Golden Ratio 1.61803
Throughout history, the ratio for length to width of rectangles of 1.61803 39887 49894 84820 has been considered the most pleasing to the eye. This ratio was named the golden ratio by the Greeks. In the world of mathematics, the numeric value is called “phi”, named for the Greek sculptor Phidias.
Why is it Important??
The golden ratio has been used to analyze the proportions of natural objects and artificial systems such as financial markets, in some cases based on dubious fits to data. The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other parts of vegetation.
Applications & Observations
Art
Leonardo da Vinci’s illustrations of Polyhedra in Pacioli’s Divina proportione have led some to speculate that he incorporated the golden ratio in his paintings. But the suggestion that his Mona Lisa for example, employs golden ratio proportions, is not supported by Leonardo’s own writings. Similarly, although Leonardo’s Vitruvian Man is often shown in connection with the golden ratio, the proportions of the figure do not actually match it, and the text only mentions whole number ratios.
Architecture
The Swiss architect Le Corbusier, famous for his contributions to the modern international style, centered his design philosophy on systems of harmony and proportion. Le Corbusier’s faith in the mathematical order of the universe was closely bound to the golden ratio and the Fibonacci series, which he described as “rhythms apparent to the eye and clear in their relations with one another. And these rhythms are at the very root of human activities. They resound in man by an organic inevitability, the same fine inevitability which causes the tracing out of the Golden Section by children, old men, savages and the learned.
Music
Erno Lendvai analyzes Bela Bartok’s works as being based on two opposing systems, that of the golden ratio and the acoustic scale, though other music scholars reject that analysis. French composer Eric Satie used the golden ratio in several of his pieces, including Sonneries de la Rose + Croix. The golden ratio is also apparent in the organization of the sections in the music of Debussy’s Reflets dans l’eau (Reflections in Water), in which the sequence of keys is marked out by the intervals 34, 21, 13 and 8, and the main climax sits at the phi position.
Nature
Johannes Kepler wrote that “the image of man and woman stems from the divine proportion. In my opinion, the propagation of plants and the progenitive acts of animals are in the same ratio”. The psychologist Adolf Zeising noted that the golden ratio appeared in phyllotaxis and argues from these patterns in nature that the golden ratio was a universal law. Zeising wrote in 1854 of a universal orthogenetic law of “striving for beauty and completeness in the realms of both nature and art”.
