There's a common mathematical ratio found in nature that can be used to create pleasing, natural looking compositions in your design work. It is called the Golden Ratio, although it's also known as the Golden Mean, The Golden Section, The Divine Proportion or as the Greek letter phi, φ. Whether you're an illustrator, web designer, art director or graphic designer, it's well worth considering the Golden Ratio on any of your projects.
Well-known to the ancients: The Pyramids of Giza, the Parthenon and Da Vinci’s painting of The Last Supper are all said to be designed and composed within the parameters of this ancient equation. The Golden Mean is derived from the famous mathematical Fibonacci Sequence in which each number is the sum of the two numbers before it.
The Fibonacci numbers are the numbers in the above integer sequence, called the Fibonacci sequence, and characterized by the fact that every number is the sum of the two preceding ones.
Named after Fibonacci, also known as Leonardo of Pisa or Leonardo Pisano, Fibonacci numbers were first introduced in his Liber abaci in 1202.
The sequence Fn of Fibonacci numbers is defined by the recurrence relation:
With seed values:
The difference between any two numbers in this sequence isn’t always exactly equal to 1:1.618 (The Golden Ratio - expressed as a more exact ratio - is: 1.61803398875…) - but it’s rather close.
A golden rectangle (in pink) with longer side a and shorter side b, when placed adjacent to a square with sides of length a, will produce a similar golden rectangle with longer side a + b and shorter side a.
This illustrates the relationship:
In Sacred Geometry, this is known as a Divine Progression. It's truly amazing how this simple ‘formula for regenerative progression and growth’ could be expressed by a ratio that is present everywhere we look, especially in the natural world.
A Fibonacci spiral is a series of connected quarter-circles drawn inside an array of squares with Fibonacci numbers for dimensions. The squares fit perfectly together because of the nature of the sequence, where the next number is equal to the sum of the two before it. Any two successive Fibonacci numbers have a ratio very close to the Golden Ratio. The larger the pair of Fibonacci numbers, the closer the approximation. The spiral and resulting rectangle are known as the Golden Rectangle.
When applied to graphic design, the Golden Ratio simply provides us with a way of creating harmony and proportion that our subconscious mind seems to be attracted to. As we’ve previously mentioned, the Parthenon and the painting of The Last Supper appear to use the ratio, as does the Apple logo, the Twitter logo and even natural forms such as ferns, flowers, sea shells and the human face.
The golden ratio is a reminder of the relatedness of the created world to the perfection of its source and of its potential future evolution.