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.

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**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…

The Fibonacci sequence has a direct connection to the Golden ratio concept. In this series, the first two numbers are 1 and 1. To obtain the next number, add the two preceding numbers in the series as follows:

*1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13, 8 + 13 = 21…*

**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/