The most famous depiction is that of such a rectangle inlaid with a square whose sides measure 10cm. The space left over after the square is another rectangle which is again inlaid with a square. Each time a square is placed, another rectangle is revealed, creating a spiral of squares of ever decreasing size leading to the bottom right hand side of the original rectangle. This image is usually completed by a spiralling line drawn to follow the decreasing square sizes.

The Logarithmic Spiral

More modern applications of the Golden Ratio in architecture can be seen in Notre Dame in Paris, the United Nations Headquarters Secretariat building in New York and the golden ratio in nature CN Tower in Toronto. It’s commonly used in the design of products and logos and by many major corporations. It has even been used in high fashion clothing design, such as in the “Phi Collection” announced in 2004 and covered by Vogue, Elle and Vanity Fair.

• The famous Fibonacci sequence has captivated mathematicians, artists, designers, and scientists for centuries.
• The arrangement of petals often exhibits the Golden Ratio, optimizing exposure to sunlight and space.
• There are many examples of the golden ratio in nature — yet many people have no idea what it is or how to appreciate the planet’s stunning geometry.

Real-life Examples of the Golden Ratio You’ll Be Happy to Know

The proportions found in musical compositions influenced by the Golden Ratio often evoke a sense of harmony and satisfaction for the listeners. The spiral happens naturally because each new cell is formed after a turn. The horns of certain animals — like some breeds of goat and sheep — grow according to phi. It is believed to be found in the curvature of elephant tusks and the shape of a kudu’s horn among others. Take any number in the sequence, then divide it by the number before it, and you will get 1.6. The further we progress through the sequence, the closer we get to exactly phi (1.618) — or the golden ratio.

Human Body

• This ratio has been revered as divine, and called God’s fingerprint due to its presentation in numerous living as well as non-living entities.
• Why don’t you go into the garden or park right now, and start counting leaves and petals, and measuring rotations to see what you find.
• Its appeal thus ranges from mathematicians to doctors to naturalists to artists to investors to mystics.
• Many flowers have petals in numbers that accord with the Fibonacci sequence, such as lilies with three petals, buttercups with five, and daisies with 21, 34, or 55 petals.
• You’ll also find it in the shape of hurricanes, elephant tusks, star fish, sea urchins, ants and honeybees.

As we unravel the mysteries behind this fascinating ratio, we discover the hidden symmetries and connections that underpin the aesthetics of our universe. From the proportions of our fingers and limbs to the shape of our faces, the Golden Ratio can be found in various aspects of human anatomy. Artists and sculptors have historically used these ratios to create sculptures and paintings that are visually appealing and harmonious.

It’s worth noting that every person’s body is different, but that averages across populations tend towards phi. It has also been said that the more closely our proportions adhere to phi, the more “attractive” those traits are perceived. As an example, the most “beautiful” smiles are those in which central incisors are 1.618 wider than the lateral incisors, which are 1.618 wider than canines, and so on. It’s quite possible that, from an evo-psych perspective, that we are primed to like physical forms that adhere to the golden ratio — a potential indicator of reproductive fitness and health. Faces, both human and nonhuman, abound with examples of the Golden Ratio. The mouth and nose are each positioned at golden sections of the distance between the eyes and the bottom of the chin.

The golden ratio has also been observed in the physical proportions of animals. For example, the body lengths of ants and various sections of the human finger have proportions that approximate the golden ratio. The presence of the Golden Ratio across such diverse systems presents a significant challenge to materialistic explanations.

In 1509, a friar and mathematician called Luca Pacioli attributed it with celestial importance in the book The Divine Proportion. As for the “golden” moniker, this is usually attributed to mathematician Martin Ohm, who’s thought to have coined it in 1835. Vincent van Gogh’s The Starry Night incorporates the Golden Ratio in its starry spirals, which allude to spiraling galaxies.

More intriguing yet is the extensive appearance of Phi throughout the human form, in the face, body, fingers, teeth and even our DNA, and the impact that this has on our perceptions of human beauty. Some would argue that beauty is in the eye of the beholder, but there is evidence to support that what we perceive as beauty in women and men is based on how closely the proportions of facial and body dimensions come to Phi. It seems that Phi is hard-wired into our consciousness as a guide to beauty. For this reason, Phi is applied in both facial plastic surgery and cosmetic dentistry as a guide to achieving the most natural and beautiful results in facial features and appearance. In botany, the golden ratio is often seen in the arrangement of leaves, branches, and petals, a phenomenon known as phyllotaxis. The spirals seen in pinecones, pineapples, and sunflowers also exhibit patterns that correlate with the Fibonacci sequence and the golden ratio.

Fibonacci and the Divine Ratio

Similar to the spiral patterns of the seed heads, the pods of the pine cone are also arranged in a Fibonaccian spiral. Each cone consists of pairs of alternating whorls, each oriented in the opposite direction to the other whorl. The ratio of the turn of each pod and the ratio between the number of pods in successive whorls is the golden ratio, i.e., 1.618. That’s an incredible role for a single number to play, but then again this one number has played an incredible role in human history and in the foundations of life itself. The line between its mathematical and mystical aspects is thus not easily drawn.

Debunking the Golden Proportion in Nature

He used the golden ratio to create a tiling pattern, known as Penrose tiling, that exhibits fivefold symmetry and aperiodicity – a pattern that never repeats. The golden ratio’s appearance in nature remained largely anecdotal until the 19th and early 20th centuries when mathematicians and scientists began to formally document these instances. Since reality is three dimensional, we suggest to look first to see if reality might be written in the code 3D quasicrystals. Time and motion could simply be ordered sequences of different 3D quasicrystal configurations, “played” rapidly like a 3D strip of film frames. Ideas like the invariance of the speed of light could be explained using new ideas like an update of the de Broglie electron clock model. The Golden Ratio is a testimony to order in the universe—not the chaos of random processes, but the harmony of intelligent design.

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. 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. In the 20th century, physicist Roger Penrose further extended the golden ratio’s reach into the realm of quantum physics.

For pi, that’s the relationship between a circle’s circumference and its diameter. Phi is approximately 1.618, and is the unique ratio where if you divide a line into two parts, the whole line divided by the longer part is the same as the longer part divided by the shorter part. While the golden ratio’s presence in nature and its link to aesthetics is intriguing, it’s essential to approach these topics critically. Some claims about the ubiquity of the golden ratio have been debunked or exaggerated. Despite this, the golden ratio continues to captivate researchers, artists, and mathematicians alike due to its unique properties and pervasive nature.

Historical structures like the Parthenon in Greece are believed to incorporate the Golden Ratio in their design to achieve harmony and balance. However, in 1509, Italian mathematician Luca Pacioli published the book De Divina Proportione, illustrated by Leonardo da Vinci himself, which categorized, the ratio as a divine representation of simplicity and order. Where 1.618 is represented in upper case as Phi or Φ, its near twin or reciprocal, 0.618, is often represented in lower case as phi or φ.

Phi is an irrational number, a number which cannot be expressed as a ratio of two integer numbers. Pea Horsley is the Founder of the Conversations with Nature World Summit and creator of online learning, Animal Communication Made Easy, a proven 5-step method to learn how to communicate with all species of animals. Pea is the UK’s most highly regarded animal communicator, TEDx speaker, teacher, wild animal retreat facilitator and best-selling author. In 2020 Pea founded The Pride membership as an answer to the global pandemic where each month a different species communicates, guides and advises humanity. UniGuide is dedicated to nature and animal lovers, spiritual seekers, and mythology fans.

It’s also the basis for The Fashion Code, a style guide to women’s dress. Various studies have tested to see if a golden rectangle is the most pleasing rectangle to the human eye. Results of the studies are mixed, but generally point to rectangles with shapes close to the golden rectangle as being most pleasing.