1.618: the Golden Ratio. A simple number attributed with the ability to explain beauty in the world around us. First believed to have been used by the Ancient Greeks when designing the Parthenon, the golden ratio is claimed to produce some of the most aesthetically pleasing geometric forms and is a mathematical phenomenon in the world of art, architecture and design. But can one number truly be used to define beauty, or is this simple conclusion a consequence of our innate human desire to understand the world around us?
What is the golden ratio?
In simple terms, the number can be calculated when a straight line is split it into two segments, a and b, in such a way that the ratio of the bigger segment to the smaller segment (a:b) is equal to the ratio of the entire line to the bigger segment ((a+b):a). The number that this produces is irrational, or never-ending, but can be simplified to 1.618, and is represented by the Greek letter, phi.
Phi has been discovered and rediscovered many times throughout history and falls under a variety of titles (divine proportion, golden section and golden ratio, to name just a few), but was first described in literature by Greek mathematician, Euclid (325-365 BC), as the division of a line into an ‘extreme and mean ratio.’ Although claims suggest both the Ancient Egyptians and Ancient Greeks used it within architecture, written evidence of phi’s connection with aesthetics didn’t occur until the Renaissance Period, when Luca Pacioli wrote a book entitled ‘Da Davina Proportione’ or ‘The Divine Proportion.’ The illustrations by Leonardo DaVinci have led many to speculate that the artist also incorporated the ratio into his work. Interestingly, the Fibonacci Sequence, discovered in 1200AD, holds strong links with the golden ratio; taking any two successive numbers gives a ratio close to phi (89/55 = 1.61818), however there is no evidence that Fibonacci knew of this connection.
Today, the golden ratio is still widely believed to underlie beauty and perfection. Probably it’s most famous application is the Golden Rectangle, unusual in that it can be endlessly split into a smaller rectangle of the same proportion, and a perfect square. Superimposing this rectangle over DaVinci’s Mona Lisa, Dali’s Sacrament of the Last Supper and structures including Notre Dame and the UN Building suggest the golden ratio is widely embodied. Even the Apple Logo is claimed to have been designed to incorporate phi. Throughout nature it appears frequently, in nautilus shells, flower heads, pine cones and spiral galaxies. Beautiful faces, such as those of Audrey Hepburn and Angelina Jolie, have been proven to be proportional with phi and even at the very basis of life, DNA (measuring 34 by 21 angstroms along each full double helix cycle) incorporates the golden ratio. But are these appearances just coincidental or is there really an underlying pattern to perfection?
Fact or Fiction?
The importance of the golden ratio within aesthetics is a highly disputed concept among intellectuals. Claims that the Parthenon was purposefully designed to incorporate phi have been questioned due to its construction occurring approximately a century before there is any written evidence of knowledge of the ratio’s existence, and whilst many sources suggest that superimposing the golden rectangle over the Parthenon proves its compliance with the theory, they avoid the fact that recorded Parthenon dimensions vary greatly. With so many different numbers available, it is easy to pick-and-choose those that best fit with the ratio. Furthermore, whilst it is proven that Salvador Dali incorporated the golden ratio into his artwork, DaVinci’s use of phi is not certain. His painting of St. Jerome, although often used to support the theory, does not actually comply with the golden rectangle. The top of St. Jerome’s head lies far from the upper boundary.
Many have also attempted to prove that faces proportional with the golden ratio are more attractive, however when examining the human face there are endless points of measurement to choose from. It’s reasonable to assume that anyone with enough time and patience would manage to produce ratios similar to the golden ratio. In fact, being that phi is an irrational number, it is actually impossible for the golden ratio to truly be represented at all!
Finally, all evidence for the aesthetic properties of the golden rectangle appears to be based on one experiment conducted by Gustav Fechner in the 1860s, which consisted of subjects selecting the most ‘pleasing’ rectangle from a variety of ten. In addition to the small sample size used, his results indicated that ratios in the range of 1.50-1.75 were favoured, which, although includes the golden ratio, provides no strong evidence that it is preferable to any other in the range. Repeated experiments of this type have given conflicting results.
So is there any real evidence for the claimed properties of the golden ratio, or has its importance been greatly exaggerated? The titles ‘divine’ and ‘golden’ certainly suggest it is a number that can provide a deeper understanding of beauty, but perhaps we are guilty of making the golden ratio ‘fit’ where we want it to, in order to find pattern and meaning in something that can never truly be understood. More investigation certainly needs to be undertaken before its links to aesthetics can be considered anything more than coincidental. After all, ‘beauty is in the eye of the beholder,’ and explaining it with just a single number seems just a little too simplistic.