Line segments in the golden ratio
What is the Golden Ratio?
The Golden Ratio is a ratio which describes a rectangle, whereby the rectangle’s length is approximately one and a half times its width. In both the arts and mathematics, two quantities are said to be in a golden ratio when their ratio is the same as the ratio of the sum to the maximum. The golden ratio’s value is 1.62.
Origins of the Golden Ratio
Such a simple ratio has fascinated mathematicians, artists, musicians, mystics, philosophers and scientists for almost two and a half thousand years. Pythagoras, Euclid, Leonardo of Pisa, mathematician Johannes Kepler and physicist Roger Penrose have all spent countless hours poring over its properties.
The Ancient Greeks were the first to notice the Golden Ratio’s presence in geometry. This discovery is usually attributed to Pythagoras, or his followers. It was Euclid who wrote the treatise Elements, which contains the first written reference to the ratio, backing up his claim with several theorems and proofs.
In 1509, Luca Pacioli discussed the golden ratio in his work De divina proportione. During the same century, Michael Maestlin, a professor of the University of Tübingen, defined the approximate decimal of the inverse golden ratio as ‘0.6180340’.
From the 20th century onwards, the Greek letter phi (Φ or φ) has been used to describe the ratio.
Use of the Golden Ratio in Design
For centuries, architects and artists have used the golden ratio to design their works. Examples include the Parthenon in Athens, or the Mona Lisa, the famous painting by Leonardo da Vinci. It is widely believed that even the Egyptians used the ratio to help to construct the great Pyramids. An analysis into the construction of the Great Mosque of Kairouan revealed that the ratio had been consistently applied, mainly during a reconstruction of the original building.
Leon Battista Alberti wrote Vitruvius in the 16th century, a work explaining how architectural proportions can be improved by the use of the golden ratios found in the human body, as illustrated by Leonardo da Vinci’s Vitruvian Man. More recently, Le Corbusier, a Swiss architect who contributed greatly to the modern international style, used principles of proportion and harmony in his works that were partly based around the golden ratio.
Some argue that the ratio is in fact used everyday in the design of art work, televisions, posters, cards, cars and light switch plates, as well as being present in many musical compositions. Naturalists and scientists have also found the golden ratio to apply to branches in the stems of plants, leaf veins, chemical compound proportions and the geometry of crystals.
The Golden Ratio in Web Design
Jarel Remick stated in 2008 that the golden ratio can be used to effectively design web pages. A web page, Remick wrote, uses a ‘container’ within which the elements of a page are placed. Headers, logo, navigation, sidebars, ‘whitespace’, main content and footer can all be manipulated to optimum effect.