The Golden ratio

The Golden Section is a ratio based on a phi

The Golden Section is also known as the Golden Mean, Golden Ratio and Divine Proportion. It is a ratio or proportion defined by the number Phi ( = 1.618033988749895... )

It can be derived with a number of geometric constructions, each of which divides a line segment at the unique point where:

the ratio of the whole line (A) to the large segment (B)

is the same as

the ratio of the large segment (B) to the small segment (C).

In other words, A is to B as B is to C.

This occurs only where A is 1.618 ... times B and B is 1.618 ... times C

.

Who could have guessed that this innocent-looking line division would have implications for numerous natural phenomena ranging from the leaf and seed arrangements of plants to the structure of the crystals of some aluminium alloys, and from the arts to the stock market?

Sunflower seeds

In fact, with the increasing realization of the astonishing properties of this number over the centuries since Euclid's definition, the number was given the honorifics "Divine Proportion" and "Golden Ratio."

Here I shall concentrate only on one of the surprising (claimed) attributes of the Golden Ratio - its presumed association with aesthetics, since it provides a wonderful example of an attempt to mingle mathematics with the arts.

The golden ratio in the arts

Leonardo da Vinci's Mona Lisa, the ratio of the height to width of that rectangle is equal to the Golden Ratio. No documentation exists to indicate that Leonardo consciously used the Golden Ratio in the Mona Lisa's composition, nor to where precisely the rectangle should be drawn.

Sacrament of the Last Supper, by Salvador Dali

Another painter, about whom there is very little doubt that he actually did deliberately include the Golden Ratio in his art, is the surrealist Salvador Dali. The ratio of the dimensions of Dali's painting Sacrament of the Last Supper is equal to the Golden Ratio. Dali also incorporated in the painting a huge dodecahedron (a twelve-faced Platonic solid in which each side is a pentagon) engulfing the supper table. The dodecahedron, which according to Plato is the solid "which the god used for embroidering the constellations on the whole heaven," is intimately related to the Golden Ratio - both the surface area and the volume of a dodecahedron of unit edge length are simple functions of the Golden Ratio.

Is beauty in the eye of the beholder?

The pioneering (rather crude) experiments in this field were conducted by the German physicist and psychologist Gustav Theodor Fechner in the 1860s. 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 76% of all choices centered on the three rectangles having ratios of 1.75, 1.62, and 1.50, with a peak at the "Golden Rectangle" (with ratio 1.62). Fechner went further and measured the dimensions of thousands of rectangular-shaped objects (windows, picture frames in the museums, books in the library), and claimed (in his bookVorschule der Aesthetik) to have found the average ratio to be close to the Golden Ratio.

Golden in Product Design

When asked about the significance and the characteristics of a symbol or a logo, most people would say it is a mean of representing their business to their target market. I agree. But how? What are the bases of constructing one such logo which can maintain the balance and successfully project everything about your business at the same time? This is where Golden ratio comes in to play.

Let’s take the example of Toyota motors logo. The current Toyota logo consists of three ovals; the two perpendicular ovals actually represent a relationship between the customers and Toyota. These two ovals combine to form a “T” which stands for Toyota. The space in the back emphasizes the potential expansion of Toyota. Taking a closer look one can easily find the application of the golden ratio within their logo.

The ratio between the two halves of the logo, both horizontally and vertically is approximately 1.613, which is less than half of a millimeter from the Golden Ratio value. As I mentioned above the two ovals represent the relationship between the customers and Toyota itself which means they are maintaining a Golden ratio or a Divine proportion between them and their customers through their logo branding strategy.

The Pepsi brand is created by intersecting circles with a set proportion to each other. The ratio is created by two simple circles that are in a set ratio to each other: The Golden Ratio.

Apple was selling only around 6 million iPods by the year 2005 and in 2006 their sales went up to 14 million iPods all of a sudden. What is it that they did to their product? Along with other changes they actually transformed their product look using the same golden ratio principle.

The hottest product which they had in 2005 was NANO 1G IPod and as soon as they launch the classic 5g model their sales jump up by 2 times. Among other things which they did to their product design was the application of this golden ratio.

From then onwards IPOD never launched a design which doesn’t incorporate the result of the lesson they learned about the Golden Ratio principle and the designs of all their products have been swinging around the actual golden ratio.

M.E (INDUSTRIAL DESIGN) @ PUNJAB ENGINEERING COLLEGE University of Technology, CHANDIGARH