2,3,5,8,13,21,34 and 55 denote the radii of the various circles in the design. The inland titles can be applied as an abacus to sketch progression of standard polygons carved in a circle of a known radius, then made to calculate with good approximation the surfaces of the standard polygons carved."

The influence of the Fibonacci application continues to be prevalent in the current days. The sequence itself remains to be a characteristic of the layout. In Finland, the power station's smokestack in Turku is a groundbreaking that indicates the Fibonacci sequence first ten figures of 1, 1, 2,3,5,8,13,21,34 and 55. The brilliant neon numbers are playfully exhibited on a two meters height. This "Fibonacci Chimney was built by Mario, an Italian artist in1994." This indicates the unique conceptual efforts that involve the application of the Fibonacci sequence.

The Golden Mean is frequently mentioned in architectural literature. The Golden Mean has been a great determination in modeling landmark structures right from the past decades, due to its sense of balance and harmony. It is applied in any architectural layout as a technique of assurance that the design exhibits a genuine and steady order of scales. This has a minimum effect on a rectangular aspect proportion.

The modern architecture has eradicated the traditional design components that relied on the human scale. But this is exactly the numerical idea where the environment expresses Fibonacci progress and Golden Mean in the many discovered incidences. Excluding sequence organized density leaves nothing to be evaluated in a mathematics way.

Today's' architects give the least room to approaches that could enable the operator to get on a building. Alexander, 2001 stated that "A minimalist building feels foreign precisely due to its lack of mathematical information that our cognitive structure uses to evaluate the natural environment." Minimalism aims one to concentrate on one mathematical association which is the rectangular aspect ratio. The Golden Mean became common in the modern architectural designs as the few approaches in use, as the architects attempted to re-structure their bare rectangular pieces.

Conclusion

In conclusion, the nature of architecture is not only meant to convey beauty. The contemporary architects have proved that it is neither the form nor the function that makes architecture "architectural". Architecture has emerged to be the idea, the experience and the event behind the process that matters in the present world. There has been a claim that: "architecture advanced in the early 20th Century by including the message of older visual ornamentation into its inherent dimensions, thus present architecture works just as well but in a different way that is intellectually advanced", which is not the case. Ordered substructure, hierarchical scaling as well as the ornament which are the basic features for creating architectural density and adaptation were not converted. Rather, they were excluded from retaliation. Therefore, the idea of the modernist saying transmuting crucial composite information instructed as proportions is just an idiom meant to promote a minimalist geometry.

Work Cited

Mohamed, Marina, et al. "Divine Proportion in Modern Architecture: A Case Study." Jurnal Teknologi 78.10-4 (2016).

Czech, Anna, and Justyna Borucka. "The use of the language of mathematics as an inspiration for contemporary architectural design." Procedia engineering 161 (2016): 1582-1587.

Bellone, Tamara, Francesco Fiermonte, and Luigi Mussio. "The Common Evolution of Geometry and Architecture From a Geodetic Point of View." International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences 42.5/W1 (2017).