“How is an art piece related to a perfect face?” and “how is the arrangement of seeds in a sunflower related to the stock market?” These questions seem unusual but explain why some seemingly unrelated things in nature and life are connected. A simple answer to this is - Mathematics. Mathematics is everywhere around us despite us seldom noticing its presence. Being such a vast field, it becomes crucial to recognize its various subsectors and use them to their maximum potential. A field within mathematics that explains the interconnectedness of nature and mankind is pattern recognition. More specifically, a mathematical concept which facilitates this is the Fibonacci Series.
The Fibonacci Series is a recursive sequence of numbers, with the first three terms being 0, 1 and 1, followed by the next term in the series being the sum of the previous two numbers. This definition of the Fibonacci Series establishes its relationship with the Golden Ratio which forms an important base in understanding the interconnectedness of nature with mankind. The Golden Ratio is approximately 1.618 and is observed as the limit of the ratio of the consecutive terms of the Fibonacci Series. This relationship between the Golden Ratio and the Fibonacci Series is tri-symmetric in nature. Each term of the series (apart from the first three) is a sum of the previous two terms which indicates addition symmetry. Further terms are also scaled versions of the previous one due to the Golden Ratio, indicating multiplication symmetry. Growth symmetry also exists as addition and multiplication change the pattern identically. This quality of being tri-symmetric is one of the reasons why it is regarded as the epitome of perfectness in the realm of mathematics, and leads to interesting mathematical results which are also naturally occurring.
An example of this is the arrangement of the seeds of a sunflower which occur in spirals that correspond to the numbers in the Fibonacci Series. The commonly observed patterns include, 21 or 34 spirals counted clockwise and 34 or 55 spirals counted counterclockwise. Here 21,34 and 55 are terms of the Fibonacci Series. Such an arrangement allows the sunflowers to optimize the number of seeds in the given area while ensuring efficient growth and reproduction. This confirms that the pattern formed naturally is not just a coincidence and is a testament to the inherent quality of ‘perfectness’ of the Golden Ratio and the Fibonacci Series.
Another natural phenomenon is none other than humans. Even human bodies, particularly the face, contain the presence of the Golden Ratio. It can hence also help to answer the well-known question “Mirror-mirror on the wall, who is the prettiest of them all?” As it turns out through research by plastic surgeons, the Golden Ratio offers a guideline for achieving facial balance and symmetry. A visually balanced face is 1.618 times longer than it being wide, which is the Golden Ratio. Despite the concept of beauty being highly subjective the Golden Ratio helps to generalize it and explains why certain celebrities like Zendaya and Bella Hadid are regarded as role models for facial aesthetics, with the key similarity in both being their high scores on the Golden Ratio test.
Along with the human face, the Golden Ratio is also considered aesthetically pleasing in art. Vincent van Gogh’s “The Starry Night” is a testament to this. Known for its distinctive style, the dynamic nature of the visual effects in the painting is accredited to the use of the Golden Ratio. The placement of the dominant elements of the painting such as the swirling stars and the crescent moon are also believed to follow the Golden Ratio. The division of the elements of the painting across the canvas follows the segmentation based on the Golden Ratio which has also largely contributed to its iconic status in the world of art and captivated audiences with focus on singular sub-elements.
Apart from its optimization properties in nature and its status as a perfect proportion, these mathematical concepts are immense in the modern world. One widespread use of it is in the stock market. Due to the stock market’s unpredictable nature, it has earned the tag of being a gamble to invest in. Although this is partially true, the advancements in mathematics have enabled the creation of tools which help to predict changes in trends in the stock market. Pattern recognition is yet again at the helm of this while the Fibonacci Series plays a crucial role in the development of financial tools employed. One such tool that has been created through years of stock chart observations are the Fibonacci Retracements.
The Fibonacci Retracements indicate levels where stocks are likely to change trends. These levels are depicted as percentages and are based on the ratios between terms in the Fibonacci Series. For example, the lowest level which is equal to 23.6% is the ratio between the nth term and the (n+3)th term of the series with the other levels being 38.2%, 61.8%, and 78.6% which also correspond to ratios between other combinations of terms. Since these levels are interpreted as the ratios between various terms in the Fibonacci Series, they can also be represented as the inverse of the golden ratio raised to positive powers. This link between the Golden Ratio and the Fibonacci Series hence explains the values obtained for the Fibonacci Levels on a stock chart and facilitates diverse analysis. Although this technique provides valuable insight, it is not to be solely relied upon due constant unforeseen fluctuations in the stock market. The mere fact that it is able to provide reasoning to an uncertain course of events due to its periodic occurrence in charts for various stocks, further emphasizes on the ever-present nature of the Golden Ratio and the Fibonacci Series. This also confirms that it is not a coincidence that the change in trends observed is closely linked to the distinct elements of the Fibonacci Series.
In conclusion, the examples discussed above affirm that the Fibonacci Series and the Golden Ratio are concepts derived from nature which can be used to interpret phenomena in diverse facets of life. Its role in the aforementioned examples further emphasizes on its systematic occurrence. More importantly, it reveals why certain things exist the way they are. It also demonstrates how seemingly unrelated things in nature can follow a common pattern and by recognizing them, one can achieve fascinating results through mathematics.