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From hurricanes to flowers and pinecones, spiral patterns are abundant in nature. Mathematics is the science of patterns, so it’s not surprising that spirals have inspired mathematicians for centuries. 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.
Here’s a look at the golden spiral – its origin, meanings, and significance.
What Is the Golden Spiral Symbol?
The golden spiral is a pattern created based on the concept of the golden ratio—a universal law that represents the “ideal” in all forms of life and matter. In fact, it’s often cited as an example of the connection between the laws of mathematics and the structure of living things. The more we understand the math behind the symbol, the more we’ll appreciate its appearances in nature and arts.
In mathematics, the golden ratio is a special number that’s approximately equal to 1.618 and represented by the Greek letter Φ (Phi). You may wonder where this golden spiral comes from—and the answer to that lies within the golden rectangle. In geometry, the golden spiral can be drawn from a golden rectangle whose sides are proportioned according to the golden ratio.
In 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. The spiral pattern created from the golden ratio is also called the golden spiral.
The 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.
In mathematics, there are several spiral patterns and they can be measured. The golden spiral and the Fibonacci spiral are very similar in shape, and many use them interchangeably, but they’re not the same. Everything can be explained by mathematical calculations, and they won’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. Just keep in mind that not every spiral found in nature is based on the Fibonacci numbers or the golden ratio.
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.
- Life and Creation
The golden spiral is unique in its mathematical properties and proves 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.
- Balance and Harmony
The golden spiral has captured the imagination of mathematicians, designers and artists with its beauty. It’s reflected in some of the greatest works of art and architecture. It also has been associated with beauty, as many believe beauty is centered on its unique properties in mathematics and geometry. Some mystics believe that the symbol will also bring balance and harmony into one’s life.
The Golden Spiral Symbol in History
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 as overlays 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 as 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. Also, the structure is in ruins, which 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 Annuciation, but the Mona Lisa or La Joconde is still up for debate. It’s said that there are few architectural elements and straight lines to be used as reference points compared to the other two paintings. Still, you can find several interpretations of golden ratios on the Mona Lisa, featuring the golden spiral as overlays.
We’ll probably never know Da Vinci’s intent for his masterpieces, but many find the strange coincidence compelling. Given the painter’s prior usage, it wouldn’t be unexpected for him to use it on the said painting 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 difficult to conclude that all his masterpieces are based on them.
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 as overlay.
- 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 spirals. 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.