What is the golden ratio?

The golden ratio, also known as the golden number, golden proportion or the divine proportion, is a ratio between two numbers that equals approximately 1.618. Usually written as the Greek letter phi, it is strongly associated with the Fibonacci sequence, a series of numbers wherein each number is added to the last. The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21 and so on, with the ratio of each number and the previous number gradually approaching 1.618 or phi.

History of the golden ratio.

The first known mention of the golden ratio is from around 300 BCE in Euclid’s Elements, the Classical Greek work on mathematics and geometry. Euclid and other early mathematicians like Pythagoras recognised the proportion, but they didn’t call it the golden ratio. It wasn’t until much later that the proportion would take on its mystique. In 1509, Italian mathematician Luca Pacioli published the book De divina proportione, which, with illustrations by Leonardo da Vinci, praised the ratio as representing divinely inspired simplicity and orderliness.

Because of Pacioli’s book and Leonardo’s illustrations, the golden ratio gained fame among mathematicians and artists. In the centuries since Pacioli’s book, many enthusiasts have claimed that the number is naturally pleasing to the eye, that it is a mathematical distillation of beauty and that golden ratio line segments, golden rectangle side lengths and golden triangles are represented throughout art history.

Why is Golden Ratio Special?

Golden ratio is aesthetically pleasing because it’s common in the natural world. The proportions of nautilus shells and human bodies are examples of the golden ratio in nature, but these tend to vary greatly from one individual to the next. Some seashells expand in proportion to the golden ratio, in a pattern known as a golden spiral, but not all shells do. It’s true that nautiluses maintain the same shell proportions throughout their life, but the ratio of their shells is usually a logarithmic spiral, as opposed to an expression of phi. Phi does show up in other aspects of nature. Tree leaves and pine cone seeds tend to grow in patterns that approximate the golden ratio and sunflower spiral and other seeds tend to hew close to phi. Phi allows for efficient distribution or packing, so leaves that grow in relation to the golden ratio will not shade each other and will rest in relation to one another at what is known as the golden angle. There’s no evidence that use of the golden ratio is better than use of other proportions, but artists and designers are always in the business of creating balance, order and interesting composition for their work.

How would a world of Products designed with Golden Ratio as its DNA look like?