Free Essay Sample - Fibonacci Applications

Published: 2023-02-21
Free Essay Sample - Fibonacci Applications
Type of paper:  Essay
Categories:  Architecture Mathematics Art
Pages: 4
Wordcount: 1097 words
10 min read

The mathematical concept of the golden ratio is applied in art and architecture since it is capable of producing aesthetically pleasing proportions and divisions. In most cases, the human eye can scan a given image the fastest when it takes or is shaped in the form of a golden ratio rectangle; the above scenario makes the brain to perceive the image as aesthetically pleasing. In the modern computer era, the Fibonacci sequence is incorporated in programs. Artists are able to find ready-made materials that they can use to make shapes and figures of their choice. Fibonacci sequence is important for the designers and architectures. The Fibonacci sequence exhibited by the bees in their colony often define the kinds of activities that the work processes undertaken in the hives.

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Golden Ratio in Nature

While dealing with the ratio in nature, there are two major sequences of numbers, including the golden spirals and the Fibonacci numbers. In Fibonacci sequences, each number is the sum of the two preceding ones. In other words, adding the two previous numerals in the sequence leads to the next number in the arrangement. An example of a Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc. (Smart & Friedman, 2017). The ratio of the two neighboring Fibonacci number within the Fibonacci sequence is called the golden ratio. In nature, flowers, phyllotaxis, petals, and leaves often assume the pattern created by the golden ratio. However, many plants do not behave as in the above case; therefore, the entire process is not a universal property.

In some cases, both the shell of the nautilus and the Romanesco broccoli often follow the regular spiral structures, however, neither form the traditional golden spiral as indicated in some plant leaves and stalks (Devlin & Fibonacci, 2019). The above spiral usually occur by increasing the radius of the spiral by the golden proportion after every 900 (Devlin & Fibonacci, 2019). In nature, the shell of a Nautilus can be used to describe the spiral that expands by the golden ratio at an angle of 1800 (Devlin & Fibonacci, 2019). However, the above case is still an approximation.

Golden Ratio in Art and Architecture

In the architectural designs, the golden ratio is applied in the formation of pleasing patterns meant to create beauty (Brown, 2008). For instance, the floor tiles are often designed through the application of the golden ration. In modern-day construction, there are buildings possess the spiral shape; spiral shape is formed by the application of golden ratio, whereby the Fibonacci sequence is used to produce the golden ration patterns, which are then used to design the spiral shapes (Maths Survey, 2019). The golden ratio is also applicable in the analysis of the buildings or artwork. Historically, the design of the Parthenon in Athens was based on the golden ratio. The golden rectangles and measurements mainly involved the use of golden ration formulated from the Fibonacci sequence (Devlin, 2012). Also, Le Corbusier used the golden ratio in his Modular proportion system. In art, the golden ratio is applied in the production of spiral figures and shapes that often become appealing to the eye.

The concept makes it easier to determine angles as well as the shapes of different structures. Art and craft are two forms of creativity that are normally contrasted by different people. In other words, the majority of people cannot spot the difference between the two terms. In other words, art is creative merit that originates from within. From the definition, craft refers to the skilled work where there is the application of techniques that the specialists or professionals acquire through practice. Art is an application and expression of imagination, thoughts, feelings, ideas, and many other forms of human creativity. From the above scenario, art and architecture requires the application of Fibonacci sequences.

Bee Ancestry Code

The application of the Fibonacci sequence in evidenced in the bee ancestry code. In the reproduction processes, the generations of bees often tend to define the Fibonacci sequence. In the reproduction systems, if an egg is laid by an unmated female bee, it hatches male bee. On the other hand, if an egg is fertilized, by a male, it hatches a female bee (Vorobiev, 2012). Therefore, a female bee will always have two parents, while a male will only have one parent. Hence, if one can trace the ancestry of any male bee, the findings will reveal with certainty that it has one parent, two grandparents, three great grandparents, five great-grand-parents, and the sequence will continue in the same scenario. In other words, the arrangement will become, 1, 1, 2,3, 5, etc. The sequence is a Fibonacci sequence. The above situation, therefore, reveals the application of Fibonacci in nature. The bee ancestry code defines the natural organization that exists among the bee colony. The process is natural; it occurs naturally in every bee colony.

Fibonacci and Golden Ratio in Popular Culture

The application of the Fibonacci sequence is common in different cultures. The concept is applied in various activities, from building and construction to the financial market. For instance, the FOREX trading, the Fibonacci sequence is usually used to identify the price retraced approximation (Devlin & Fibonacci, 2019). While trading in FOREX, the Fibonacci retracement is a technique of technical analysis that is used in the determination of the resistance and support levels. The sequence can enable the trader to predict the direction of the trading with certainty. With the rise of digital technologies, some computer programs used the Fibonacci sequence to aid in the technical analysis. Some of the architectural software has inbuilt applications that use Fibonacci sequence to enhance the designing of different structures.


The images also depict the Fibonacci patterns; artist uses the Fibonacci sequence to establish a proportional structure that may appear appealing to the eye. Besides, there are some naturally occurring instances of Fibonacci sequence. Just like the bee ancestry code, the shape of some insects and animals appear to take the Fibonacci sequence. In the production of movies, the filmmakers often apply the concept of Fibonacci to capture the real and appealing images that add value to the film viewers.


Brown, C. M. (2008). Fibonacci analysis. New York: Bloomberg Press.

Devlin, K. J. (2012). The man of numbers: Fibonacci's arithmetic revolution. London: Bloomsbury.

Devlin, K. J., & Fibonacci, L. (2019). Finding Fibonacci: The quest to rediscover the forgotten mathematical genius who changed the world. Princeton: Princeton University Press.

Maths Survey (2019). FIBONACCI SEQUENCE. Retrieved from:, M. K., & Friedman, R. D. (2017). The golden ration & Fibonacci sequence: Golden keys to your genius, health, wealth & excellence.

Vorobiev, N. N. (2012). Fibonacci Numbers. Basel: Birkhauser Basel.

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