Beauty and aesthetics have been praised from time immemorial. But little did people know that the most effective, perfectly balanced, and visually compelling creations followed the tid-bits of mathematics. At least not until 1860, when German physicist and psychologist Gustav Theodor Fechner proposed that a simple ratio, an irrational number defines the balance in nature. The Golden Ratio! Fechner’s experiment was simple: ten rectangles varying in their length-to-width ratios were placed in front of a subject, who was asked to select the most pleasing one. The results showed that the most favored choice was the “Golden Rectangle” (with ratio 1.618).
Golden Mean, Golden Section, Divine Proportion are all common names for what is known as the Golden Ratio which is based off the number phi (φ) = 1.61803398874… discovered by Italian Mathematician Fibonacci. Phi (φ) is the ratio between the number sequence 1, 1, 2, 3, 5, 8, 13, 21 etc. where the next number in the sequence is derived by adding 2 numbers together. So, 1+1 = 2, and 1+2 = 3, 2+3 = 5 and so on. When we divide two sequential numbers i.e. 5/3 = 1.67 and 21/13 = 1.615 the ratio between these numbers soon become very close to φ (1.618). Fibonacci’s 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been described earlier in Indian mathematics, by Brahmagupta in 598 almost a thousand years earlier.
What’s so amazing about this number? Some believe that it is the most efficient outcome, the result of natural forces. Some believe it is a universal constant of design, the signature of God. Whatever you believe, the pervasive appearance of φ in all we see and experience creates a sense of balance, harmony and beauty in the design of all we find in nature. It should be no surprise then that mankind would use this same proportion found in nature to achieve balance, harmony and beauty in its own creations of art, architecture, colors, design, composition, space and even music. From the Parthenon to Monalisa, from the Egyptian pyramids to credit cards, φ has been there, always.
Logos with golden ratio
So, it was not surprising when I found the invasion of φ in logo designs. Let us have a look at some of the most popular brands which have used the golden ratio to induce the perfect harmony and balance in their logos.
Remember the yellow square in the National Geographic logo? Have you ever wondered why that simple logo appears to be so appealing? The answer is, as you might know, the Golden Ratio! The length and width of the square have a ratio of 1.61. It is quite fitting for an organization with a motto of “inspiring people to care about the planet” to have a logo based on the golden rectangle.
The new logo of Pepsi has been much simpler and effective, characterized by spare, pure design. It looks intriguing and beautiful. Almost like a laughing emoticon in red and blue. But did you know that the underlying backbone of the Pepsi logo follows the golden ratio? The Pepsi brand is created by intersecting circles with a set proportion to each other. And, the proportion: Golden Ratio (φ) !
Apple is one of those very few companies that do not have the company name in their logo. Yet, the Apple logo is one of the most recognized corporate symbols in the world. The logo is perfectly balanced, and the outlines that map the logo are circles with diameters proportionate to the Fibonacci series. Did Rob Janoff really considered the Fibonacci series while designing it, or is it a coincidence? Well, somebody needs to ask Mr. Janoff. Interestingly, in a different context, in an interview, Rob Janoff said, “… and years later you find out supposedly why you did certain things. And, they are all BS. It’s a wonderful urban legend.”
Another product from Apple, and again a masterpiece of design. The ripples on the cloud are made up of circles whose diameters are proportional to the you-know-what number. Also the containing rectangle, as shown below, is a golden rectangle. In fact, most of the Apple products, ranging from ipods to iPhone are golden rectangles. These amazing Apple designers!
BP is one of the world’s leading international oil and gas companies. They launched their new logo in 2000. What appears to be an attractive logo, however, turns out to be formed of concentric circles, again proportional to the Fibonacci sequence. Is it a mere co-incidence or a planned execution?
The logo of Toyota consists of three ovals. “The two intersecting ellipses are intended to represent the customer and the product… and the importance of that relationship”, according to an e-mail from Mike Michels, VP of Communication at Toyota Motor Sales USA, Inc. “The outer ring represents the world and the global nature of our business.” On a closer look one can easily find a grid based on φ in their logo. The phi-grid is formed by gridlines at certain separation – the separations being in the ratio of the golden ratio φ.
The logo of the Brazilian company Grupo Boticário was designed by the Brazil office of Futurebrand. This logo uses a golden spiral. In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes. The golden spiral is very closely approximated by the Fibonacci spiral (shown above). The golden spiral is very common in nature, for example, the spiral galaxies and mollusc shells. Do you like the use of golden spiral in this logo?
Golden Ratio in nature – a short film
I sincerely do believe that any discussion on golden ratio or the Divine Proportion (a name more appropriate) remains incomplete without showing how accurately the number φ finds its way into a plethora of natural creations. I found this nice and short video on the interwebs to do the job easier for me.
- Singh, Parmanand (1985). “The So-called Fibonacci numbers in ancient and medieval India”. Historia Mathematica 12 (3): 229–244. doi:10.1016/0315-0860(85)90021-7
- goldennumber.net: a website dedicated to φ
- The beauty of the golden ratio
- The golden section and the golden rectangle by Michael Lahanas
- The golden rectangle and the golden rectangle by Jim Loy
- The golden section by Jean NJ
- The golden geometry of the great pyramid
- Apple logo: Breakdown into golden ratio
- Pepsi logo design brief
- The golden ratio of branding and success