Illustration of the Golden Ratio (Photo: knowledge.depositphotos.com)
The Golden Ratio, denoted by the symbol φ (phi), is a ratio that is considered highly aesthetic and has many applications in art, architecture, and nature. The value of φ, approximately 1.618, has existed since ancient times and has attracted the attention of many artists, scientists, and mathematicians throughout history. This concept symbolizes beauty and perfect proportion often found in various contexts.
The origins of the Golden Ratio can be traced back to ancient civilizations. Some early records of the use of this ratio appear in the works of the Greek mathematician Euclid, around 300 BC. In his famous book, Elements, Euclid describes proportions that are considered ideal for dividing a line, which later became the foundation for the understanding of the Golden Ratio (Beckmann, 1971).
One of the most famous examples of the Golden Ratio in art is the work of Leonardo da Vinci, particularly the paintings Mona Lisa and The Last Supper. Da Vinci is known for using this ratio to create harmonious and balanced compositions. Other artists and architects, such as Le Corbusier and Salvador Dalí, have also adopted the Golden Ratio in their works, adding visual appeal and beauty to their designs (Livio, 2008).
In architecture, the Golden Ratio has significant applications. The most famous example is the Parthenon in Athens, Greece, which was designed with proportions in line with the golden ratio. The structure and proportions of this building create a highly impressive aesthetic impression, making it one of the symbols of classical architecture. This design is not only beautiful but also functions practically, demonstrating how the Golden Ratio can integrate beauty and functionality (Dunham, 2007).
The Golden Ratio can also be found in various phenomena in nature. For example, the growth patterns of sunflowers, leaves on plants, and the structure of mollusk shells often follow proportions close to φ. This phenomenon shows that the Golden Ratio is not just a mathematical concept, but also part of the natural structure of the world around us (Marples & Williams, 2022). Research indicates that growth patterns that follow this ratio can help organisms obtain light and nutrients more efficiently.
In mathematics, the Golden Ratio also appears in the Fibonacci sequence, where each number in this sequence is the sum of the two preceding numbers. When we take the ratio of two consecutive numbers in the Fibonacci sequence, we find that the value approaches φ as the numbers grow larger. This shows a close relationship between the Fibonacci sequence and the Golden Ratio (Koshy, 2001).
Although the Golden Ratio is often praised for its beauty and harmony, it is important to remember that not all forms deemed beautiful subjectively must adhere to this ratio. However, many artists and designers find that using φ can enhance the visual appeal of their works and create a sense of balance (Simonton, 2004). Some studies show that people tend to prefer images or shapes that follow the golden ratio, thus influencing product design, logos, and advertisements.
In recent decades, the Golden Ratio has become the subject of extensive research in the fields of mathematics and psychology. Researchers have explored how this proportion affects visual perception and emotions, as well as how this ratio can be applied across various disciplines, from graphic design to landscape architecture.
The Golden Ratio (φ) is an amazing example of the interconnection between mathematics, art, and nature. From classical artworks to modern designs and natural phenomena, φ continues to play a role in creating beauty and harmony. As our understanding of proportions and aesthetics continues to evolve, the Golden Ratio will remain one of the most intriguing and influential concepts across various fields.
Keywords: Aesthetics, Golden Ratio, Mathematics
References
Beckmann, P. (1971). A History of π. Golem Press.
Dunham, W. (2007). The Genius of Euler: Reflections on His Life and Work. MAA Press: An Imprint of the American Mathematical Society. ISBN: 978-1-4704-5744-0.
Livio, M. (2008). The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number (Reprint ed.). Broadway Books. ISBN 1435298330, 9781435298330. 294 pages.
Marples, C. R., & Williams, P. M. (2022). “The Golden Ratio in Nature: A Tour across Length Scales.” Symmetry, 14(10), 2059. https://doi.org/10.3390/sym14102059.
Koshy, T. (2001). Fibonacci and Lucas Numbers with Applications. Wiley-Interscience. http://doi.org/10.1002/9781118033067.
Simonton, D. K. (2004). Creativity in science: Chance, logic, genius, and Zeitgeist. Cambridge University Press. https://doi.org/10.1017/CBO9781139165358.
Author: Silvina Rosita Yulianti