The Golden Ratio

Part I | Defining the Golden Ratio

The divine proportion in art, called the golden ratio, is an irrational number of 1.618, that when executed in mathematical precision, creates an almost perfect spiral. There are countless examples of this phenomenon occurring naturally in artwork throughout history—artists have long used this notion of the golden ratio as a way to create harmony and balance within their work. Here, we will explore a few famous works in history that demonstrate this peculiarity, because if not looked at closely enough, it could be missed.

Briticanna defines the golden ratio as “the ratio of a line segment cut into two pieces of different lengths, such that the ratio of the whole segment to that of the longer segment is equal to the ratio of the longer segment to the shorter segment.” The definition is a mouthful and complex to understand without looking at visual examples.

Part II | Mathematics and Aesthetics

The ancient Greeks used the mathematics of the golden ratio throughout their entire society and culture, from art and architecture to geometry in education. It was most significantly coined as the key to the perfect aesthetic of geometric proportion, especially in rectangles. The Parthenon in Athens, Greece, has been long debated as to the proper execution of the golden ratio in the ancient culture, and in the architecture it was dedicated to. It was believed that Phidias, mathematician, artist, and architect of the Parthenon, used the golden ratio extensively in its design and construction. Despite the evidence that debunks this claim, the dimensions and harmonically divided segments are hard to ignore. While research is inconsistent, the golden ratio is undeniably visible in terms of the facade and floor plan.

While the mathematics of the golden ratio and its relation to the Fibonacci sequence is complex, we turn to visuals to view the use of the perfect proportion throughout art history. Leonardo da Vinci’s The Last Supper and the Mona Lisa are striking examples of how the theory was magnified by unforgettable Renaissance artists.

The Last Supper (1494-98) impeccably visualizes the use of the ratio. Details of the painting present the golden ratio, from the shields in the top frieze to the width of the table. A perfect example is the center of the painting, where Jesus is the midpoint between the table top and the ceiling, then to the top of his head, and to the window frieze behind him, creating the mathematical spiral.

The Mona Lisa (1503), one of Da Vinci’s masterpieces, is a definitive example in which the “True Golden Spiral” is evident. The Mona Lisa Foundation eloquently examines the work, describing the golden ratio as it “nestles against the edge of the left column, and, coming across the top of her head, exactly meets the leg of the triangle. At the same time, the spiral beautifully frames her face, with the rounded side on the right, and the vertical side on the left.” The decision to draw allure to the Mona Lisa’s eyes is conscious, for it calls attention to her hard, yet soft, expression and strangely magnetic eyes.

Part III | The Golden Allure

The golden ratio is, and has been, used by artists to elevate certain features of their subjects. For example, Vermeer’s Girl with the Pearl Earring employs the Fibonacci spiral to draw attention directly to the girl’s glazed, captivating eyes. In the composition, the girl’s stance faces the left side of the frame, but her head is slightly turned, enhancing her jawline and the top of her headscarf. She is set in the forefront of a dark, hollow-like background, which further intensifies the segmental proportions. The use of the mathematical theory adds a layer to how geometry can allure the viewer to what is seemingly simply portraiture.

Botticelli’s The Birth of Venus also exemplifies the use of the golden ratio in Renaissance art. We can determine the use of the golden ratio in the painting by the dimensions. According to The Golden Number, “the dimensions of the canvas is 172.5 cm × 278.5 cm (67.9 in × 109.6 in). The ratio of the width to the height (based on the more accurate measures in centimeters) is thus 1.6168, which is only a 0.08% variance from the Golden Ratio of 1.618.” Compositionally, the ratio is embedded into the vertical and horizontal lines, as well as the specific lines that run through Venus’ navel. The article identifies the golden ratio in the detail of Venus, and describes that her navel is the perfect ratio point for her height. It is also apparent in the complementing figures, where it visually spirals into the elbow of the left-hand figure, and at the knee of the right-hand figure.

Part IV | An Abstract Conclusion

While Piet Mondrian’s modern art is a visual geometric grid of rectangles, the golden ratio is apparent in the segmental dimensions throughout his canvases. While color fills some spaces, the other “negative” space didn’t go without thought. Mondrian’s artistic philosophy entails the idea of separate but together. While each rectangle is unique, they act as a unit. The golden spiral is applied in several ways in his piece Tableau 1 (1921), but most obviously by the dimensional golden rectangles. Less obvious is the way the spiral appears based on the colors. From the middle of the far-right yellow rectangle, the spiral comes to its curl in the outer-end of the blue shape. Once the overlay of the golden spiral is applied, it is apparent that the entire composition is a mathematical equation in itself. states that the Golden Ratio “govern[s] the development of many patterns in nature…from the microscopic structure proportions of living beings on Earth to the relationships of gravitational forces and distances between bodies in the universe.” There are countless pieces of artwork and architecture examples that we can point to and identify as indicative of the golden ratio. But beyond art, the golden ratio is everywhere, from the spiral galaxy Messier 83 to the spiral aloe plant.

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