CLIL MATHEMATICS PROPORTIONS: THE GOLDEN RATIO1 Proportions are based on measurements expressed in numbers. In a building, it is natural for the designer to look for a harmonizing division of the space; the best way to do this is through a visual proportional system. The theory of proportions has been an object of interest for architects since antiquity. Vitruvius drew the proportions of the human body, which he then transported to spatial dimensions. In architecture, an important tool for creating harmonic composition was the Golden Ratio, which was considered to be perfect because it could be reproduced infinitely. The total length a + b is to the longer segment a as a is to the shorter segment b. The Golden Ratio is an irrational mathematical constant denoted by the Greek letter phi ( ) approximately 1.6180339887. astonishing: straordinario navel: ombelico ponder: meditare, riflettere The Greeks knew it and used it extensively for beauty and balance in the design of the Parthenon and other architecture. At least since the Renaissance, many artists and architects 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 section believing this proportion to be aesthetically pleasing. The Swiss architect Le Corbusier centred his design philosophy on systems of harmony and proportion. He explicitly used the Golden Ratio System for the scale of architectural proportion. He saw this system as a continuation of the long tradition of Leonardo da Vinci s Vitruvian Man . 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 the Golden Ratio, then subdivided those sections in the Golden Ratio at the knees and throat; he used these Golden Ratio proportions in the Modulor system. Throughout history, thinkers from mathematicians (such as Leonardo Fibonacci of Pisa) to theologians have pondered the mysterious relationship between numbers and the nature of reality. This curious mathematical relationship, widely known as The Golden Ratio , was discovered by Euclid more than 2,000 years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. 1. A ratio compares the relative sizes of two or more quantities.