The Golden Ratio

The golden ratio, also known as the golden number, golden proportion or the divine proportion (or section) , is a ratio between two numbers. It has been used throughout history to create visually appealing designs. It frequently appears in geometry (in such shapes as pentagons and pentagrams). The ratio is based on the relationship between consecutive numbers in the Fibonacci sequence (named after a medieval Italian mathematician).

Each number in the Fibonacci sequence is simply the sum of the two numbers before it. It begins with 1, 1 (i.e., 1 + the unseen 0 = 1), and the first 10 members of the sequence are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55. It continues infinitely. We can calculate the ratio using the formula above (we use the Greek letter Phi to represent the output). The ratio is approximately 1.618. It is an artistic concept that comes directly from mathematics and that we can also find all around us. It is a fundamental part of making a design that is inherently pleasing to the user’s eye – you know it looks good, but you don’t know why. What is the appeal of this ratio? It is everywhere in nature: the unfurling fronds of a fern, storm clouds, shells, vegetables, even the human form!

For centuries, it has been thought that art, architecture and nature are more appealing to the eye when the proportions of designs and structures are based on the golden ratio. You can find examples of the golden ratio as far back as Ancient Greece. The Parthenon statues appear to show the golden ratio in their form, and some of Plato’s five solids (including the cube and the dodecahedron) are related to it, too. The golden ratio was popularized in the Renaissance era, and the artists of that period sought to ensure that it was used to deliver aesthetically pleasing works. Today, we can use the golden ratio in our web and app designs to improve the layout and appeal to the eye, placing full confidence in this time-honoured fact.

How is the ratio used in design? Think of a rectangle, with a short side of length 1. To calculate the most aesthetically pleasing rectangle, you simply multiply the length of the short side by the golden ratio approximation of 1.618. So, the long side, in this instance, would have a length of 1.618.We can find the golden ratio throughout the world of design. The ratio between the base and height of the Acropolis in Greece: the dimensions of the vast majority of books on your physical bookcase. It’s literally everywhere you look. Perhaps because we’re surrounded by figures and shapes derived from the golden ratio, we’ve grown especially used to it. We can also use the golden ratio to balance elements within other elements. The logos of Toyota and Pepsi make use of this fact. Toyota uses the ratio to balance the ovals within their logo, and Pepsi uses it to balance the circles in theirs. Can you think of any other brands that exploit this “magic” ratio? Perhaps it’s what can make logos truly iconic!

The equation for calculating the ratio is simple. It is the relationship between two sides of a design (usually the horizontal and the vertical). It does not matter which side we choose as the longest (A) and which we choose as the shortest (B).

The formula for this is: A/B = (A+B)/A = 1.618033987 = Φ

Φ is the Greek letter Phi – how we represent the golden ratio. Why does A/B = (A+B)/A? It does because we are following the Fibonacci sequence and A and B (if expressed in whole numbers) are simply two consecutive numbers in that sequence. Fortunately, we can approximate this to 1.6 or 1.61 or 1.618 in designs without surrendering the aesthetic appeal of the golden ratio. Our eyes aren’t bothered with such slight deviations.

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