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From hurricanes to flowers and pinecones, spiral patterns are abundant in nature. One of these spirals is the Golden Spiral, thought to be a sort of code that governs the architecture of the universe. The Golden Spiral is a broad, fascinating subject that has played a prominent role in history and works of art. It’s inspired mathematicians and philosophers for thousands of years. Let’s take a closer look at its origin, meanings, and significance.
What Is the Golden Spiral Symbol?
The story of the Golden Spiral begins with a number: the Golden Ratio, represented by the Greek letter Phi (�ϕ). Its value is an unending number approximately equal to 1.6180339887. In the 1800s, German mathematician Martin Ohm called the special number 1.618 golden, likely because it has always existed in mathematics. Further back in time, it was even described as divine because of its frequency in the natural world.
So, how do you get the golden ratio? The Golden ratio is “found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part”. The Golden Spiral can be drawn within the Golden Rectangle, whose sides are proportioned according to the Golden Ratio.
The Golden Spiral is unique in its mathematical properties and indicates that we live in a universe governed by mathematical laws. While others believe that it is just a very strange coincidence, many scientists and researchers regard it as an evidence of a Master Mathematician or a Creator. After all, the intelligent design in nature is complex, and it might seem illogical to some to think that it came about by chance.
Meaning and Symbolism of the Golden Spiral
The Golden Spiral symbol has inspired countless people throughout history. It’s been associated with the the fundamentals of life, spirituality and creation. Here’s what it represents.
- Natural Harmony and Beauty: The Golden Spiral is frequently found in nature, from the arrangement of leaves on a plant stem to the spiral galaxies in the universe. Its prevalence suggests a kind of universal harmony and order.
- Growth and Evolution: The spiral can be seen as a symbol of life’s unfolding mysteries. Given that it widens (or gets further away from its origin) with every quarter circle it draws, the spiral symbolizes expansion, growth, and the constant process of evolution and learning.
- Infinite Possibilities: Since the spiral never truly concludes but rather continues to grow indefinitely, it can symbolize infinity, endless possibilities, or eternity.
- Spiritual Journey & Enlightenment: In some cultures and spiritual paths, the spiral represents the journey towards enlightenment, with the spiral’s center symbolizing the starting point of a person’s journey and the outer end indicating enlightenment.
- Creativity and Innovation: As the spiral moves outward, it can be seen as an ever-expanding canvas, symbolizing the endless depths of creativity and the constant evolution of ideas.
- Connection and Unity: Given its consistent and repetitive structure, the Golden Spiral may also symbolize the interconnectedness of all things and the unity of existence.
Some Examples of the Golden Spiral in Use
The fascination with the Golden Spiral symbol has led many artists to use it in their masterpieces. There’s a good chance that you’ve already seen the symbol overlaid on various art forms, from the Parthenon to the Mona Lisa. Unfortunately, there are many confusing claims about the subject, so we’ll help you decide whether they’re grounded in myth or math.
- The Parthenon
Built between 447 and 438 BCE, the Parthenon in Athens, Greece is one of the most aesthetically pleasing structures ever made. Many speculate that it was constructed based on the Golden Ratio. You’ll even see several depictions of the front facade of the temple with the Golden Spiral and Golden Rectangle on it.
There’s no doubt that the ancient Greeks incorporated mathematics and geometry into their architecture, but scholars can’t find concrete evidence that they used the Golden Ratio in building the Parthenon. Many find it a myth because most of the mathematical theorems were only developed after the construction of the temple.
What’s more, precise measurements are needed in order to conclude that the Golden Ratio and Golden Spiral were used in the design. According to experts, the Golden Rectangle should be framed at the base of the steps approaching the Parthenon, not at the base of its columns—as commonly shown in several illustrations. But all this is speculation because, as the structure is in ruins, it makes its exact dimensions subject to some estimation.
- Leonardo da Vinci’s Paintings
Leonardo da Vinci has long been dubbed the “divine” painter associated with the Golden Ratio. This association was even supported by the novel The Da Vinci Code, as the plot involves the Golden Ratio and Fibonacci numbers. While everything is subject to interpretation, many have speculated that the painter intentionally used the Golden Spiral in his works to achieve balance and beauty.
Da Vinci’s use of the Golden Ratio is evident in The Last Supper and The Annunciation, but the Mona Lisa or La Joconde is still up for debate. There are few architectural elements and straight lines to be used as reference points compared to the other two paintings.
We’ll probably never know Da Vinci’s intent for his masterpieces, but many find the coincidence compelling. Given that da Vinci had used the Golden Spiral before, it wouldn’t be unexpected for him to use it on the Mona Lisa as well. Just keep in mind that not every Da Vinci’s painting has clear evidence of the incorporation of the Golden Ratio and the Golden Spiral, so it’s we can’t conclude that all his masterpieces are based on them.
Golden Spiral vs. the Fibonacci Spiral
The Golden Ratio occurs in many mathematical contexts. That’s why the Golden Spiral is often associated with the Fibonacci sequence—a series of numbers closely linked to Phi. Technically, the sequence begins with 0 and 1 and continues infinitely, and if you divide each number by its predecessor, the result would converge to the Golden Ratio, approximately 1.618.
The golden spiral and the Fibonacci spiral are very similar in shape, and many use them interchangeably, but they’re not the exactly same. These two numbers don’t have the same exact pattern when measured.
It’s said that the Fibonacci spiral only matches the golden spiral at a certain point, when the former approaches the golden ratio or 1.618. In fact, the higher the Fibonacci numbers are, the closer their relationship is to Phi. In other words, not every spiral found in nature is based on the Fibonacci numbers or the Golden Ratio.
The Golden Spiral Symbol in Modern Times
The Golden Spiral contributes to our understanding of life and the universe. Here are some of the recent discoveries regarding the symbol:
- In Mathematics
The Golden Spiral plays a role in the geometry of fractals, a complex pattern that repeats forever. American mathematician Edmund Harriss became popular for his fractal curve based on the Golden Spiral, now known as the Harriss Spiral. It’s said that he aimed to draw branching spirals that look aesthetically appealing, but he ended up with a unique spiral by using a mathematical process.
- In Biomechanics
The Golden Spiral is thought to hold a fascinating influence over the motion of the human hand. According to an anatomist, the movement of human fingers follows the pattern of the Golden Spiral. You’ll even find images of a clenched fist with the spiral symbol overlaid on it.
- In Design and Composition
Nowadays, many designers overlay a Golden Spiral symbol on an image to illustrate its Golden Ratio proportions in hopes of achieving visual harmony in their works. Some modern logos and icons are based on them, where designers apply the so-called concept of “ratios within ratios.”
- In Nature
Nature is full of spiral patterns but finding the actual Golden Spiral in nature is rare. Interestingly, scientists have found out that falcons fly in a Golden Spiral path when approaching their prey, likely because it’s an energy-efficient flight path.
Contrary to popular belief, the nautilus shell isn’t a Golden Spiral. When measured, the two wouldn’t match no matter how they were aligned or scaled. Also, not every nautilus shell is created equal, as each has variations and imperfections in shapes.
The spirals of sunflowers and pinecones are pretty, but they’re not Golden Spiral. In fact, their spirals don’t even wrap around the center, as opposed to the Golden Spiral. While some flowers have number of petals that correspond with the Fibonacci numbers, there are several exceptions found.
Experts also say that a galaxy or occasional storm cloud that fits a part of a Golden Spiral shouldn’t be a conclusion that all galaxies and hurricanes are based on the golden ratio.
Our universe is filled with spirals, so it’s not surprising that many have become interested with the math behind them and their meanings. Artists have long recognized the Golden Spiral as the most pleasing to the eyes. It’s indeed one of the most inspiring patterns in nature that can be translated to creative artistic expressions.