Ancient Greek mathematicians first studied the ‘Divine Proportion’, which is what we call now the ‘golden ratio’, or ‘golden mean’, ‘golden proportion’, because of its frequent appearance in geometry.
In mathematics, two quantities are ‘in the golden ratio’, or golden mean, if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebrically, for quantities a and b, with a > b > 0,
a+b/a = a/b = φ The Greek letter ‘phi’ or φ represents the golden ratio. Its value is:
φ = (1+square root of 5)/2 = 1.6180339887….
A rectangle, for instance, is ‘golden’ when the ratio between its long side (a) and its short side (b) is the same as the ratio beween the sum of its two side and its long side (a/b=(a+b)/a).
But the fascination with the Golden Ratio is not confined to just mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal.
In architecture: the Parthenon’s façade as well as the elements of its façade are said to be circumscribed by golden rectangles. Whether by accident or by design, the Egyptian pyramids, especially the Great Pyramid of Giza, are very close in proportion to what is called a ‘golden pyramid’.
The 16th century philosopher Heinrich Agrippa drew a man over a pentagon inside a circle, implying a relationship to the golden ration. Leonardo da Vinci’s illustrations of polyhedra in ‘De Divina Proportione’ (On Divine Porportion) and his views that some bodily proportions exhibit the golden ratio have led some scholars to speculate that he incorporated the golden ratio in his paintings.
Some 20th century artists and architects, including Le Corbusier and Dali, have proportioned their works to approximate the golden ratio – especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio – believing this proportion to be aesthetically pleasing.
Salvador Dali explicitely used the golden ratio in his masterpeice, The Sacrament of the Last Supper. The dimensions of the canvas are a golden rectangle. A huge dodecahedron, in perspective so that edges appear in golden ration to one another, is suspended above and behind Jesus and dominates the composition.