“Geometry has two great treasures; one is the Pythagorean theorem; the other, the auric ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.” – Johannes Kepler
The newspaper pages that you are reading, the screen of your computer, your credit card, the petals of a beautiful flower, the leaves of that tree, the building in front of your house—everything is governed by a principle, a proportion, a harmonic value. The universe seems to whisper a code—unique and harmonious in its beauty—that permeates nature’s every corner. Some call it “the golden ratio,” others “the divine proportion.”
Behind the apparent chaos that reigns within the universe, a place where every event and measurement should follow a random destiny, there is, however, a hidden order. Since Pythagoras’s times, this order (which has intrigued both mathematicians and scholars studying different branches of knowledge) has remained a mystery.
A contemporary study conducted on individuals belonging to different ethnicities showed that, among a sample of several rectangular figures, almost all people chose the same figure as the most harmonious. In this geometric figure, the quotient of the rectangle’s largest side divided by its smallest side is equal to 1.618—a number that in mathematics is known as “golden” or “excellent” and indicates that two quantities are in the golden ratio.
Golden rectangles, rectangles whose side lengths are in the golden ratio, can be found in thousands of architectural works all over the world, as well as in matchboxes, books, business cards, and numerous other everyday objects—for the simple fact that it is harmonious and aesthetically pleasing to the human eye.
The Great Pyramid of Giza, the U.N.’s headquarters in New York, Notre Dame Cathedral – all these buildings present golden ratios within their structures. Even the Greek Parthenon seems to be, in fact, an ode to this auric proportion.
One could guess that plastic arts, the utmost expression of beauty and human wisdom (excluding some contemporary currents), could absolutely not be from the golden ratio or auric proportion. Several artists that operated during the Renaissance included the golden number in their works. Among them was Leonardo da Vinci, who made use of these proportions in his works “The Last Supper” and the “Vitruvian Man.”
Music is also not exempt from this enigmatic code. Mexican artist Silvestre Revueltas used the proportion to organize the parts of his work “Alcancías.” The composers Bela Bartok and Olivier Messiaen utilized the Fibonacci sequence to determine the length of the notes in some of their musical pieces.
Although it can be refuted, arguing that architecture, plastic arts, and music are human inventions and therefore the golden ratio could just be a collective and unconscious appreciation rooted in the human species, there is yet no theory that explains why the golden pattern reiterates itself in countless inanimate objects in nature.
Both rectangles and golden spirals (those that arise from the union of points of many nested golden rectangles nested) can be found everywhere: in rams’ horns, mineral crystals, whirlpools, tornadoes, fingerprints, rose petals, the concentric patterns of cauliflowers and sunflowers, birds, insects, fish, the Milky Way, other galaxies like our neighbor M51… or even a snail. The Nautilus, a beautifully perfect mollusk, is practically golden ratio incarnated. Many trees also present a golden ratio between the thickness of a branch and the branch immediately above it.
The Phi, also known as the golden number, can also be found within the aesthetics that govern the human body. In harmonious bodies, the height from head to toe divided by the length from navel to toe equals to the perfect number 1.618. The same result can be found in the quotient between a human head’s length and the distance between the eyes and chin. Another example would be the quotient between the distance from nose to chin and the one from corner lip to chin. The more a face approaches these proportions, the more harmonious it will appear. Despite everything, there must be a hidden code that dictates aesthetical taste.
The number Phi, as well as its cousin Pi (the ratio of a circle’s circumference to its diameter), is extremely complex. More than a trillion decimals have been calculated so far, and the search seems far from over. The occult motive that connects this code to the power to govern harmony and beauty is something that has delighted many scientists, and it still remains an enigma today.
How can a spiral be the common denominator between thousands of biological entities, which supposedly evolved unpredictably and haphazardly? Could it be related in any way to the fact that the displacement of the DNA’s spiral turn, divided by its diameter equals to nothing other than Phi? Since this number seems to be the codex common to all living forms, the harmonic note to which the whole universe vibrates with, it makes sense for humanity to find the divine proportion harmonious – since we come from the universe, and to it, we belong.