Golden Ratio

The golden ratio, usually denoted , expresses the relationship that the sum of two quantities is to the larger quantity as the larger is to the smaller. The golden ratio is the following algebraic irrational number with its numerical approximation:



The figure of a golden section on the right illustrates the defining geometric relationship. Expressed algebraically:



Le Corbusier explicitly used the golden ratio in his Modular system for the scale of architectural proportion. He saw this system as a continuation of the long tradition of Vitruvius, Leonardo da Vinci's "Vitruvian Man", the work of Leon Battista Alberti, and others who used the proportions of the human body to improve the appearance and function of architecture. In addition to the golden ratio, Le Corbusier based the system on human measurements, Fibonacci numbers, and the double unit. He took Leonardo's suggestion of the golden ratio in human proportions to an extreme: he sectioned his model human body's height at the navel with the two sections in golden ratio, then subdivided those sections in golden ratio at the knees and throat; he used these golden ratio proportions in the Modular system.