What is the Fibonacci sequence and how is it related to architecture?

One of the most famous series of numbers in history, the Fibonacci sequence was published by Leonardo of Pisa in 1202 in the “Liber Abaci”, the “Book of Calculation”. The famous sequence of numbers has become known as “nature’s secret code” and can be seen in the natural world in several instances. But, after all, how does this sequence relate to architecture?

Leonardo of Pisa, better known as Fibonacci, wrote his sequence of numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233…) to solve a hypothetical breeding rabbit problem in your math book. In its content, the main thing is to know that whatever number is in the sequence, it is the result of the sum of the two previous ones. For example: 2 + 3 = 5, 5 + 3 = 8, etc. This constant creates a very close relationship with the golden ratio (1.61803399), called the golden ratio, which mathematically represents the “perfection of nature”. After all, dividing a number from the Fibonacci sequence by its previous one will bring the result closer and closer to 1.618. The higher the numbers chosen, the closer the result is to the golden ratio.

Antiquity already studied this proportion given by the golden ratio and applied it in their constructions and artistic works, because it was said to have the characteristic of being naturally pleasing to the human eye. Therefore, this can be verified in several architectural works such as the Parthenon, in which the width and height of the facade follow the golden proportion; in the Egyptian pyramids, in which each block is 1,618 times larger than the block of the level immediately above, and in some of them the interior chambers are 1,618 times longer than wide; and even the Taj Mahal, whose design some theorists link to the golden ratio.

These ratios of proportions bring several possible readings in the way the scale of architecture and the way a building is designed is given, even unconsciously, by the Fibonacci sequence, since one of the attributions of a building made by an architect is that it is beautiful, pleasing to the eye: quality generated by the proportion given by this mathematical series.

More than that, this sequence of numbers is found in several species of nature – from the snail to the sunflower, in its most classic examples – and it is also present in the human body as shown by Modulor, one of the most famous editions of Le Corbusier. Launched and revised in the middle of the 20th century, this study demonstrates the effort of one of the most famous architects in history to find the mathematical relationship between the measurements of man and nature. Based on the investigations carried out by both Vitruvius and Da Vinci, the French architect presented a system of measurements on a human scale based on the golden ratio. Composed of three main measurements, the final model of the Modulor arrives at a human body divided into three intervals that generate a golden section: a man of 1.83 m, which with the raised arm would measure 2.26 m and at the navel 1.13 m, which is half.

Nowadays, fortunately, the discussion on the standardization and universalization of the human body is much more advanced and does not abandon itself only to mathematical factors. Moreover, many mathematicians and designers are already questioning whether the golden ratio is a universal formula for aesthetic beauty. According to Keith Devlin, a British mathematician and subject matter expert, all the theories that cover aesthetic appeals according to this constant only exist because we humans are good at recognizing patterns and we ignore anything that contradicts them. In short, it is a debate that will remain constant, after all, scientific data is not enough to translate what is beautiful – this notion being subjective and constructed according to the references and cultures specific to each one. However, it is a fact that the golden ratio was of fundamental importance for the cultural sector and in the construction of an aesthetic sense, especially in the West. By the way, it should be mentioned that it was not on this side of the globe that the Fibonacci sequence was written for the first time, it had already appeared in a book on metrics written by the Indian mathematician Pingala, between 450 and 200 BC, demonstrating that the sources of beauty and wisdom go beyond the European cradle.

Sources: BBC News Brasil, Super Interesting

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