The Divine Proportion: A Ratio of Harmony in the World
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(Image Credit: Singulart)
(Image Credit: United Nations)
April 29, 2025
Caroline Cronin
9th Grade
Fairfax High School
The Golden Ratio, commonly represented by the Greek letter ϕ (pronounced “phi”), is equal to approximately 1.618… and surrounds the world in art, architecture, and nature. Also known as the golden section, golden mean, golden proportion, and divine proportion, this fascinating yet complex concept is present everywhere. Mathematically, it is expressed as (1+√5)/2, and when plugged into a calculator, it indeed comes out as 1.618 and so on (meaning that there are many more numbers following the .618). This means that when 1 is added to the square root of 5 and this expression is divided by 2, the answer will be 1.618.
Geometrically, this phenomenon demonstrates that if you cut a line segment into two pieces, the ratio of the longer length to the shorter length is equivalent to the ratio of the sum of the long and short lengths divided by the long length. However, that is quite difficult to understand, and line segments are already present enough in math class, so using the Golden Rectangle to visualize this concept is a great way to interpret the complex definition. Pretend someone has a delicious, melt-in-your-mouth chocolate bar. (And if you don’t like chocolate, you can imagine your favorite candy bar instead!) Their best friend approaches and asks if he or she can have some, so they say yes and break off a piece. Now, the entire chocolate bar is a rectangle, and the broken-off piece is a square.
If one were to place the smaller square piece on another full bar, they would find that the square’s sidelengths are the same as the shorter sides of the chocolate bar as a whole. Notice that when this occurs, another smaller rectangle is created. In this case, it can be thought of as a mini chocolate bar. The amazing fact about this concept is that it can be repeated forever, eventually creating the spiral, a well-known depiction of the Golden Ratio.
If this image looks familiar, it’s because it can also represent the Fibonacci Sequence. The Fibonacci Sequence is a pattern of numbers that goes as follows: 1, 1, 2, 3, 5, 13, 21, 34, 55, etc. Notice how two consecutive numbers are equal to the next number in the string, so 1 plus 1 is 2, 1 plus 2 is 3, 2 plus 3 is 5, etc. The relationship between this sequence and the Golden Ratio is that if any two consecutive numbers in the pattern are divided, the result is a number very close to 1.618. For example, ⅔ is 1.5, ⅗ is 1.666666, etc. The interesting fact is that both create a spiral that can go on forever and closely resemble a nautilus shell. This means that if one were to keep drawing lines inside the rectangles, it would always create another rectangle. However, the nautilus shell does not provide an accurate depiction of the Golden Ratio. Instead, it forms a logarithmic spiral pattern, which differs from the ratio itself.
The Golden Ratio is present in art and architecture. In art, the Golden Ratio can be found in Rembrandt’s “Self-Portrait” and Dali’s “The Persistence of Memory”, to name a few. In architecture, the Taj Mahal and the United Nations headquarters represent the Golden Ratio in certain elements of construction. It is also present in the structure of the human face, such as the width of the face to its height and the eye distance to nose width. The entire face, from top to chin, can be divided by the width, from cheek to cheek, which will result in an estimate very close to the Golden Ratio. Similarly, the nose width is around 1.618 times the distance between the eyes.
The Golden Ratio has stunned, confused, and awed many people, yet it has also explained how many things have come to be. From masterpieces by famous painters to something as simple as the human face, this divine proportion is truly present everywhere and continues to make itself known. It has proven that ratios are so much more than just math.
Reference Sources
Aliu, Dori. “9 Examples of the Golden Ratio in Nature, from Pinecones to the Human Body.” Mathnasium.com, Mathnasium, 25 July 2024,
www.mathnasium.com/blog/golden-ratio-in-nature.
Byju's Future School. “Real-World Examples of the Golden Ratio in Everyday Life.” BYJU’S Future School Blog, 18 July 2022,
www.byjusfutureschool.com/blog/real-world-examples-of-the-golden-ratio-in-everyday-life/.
Mads Soegaard. “The Golden Ratio - Principles of Form and Layout.” The Interaction Design Foundation, Interaction Design Foundation, 30
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