What is the Golden Ratio and where does it appear in our lives? In this post, we’ll explore all aspects of the Golden Ratio, from its origins to where it appears in nature, art, and architecture as well as what it means in the field of sacred geometry.
What is the Golden Ratio?
The Golden Ratio is a unique mathematical principle that appears throughout the natural world as well as in human-made structures, such as art and architecture. And because of its existence in the natural world, it has special meanings in the field of sacred geometry.
In mathematics, the Golden Ratio is an irrational number that is approximately equal to 1.618. In other words, it’s a ratio of 1 to approximately 1.618.
The Golden Ratio is denoted by the Greek letter phi (φ).
A Golden Ratio occurs when you add two unequal numbers together, and the sum of those two numbers has a ratio of 1.618 to 1 when that sum is compared to the larger of the first two numbers.
As you can imagine, the relationship of something that is 1 to 1, or 1:1, implies symmetry and balance. The relationship of the two parts in the Golden Ratio: 1:1.618, on the other hand, while not symmetrical, has special properties that also contain their own unique balance and beauty.
Where did the Golden Ratio get its name?
The Golden Ratio was a concept known to ancient people before it was called the Golden Ratio. In fact, the 300 BCE Greek mathematician Euclid called it “the extreme and mean ratio.” And in the late 15th century, the Italian mathematician Luca Pacioli referred to it as the “divine proportion” in his book Divina Proportione, which was illustrated by Leonardo da Vinci.1
It wasn’t until the 19th century when mathematician Martin Ohm referred to it as goldener schnit, or “golden section,” in his his book Die reine Elementar-Mathematik, published in 1815.2
The Fibonacci Sequence
The Golden Ratio is closely related to another mathematical concept: the Fibonacci Sequence.
Discovered by the Italian mathematician Leonardo Fibonacci in the early 13th century, the Fibonacci Sequence describes a sequence of numbers in which each number in the sequence equals the sum of the two preceding numbers: 0 + 1 = 1, then 1 + 1 = 2, 1 + 2 = 3, and so on. Notably, the sequence goes as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, and continues infinitely.
As you progress in the Fibonacci Sequence, the ratio of the two consecutive numbers increasingly approaches the relationship of the numbers in the Golden Ratio: 1.618. For example, this is illustrated in the numbers 13 to 21, or the ratio of 13:21.
Like the Golden Ratio, the Fibonacci Sequence has beautiful representations in nature, which we’ll explore in the next section.
Golden Ratio in Nature
The Golden Ratio appears in wonderful ways in the natural world.
One way that the Golden Ratio and the aforementioned Fibonacci Sequence appear in the natural world is in spiral patterns. If these two mathematical concepts are drawn as a two-dimensional illustration, a spiral pattern is the result.
The Golden Ratio and the Fibonacci Sequence appear in nature in the form of spirals, such as in:
- Leaves growing around a stem
- Fern fronds
- Sunflower disc florets (the center where the seeds are formed)
- Chameleon tails
- Seahorse tails
- Snakes curled up when resting
- Nautilus and other seashells
For those who believe in sacred geometry, the Golden Ratio appearing in the natural world reflects a universal harmony and mathematical beauty that demonstrates creative divine planning.
Golden Ratio in Art
For centuries, artists have adhered to the Golden Ratio in the composition of their artwork. This is because it is believed to embody universal beauty and harmony. Indeed, some of these works are recognized as masterpieces by people around the world. Here are few examples:
Leonardo da Vinci
While it’s unknown whether certain artists intentionally created using the principles of the Golden Ratio and sacred geometry in their artwork (even if they appear), we do know that Leonardo da Vinci did apply these concepts. For example:
As mentioned earlier, da Vinci illustrated Luca Pacioli’s book Divina Proportione, which was about geometric mathematical proportions, including the Golden Ratio, and their applications in art and architecture.
da Vinci’s illustrations were so popular that they had a strong influence on the art and architecture of that period and beyond.3
The Last Supper
In The Last Supper, da Vinci incorporated the Golden Ratio in both the overall composition, from Jesus and his Apostles, to the proportions of the table and the architectural features in the painting.
The Mona Lisa
In The Mona Lisa, da Vinci incorporated the Golden Ratio in the composition of the Mona Lisa’s face, including the line of her eyes in proportion to her face, as well as the proportion of her body and hands.
Furthermore, the dimensions of the painting itself are believed to have the dimensions of the Golden Ratio, or a “golden rectangle.”
Salvador Dali – The Sacrament of the Last Supper
Like da Vinci, in his painting The Sacrament of the Last Supper, Salvador Dali incorporated the Golden Ratio in a few ways. To begin, the canvas itself has dimensions that are a ratio of 267/166.7, which is approximately equal to the Golden Ratio.
Additionally, the painting features a huge dodecahedron, the twelve-faced Platonic Solid, which is engulfing the supper table.
A fundamental sacred geometry shape, the dodecahedron’s surface area and volume are simple functions of the Golden Ratio. (Plus, its number of sides holds religious significance, representing the twelve hours of the day, twelve months of the year, the twelve pentagons of the dodecahedron, and Jesus’ 12 Apostles.)4
Vincent van Gogh – The Starry Night
Vincent van Gogh’s The Starry Night incorporates the Golden Ratio in its starry spirals, which allude to spiraling galaxies. In addition, the golden color or the spiraling stars reflect the concept of a golden harmony to the Universe.
Sandro Botticelli – The Birth of Venus
Botticelli’s painting The Birth of Venus is also said to follow the Golden Ratio in a few ways. To begin, the dimensions of the canvas have a ratio of height to width that is approximately 1:1.618.5
In addition, some art historians say the painting’s composition follows the Golden Ratio. (Though it is unknown whether Botticelli did this purposefully or not.) For example,the position of Venus’s navel and the height of the painting correspond to the Golden Ratio.
As well, some believe Golden Ratio proportions appear in relation to the shell and Venus as well as with the other figures in the painting.6
The Golden Ratio also appears in many famous architectural masterpieces. Here are some examples:
The Parthenon in Athens, Greece
The Parthenon in Athens, Greece incorporates the Golden Ratio in the proportions of the temple’s facade, as well as various other elements of its design.
The Great Pyramid of Giza, Egypt
Archaeologists believe the proportions of the Great Pyramid closely resemble the Golden Ratio. The ratio of the height to the half-base of the pyramid approximates the Golden Ratio, suggesting that the ancient Egyptians might have employed these principles in its construction.
Notre Dame in Paris, France
The famous French cathedral features Golden Ratio proportions in various parts of its structure, including the relationship between the central rose window and the surrounding elements.
The United Nations Secretariat Building in New York City, USA
This modern building displays the Golden Ratio in its facade. The ratio of the height to the width of the building aligns with the Golden Ratio, contributing to its aesthetic appeal.
Taj Mahal in Agra, Inda
The Taj Mahal is another example where the Golden Ratio is believed to have been used in its design. The proportions of the main dome, the central arch, and the height of the building in relation to its width all reflect the principles of the Golden Ratio.
In the field of sacred geometry, the Golden Ratio reflects universal harmony and an order to a Universe in which we feel that we fit in. In a way, the appeal of its proportions make us feel connected to it and at home. And on a spiritual level, it suggests a connection between the physical and metaphysical worlds and an order in the natural world that reflects the divine.
Frequently Asked Questions
How is the golden ratio used in real life?
The Golden Ratio is used in art, architecture, and other forms of design, including in technology, to create visually appealing and balanced proportions In addition, it’s used in science to study the patterns of growth and structures of plants and animals. As well, in physics and cosmology, it’s seen in the structure of atoms and the distribution of galaxies.
What is the golden ratio in the natural world?
In the natural world, the Golden Ratio appears in spiral patterns, such as that of leaves around a stem, nautilus and other shells, seahorse and chameleon tales, cyclones, hurricanes, and galaxies, reflecting a common pattern of growth and structure.
What is the theory behind the Golden Ratio?
The theory behind the Golden Ratio is that it represents an ideal, aesthetically pleasing proportion found both in geometry and nature, believed to be a mathematical expression of beauty and harmony.
You might like these other articles on UniGuide:
- Sacred Geometry Symbols
- Platonic Solids
- Seed of Life
- Flower of Life
- Chameleon Symbolism
- Angel Numbers Guide