CLIL MATHEMATICS PROPORTIONS: THE GOLDEN RATIO Since ancient times, an important tool for creating harmonic compositions in architecture has been the , which is considered to be the perfect proportion because it can be reproduced infinitely. Golden Ratio 1 The total length ( a + b ) is to the longer segment ( a ) as ( a ) is to the shorter segment ( b ). The Greeks knew the Golden Ratio and used it extensively in the design of the Parthenon and other architecture. Since the Renaissance, many artists and architects have proportioned their works using the . In the 20 century, Le Corbusier explicitly used the for the scale of architectural proportion and described it in the (1948), expressing his support of the research that , , and started centuries before: to find the mathematical relationship between human dimensions and nature. Golden Ratio th Golden Ratio System Modulor Vitruvius Leonardo da Vinci Leon Battista Alberti The ratio 1:1.61 occurs over and over in nature. It may be found in everything from the shape of our universe, the structure of clouds, the petals of flowers, and even the proportions of the human body, confirming that the Golden Ratio is the most aesthetically pleasing proportion in existence. The Golden Ratio is an irrational mathematical constant denoted by the Greek letter phi (φ) approximately 1.61. 1. 12. Read the text and answer the questions. What has the tool to create harmonic compositions been since ancient time? Why is the Golden Ratio considered to be the perfect proportion? Where did the ancient Greeks apply the rule of the Golden Ratio? What did Vitruvius, Leonardo da Vinci and Leon Battista Alberti research? Which famous architect used the Golden Ratio System? Where did he describe this scale of architectural proportions? Beyond architecture, in what spheres may the ratio 1:1.61 occur? What does it confirm?