The Egyptians supposedly used it to guide the construction the Pyramids. The architecture of ancient Athens is thought to have been based on it. Fictional Harvard symbologist Robert Langdon tried to unravel its mysteries in the novel The Da Vinci Code.
"It" is the golden ratio, a geometric proportion that has been theorized to be the most aesthetically pleasing to the eye and has been the root of countless mysteries over the centuries. Now, a Duke University engineer has found it to be a compelling springboard to unify vision, thought and movement under a single law of nature's design.
Also know the divine proportion, the golden ratio describes a rectangle with a length roughly one and a half times its width. Many artists and architects have fashioned their works around this proportion. For example, the Parthenon in Athens and Leonardo da Vinci's painting Mona Lisa are commonly cited examples of the ratio.
Adrian Bejan, professor of mechanical engineering at Duke's Pratt School of Engineering, thinks he knows why the golden ratio pops up everywhere: the eyes scan an image the fastest when it is shaped as a golden-ratio rectangle.
The natural design that connects vision and cognition is a theory that flowing systems -- from airways in the lungs to the formation of river deltas -- evolve in time so that they flow more and more easily. Bejan termed this the constructal law in 1996, and its latest application appears early online in the International Journal of Design & Nature and Ecodynamics.
"When you look atwhat so many people have been drawing and building, you see these proportions everywhere," Bejan said. "It is well known that the eyes take in information more efficiently when they scan side-to-side, as opposed to up and down."
Bejan argues that the world -- whether it is a human looking at a painting or a gazelle on the open plain scanning the horizon -- is basically oriented on the horizontal. For the gazelle, danger primarily comes from the sides or from behind, not from above or below, so their scope of vision evolved to go side-to-side. As vision developed, he argues, the animals got "smarter" by seeing better and moving faster and more safely.
"As animals developed organs for vision, they minimized the danger from ahead and the sides," Bejan said. "This has made the overall flow of animals on earth safer and more efficient. The flow of animal mass develops for itself flow channels that are efficient and conducive to survival -- straighter, with fewer obstacles and predators."
For Bejan, vision and cognition evolved together and are one and the same design as locomotion.The increased efficiency of information flowing from the world through the eyes to the brain corresponds with the transmission of this information through the branching architecture of nerves and the brain.
"Cognition is the name of the constructal evolution of the brain's architecture, every minute and every moment," Bejan said. "This is the phenomenon of thinking, knowing, and then thinking again more efficiently. Getting smarter is the constructal law in action."
While the golden ratio provided a conceptual entryway into this view of nature's design, Bejan sees something even broader.
"It is the oneness of vision, cognition and locomotion as the design of the movement of all animals on earth," he said. "The phenomenon of the golden ratio contributes to this understanding the idea that pattern and diversity coexist as integral and necessary features of the evolutionary design of nature."
In numerous papers and books over past decade, Bejan has demonstrated that the constructal law (www.constructal.org) predicts a wide range of flow system designs seen in nature, from biology and geophysics to social dynamics and technology evolution.
Bejan's research is supported by the National Science Foundation.
FAQs
Why does the Golden Ratio, also known as the golden proportion, seem so aesthetically pleasing to the human eye? Researchers believe that our attraction to this ratio, often referred to as the golden mean ratio, is linked to the human brain's innate tendency to recognize and appreciate symmetry and proportion.
What is the story behind the golden ratio? ›
History of the golden ratio.
The first known mention of the golden ratio is from around 300 BCE in Euclid's Elements, the Classical Greek work on mathematics and geometry. Euclid and other early mathematicians like Pythagoras recognized the proportion, but they didn't call it the golden ratio.
What is the best explanation of golden ratio? ›
Putting it as simply as we can (eek!), the Golden Ratio (also known as the Golden Section, Golden Mean, Divine Proportion or Greek letter Phi) exists when a line is divided into two parts and the longer part (a) divided by the smaller part (b) is equal to the sum of (a) + (b) divided by (a), which both equal 1.618.
What is the theory behind golden ratio? ›
The two sections are in golden ratio if the ratio of the length of the larger section (say, “a”) to the length of the smaller section, (say, “b”) is equal to the ratio of their sum “a + b” to the larger section “a”.
What did Fibonacci say about the golden ratio? ›
The Golden Ratio is a relationship between two numbers that are next to each other in the Fibonacci sequence. When you divide the larger one by the smaller one, the answer is something close to Phi. The further you go along the Fibonacci Sequence, the closer the answers get to Phi.
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.
What is the golden ratio for dummies? ›
It is the ratio of a line segment cut into two pieces of different lengths such that the ratio of the whole segment to that of the longer segment is equal to the ratio of the longer segment to the shorter segment.
What does the golden ratio mean spiritually? ›
The golden ratio, seen in structures as vast as galaxies or as intricate as DNA, has long been the symbol of ideal harmony. Duke University's Adrian Bejan ties this unique ratio to a universal law of nature's design. Through his work on the constructal law, Bejan reveals how nature shapes itself to ease flow.
What is golden ratio in our life? ›
The golden ratio occurs when the ratio of the sum of two quantities equals the ratio of the quantity as a whole, which is symbolized by the number 1.618 or the Greek letter “phi.” It has been used to create what are regarded as the most esthetically pleasing designs that display perfect symmetry in architecture and art ...
Why is the golden ratio so fascinating? ›
The golden ratio has the amazing property of being the most irrational number of them all. This means that not only is it not possible to represent it exactly as a fraction, it isn't even possible to approximate it easily by a fraction.
In conclusion, the Golden Ratio is a mathematical ratio that is commonly found in nature and is frequently used in design to create compositions that are naturally pleasing to the human eye.
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.
Why is the golden ratio divine? ›
Golden ratio enthusiasts argue that the golden ratio is aesthetically pleasing because it's common in the natural world. The proportions of nautilus shells and human bodies are examples of the golden ratio in nature, but these tend to vary greatly from one individual to the next.
What is the God number in nature? ›
The golden ratio is 1.618, represented by the Greek letter 'phi', is said to be is a mathematical connection between two aspects of an object. It is also called the Fibonacci sequence and it can be found across all of nature: plants, animals, weather structures, star systems – it is ever-present in the universe.
Why is the golden ratio perfect? ›
Summary: The Golden Ratio is special because it perfectly balances addition and multiplication. The Golden Ratio (1.618...) is often presented with an air of mysticism as "the perfect proportion".
What is the golden ratio of the human hand? ›
It is approximately 1.618.
What does the golden ratio symbolize? ›
Furthermore, the golden ratio is also associated with the idea of divine proportions or cosmic harmony. Many artists and philosophers throughout history have attributed spiritual or metaphysical significance to the golden ratio, seeing it as a representation of divine or universal order.
Why is the golden ratio important in life? ›
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.
What is the golden ratio in the human body? ›
It has been suggested that the ideal human figure has its navel at the golden ratio ( , about 1.618), dividing the body in the ratio of 0.618 to 0.382 (soles of feet to navel:navel to top of head) ( 1⁄ is. -1, about 0.618) and Leonardo da Vinci's Vitruvian Man is cited as evidence.
What are some interesting facts about the golden ratio? ›
This ratio, known as the golden ratio, creates a spiral when plotted on a graph (the famous Golden Spiral). The golden ratio is an irrational number represented by (1 + √5)/2, roughly 1.618. It's a ratio found in mathematics, geometry, art, and architecture, often denoted by the Greek letter phi (φ).
