The Beauty of the Golden Ratio (2024)

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BYJU'S FutureSchool Last Updated: Mar 6, 2023, 8:08 AM CST

4 Min Read

Mathematical esthetics can be seen in nature, classic art, architecture, and much more. The golden ratio is significant for its connection to nature, as well as the genesis of the universe and the human body. Inspired by its beauty, famous artists integrated it into their designs and compositions of architectural marvels. In this post, we’ll look at how the golden ratio appears intentionally or unintentionally in nature and man-made structures and what makes them pleasing to the eyes.

The Greeks formulated the golden ratio, and the application of this mathematical phenomenon is seen in art and architecture to this day. Earlier, esthetics was used to analyze beauty with harmony as its foundation. So, how do we achieve harmony? It’s pretty simple—just organize the parts, which are usually dissimilar, into a specific exact ratio so that they meet and create beauty.

The Golden Ratio

The “golden ratio” is a 1.618:1 mathematical ratio, and the number 1.618 is known as “phi.”

Golden ratios can be found in shells, plants, flowers, and animals, among other places. It is believed to be one of the strongest and oldest connections between math and creative arts.

The Golden ratio is known by multiple names, like Divine proportion, Golden number, or Golden mean. Some examples of well-known works that demonstrate this proportion are:

● Khufu’s Pyramid in Egypt

● The Parthenon in Athens, Greek sculpture

● Leonardo Da Vinci’s “Mona Lisa”

● Beethoven and Mozart’s music

Golden Ratio and its History

The Golden Ratio is an irrational number roughly equal to 1.618 and is symbolized by the Greek letter phi. In this ratio, the digits after the decimal keep going and never end, like 1.61803398874989484820…

Golden Ratio and Nature

Golden ratio can be seen in nature in golden spirals and golden pentagons. Likewise, golden symmetry can be found in abundance in the plant and animal worlds, both inside and outside.

Some animal horns grow from one end, resulting in an equiangular spiral. For example, golden spirals are found in the horns of rams, goats, antelopes, and other horned species. Another example is the spiral twist in plant tendrils or in tree trunks and sunflower seeds.

Similarly, shapes with pentagonal symmetry are common in nature. Some common examples are: water lily, wild rose, hawthorn, little nail, pear, apple, strawberry, and other flowers with five petals.

Golden Ratio and the Human Body

The golden ratio governs the human body and all of its components. Human bodies that do not adhere to golden proportions appear to be formless. Your belly button represents the golden ratio. Your navel is positioned such that the ratio of the short half to the long half equals the golden ratio. Similarly, your forearm and hand form the ratio, i.e., 1.618, the golden ratio.

The human face is entirely based on the golden ratio. The head, in particular, is shaped like a golden rectangle, with the eyes in the middle. The mouth and nose are both in the golden

ratio with the distance between the eyes and the bottom of the chin. The length of the nose, the position of the eyes, as well as the length of the chin are all proportioned according to the Golden ratio.

Surprisingly, it’s also been seen in DNA sequences. For each whole cycle of the double helix spiral, for example, a DNA molecule measures 34 angstroms by 21 angstroms. When you divide the number 34 by 21, you get 1.61904, which is quite near to 1.618 in precision to at least two decimal places to the right. ¹

Golden Ratio in Architecture

The golden ratio is not only observed in people but is also used in architecture and artwork. For example, in the Great Pyramid of Giza, the length of one side of the base is about 756 feet, and the height of the structure is 481 feet. The ratio of the base to the height is around 1.6 (after rounding it off).

The golden ratio is used in both ancient and modern construction. The majestic Parthenon, the goddess Athena’s temple, is an exclusive human masterpiece of architectural and sculptural grandeur. The exquisite harmony of its elements based on the golden ratio is the main source of its beauty.²

Similarly, the Taj Mahal’s main structure is another example of oriental architecture that uses the golden ratio. All of the rectangles that serve as the fundamental outline for the building’s exterior are in the golden ratio. Notre Dame de Paris, built between 1163 and 1250, seems to have golden ratio proportions in several major design aspects.

Ancient Egypt’s colossal pyramids are majestic creations that bear the golden ratio. These massive structures were built to honor Pharaoh’s sovereignty while preserving his body and spirit. Egyptian pyramids predate Pythagoras’ time, indicating the Egyptians’ mathematical prowess and keen interest in applying the concept of pyramids.

Golden Ratio and Art

Famous artworks such as “Mona Lisa” and “St. Jerome” are all works by Leonardo Da Vinci that use the golden ratio. In addition, several great paintings, including Michelangelo’s The Holy Family and Raphael’s The Crucifixion, employ golden triangles and stars in their compositions. The application of the golden ratio can also be seen in other art forms, such as the statue of Athena in ancient Greece and the sculpture of Apollo in the “Belvedere.”

Math is motivated by curiosity and imagination, as art is required to refer to the outer world. The architects studied the relationship between geometrical design and artistic beauty when incorporating the golden ratio into their design. The golden ratio isn’t only a high mathematical theory; it appears in everyday life.

If you want to know more about the golden ratio, read through our informative series at the BYJU’S FutureSchool blogs.

References

DNA spiral as a Golden Section. (n.d.). Retrieved January 16, 2023, from https://www.goldennumber.net/dna/
Phi and the Golden Ratio / Golden Section in Architecture. (n.d.). Retrieved January 16, 2023, from https://www.goldennumber.net/architecture/

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FAQs

The Beauty of the Golden Ratio? ›

The Golden Ratio, a ratio of 1:1.618 is found in the proportions of the Egyptian pyramids, the nautilus shell, beautiful faces and the ideal body. Our eyes are attracted to objects with this ratio and find them visually appealing.

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What is so special about the golden ratio? ›

The Golden Ratio is a mathematical ratio you can find almost anywhere, like nature, architecture, painting, and music. When specifically applied to design specifically, it creates an organic, balanced, and aesthetically pleasing composition.

View Details ›

What is the math behind beauty golden ratio? ›

Spanning all the way back to ancient Greece, the Golden Ratio considers the proportion of 1:1.618 as appealing — whether it's in art or the human body. The closer your face comes to this ratio, the more beautiful you are.

Learn More Now ›

Who has the perfect golden ratio face? ›

The “Killing Eve” actress, who's 29, has a face that's 94.52% close to the Golden Ratio – a standard that defines beauty. When measuring features like her eyes, nose, lips, and chin, Jodie's face closely aligned with what the ancient Greeks considered perfect.

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What is the golden ratio for a woman's body? ›

Results: There is a golden ratio in the distances between xiphoid to waist and waist to the abdominal crease that is close to 1:1.66, and the waist is at the junction of the upper 2/5th and lower 3/5th of the height from xiphoid to abdominal crease.

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Is the golden ratio attractive? ›

Our eyes are attracted to objects with this ratio and find them visually appealing. The Golden Ratio, also known as Phi (a letter of the Greek alphabet), is derived from the ratio of line segments that occur when it is divided so that the ratio of B to A is the same as the ratio of C to B (see below diagram).

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What is the golden ratio of God? ›

This ratio - 1.618 - is an approximation of its true value of [1+√5)/2]. This ratio has served mankind in three ways: it provides beauty, function, and reveals how wise, good, and powerful the Creator is.

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How do I check my face Golden Ratio? ›

The distance from the top of the nose to the center of the lips should be around 1.618 times the distance from the center of the lips to the chin. The hairline to the upper eyelid distance is classically 1.618 times the length of the top of the upper eyebrow to the lower eyelid.

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What is the prettiest face shape? ›

Oval: Your face is often longer than wide, with the forehead standing out as the largest area of your face. According to Papanikolas, this form is typically regarded as the most attractive facial shape.

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What is the most attractive female body ratio? ›

These studies have found that a low waist to hip ratio (WHR) of approximately 0.7 [9] and a low Body Mass Index (BMI; weight scaled for height) of approximately 18–19 kg/m² [10] are perceived as most attractive in female bodies, while a low waist to chest ratio (WCR) of approximately 0.7, and relatively high BMI ( ...

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What is the perfect figure size for a woman? ›

The specific proportions of 36–24–36 inches (90-60-90 centimeters) have frequently been given as the "hourglass" proportions for women since at least the 1960s (these measurements are, for example, the title of a hit instrumental by The Shadows).

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Why is the golden ratio significant in history? ›

The golden ratio has been famed throughout history for its aesthetic properties and it is claimed that the architecture of Ancient Greece was strongly influenced by its use.