Golden Ratio – guide rather than law

Since the Renaissance, many artists, and architects have proportioned their creations to approximate the golden ratio. The ratio itself has been known by many names, including the Phi Ratio, the Fibonacci Ratio, the Divine Ratio, the Golden Mean, and the Golden Section.

The Fibonacci series is an infinite sequence of natural numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, … The first two numbers of the sequence are 0 and 1. The other terms are the sum of 2 above terms in succession: 0 + 1 = 1, 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13 .

Guide to Proportion

It is probably the most well-known guide to the proportion which can dramatically improve the communication of your design.  While it is not meant to be prescriptive one of the key aspects of design is composition and it still should be something you feel rather than create logically. However, the Golden Ratio’s mythical status in art and design should not be completely ignored.

This sequence is owed to Leonardo of Pisa, also known as Fibonacci, a thirteenth-century Italian Mathematician. The sequence he discovered can be found in computing, mathematics, game design, in the arrangement of cones, music, art and nature.

Golden Ratio was used by the Masters

The Last Supper
Last supper and the Golden Ratio

The Golden Ratio proportions have been used by renowned artists in their masterpieces in the past. The value of the golden ratio is equivalent to 1.618, which is used to determine the dimensions of a painting when it comes to size, composition and colours. Leonardo’s ‘The Last Supper’ is based on the Golden Ratio. Whether this is by design or accident is still subject to speculation.

Fractal Geometry

Fractal Geometry
Fractal Geometry – Two of the most important properties of fractals are self-similarity and non-integer dimension

Fractal geometry consists of infinite repeating patterns. Fractals are most evident to us in Geometry. They demonstrate the geometrically spiralling pattern of the Golden Ratio. In nature there are other “beautiful line patterns to be found; for example spider’s webs, leaf vein patterns, the arc of a rainbow, the line of tree buttresses”. 

Facial Beauty

George Clooney - Golden ratio
George Clooney – Golden ratio. Maths can be used to explain why George Clooney is one of the best looking men in the world.

The face of perfect beauty is one where the distance between various facial features such as from the tip of the nose to the chin, the top of the head to the pupil of the eye and so on. Jessica Simpson, George Clooney and Paula Zahn have this so-called perfect facial beauty.

Music

In music the golden ratio is apparent is the organisation of the sections in the music of Debussy and Bartok. For example in Debussy’s piece, ‘Reflection in Water’ the sequence of keys is marked out by the intervals of 34,21,13, 8. The transcendental quality of this piece of music owes as much to the pianist as a product of a mathematical formula.

The Golden Ratio can help create a feeling of harmony and balance, and it is in this context that I would apply it to my designs.  The message of my design and its application of the Golden Ratio would meet my design objectives.  Does it communicate what I need it to?

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