Proportions are understood as the cooperation of different parts into a whole. It is a commonly known term called proportion. But trying to understand proportions in architecture turns out to be more complex due to the huge amount of hidden information and theories, but these things allow us to understand the true meaning of proportions and their role in architecture. Proportions are considered the combination of mathematics with art. This topic is connected to others such as metaphysics, metrology, music, morphology, anthropometry, archeology etc. Say no to plagiarism. Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an Original Essay Proportions, numbers and geometry are three main things in terms of architecture, which allow it to exist and develop. The Pythagoreans had their own theory of beauty. They relied on numbers, because they thought they were everywhere. Pythagoras stated that "everything is a number" and wanted to prove that anything can be described using numbers and fractions. He held up God as an example of perfection, and while He would not create anything that was not as good as Himself, He would only create things He considered perfect. Plato said that “All that is good is beauty, and beauty is not without regular relations or proportions” And from this he believed that beauty was all about measures and numbers (TATARKIEWICZ, 1962, p. 154). All he beginning the topic of beauty became something that everyone referred to, because beauty is something that people have been trying to achieve for centuries. It was said that something was beautiful when it had proper proportions and symmetry. Referring to beauty as a whole, it is important, but focusing on the beauty of individual objects - forms, is a wrong way of understanding proportions in architecture. The supposed beauty of several singular forms is useless because it is a very dubious assumption, on which a theory of proportions could be based. use of those forms in practice can only be justified as a way to achieve a goal and therefore it does not matter whether those forms individually are considered beautiful or not (Scholfield, p. 5). The criteria of beauty have been along architecture and its creation since the beginning having a vital impact on its shape and form. Alberti thought that architecture was focused on beauty. He described beauty as harmony, which is a coherent arrangement of parts and perfect proportions. Alberti did not copy ancient theories, but used them as an example. What connected all these theories was beauty. Because Alberti based himself on the mathematical system of harmonic proportions, as he said, beauty defines harmony: "Beauty is the adaptation of all parts in a proportionate way so that they cannot be added or subtracted or changed without compromising the 'harmony of the whole" (Wittkower, p. 29). He said that there are 3 perfect proportions: arithmetic, geometric and musical and all of them are pleasing to the eyes and ears and are valid in music and architecture or even sculpture. From Alberti's general opinion on art two conclusions can be made: the purpose of art is beauty and the way to follow it is nature. Nature, if not always perfect, was the most accurate model of beauty, which was what the ancients understood when they aimed to imitate nature as it was. the best artist in all types of composition(Scholfield, p. 55).Architecture, nature and geometry are in a very important relationship due to the observations of early humans on nature since they began to exist nature and tried to learn from it. They found that it has some geometric proportions in the things it creates, even in humans themselves. Vitruvius had the idea of ​​onesource of beauty which was the importance of proportion. The parts had to be related to each other and to the whole and not be left simply to intuition. The harmonic scale is his most important contribution to the practice of proportion. He left many clues about the rules of proportion in things like houses, temples, orders. There are very few signs of the presence of a system, but occasionally a √2 can be spotted when talking about a rectangle (Scholfield, p. 51). Vitruvius noted the relationships between a human body and basic geometric figures such as a circle and a square. As a result of his research, Vitruvius created his own system of human proportions. He was convinced that in architecture it was a duty to use rules taken from the nature of the human body. In the first chapter of his third book he wrote about proportions and symmetry. Symmetry comes from the proportion called analogy. Proportion is what we call the use of the fixed form in each work, both in the relationship with the other parts and in the whole. No building can have a correct plan without symmetry and good proportions which should be based on a well-built human body. (Vitruvius, p.63) The most basic role in the creation of the architectural composition was left to the module. Thanks to it, the architect was able to create perfect proportions between the different parts of the building. A work created and constructed following those rules had to be a representation of harmony and rhythm. The perfection of the human body is shown by "Vitruvius Man", a work by Leonardo Da Vinci. He was the first artist to be interested in the entire human autopsy. Based on his findings he created a model based on Vitruvius' theories. His work had perfect proportions and symmetry. He found the perfect proportion to draw a human being in both a square and a circle. Creating a harmony between the human body and geometry was something that architecture needed and Da Vinci was the one who made it happen. The diagram has many layers, really many, so if you look closer you can see the geometry. The human body is considered something perfect and a model of the world. The shapes used by Da Vinci also refer to Vitruvius, because the circle and the square were considered perfect shapes. The next layer of meaning in the diagram is architecture, the main principles of form, function and beauty that Leonardo applied to Vitruvius' Man by connecting these three principles, which where previously mistakenly considered separate things. That Man is a universal context. In Luca Pacioli's De Divina Proportione we read: "First of all we will talk about human proportions, because all the measurements with their names come out of the human body and all the different kinds of proportions can be found there". So it is not unusual for people to try to find the same numerical ratios and harmony that could bring beauty to music and architecture. If the limbs of the body are proportional to the width of the face, then their shape will be beautiful even if the limbs alone are not beautiful, because only proportions create beauty. The Florentine sculptor Lorenzo Ghiberti wrote (tatarkiewicz, t.3 p. 73). Research on the topic of architecture shows mathematical connections that are constantly repeating and which cannot have appeared by chance. In the Renaissance it was believed that the most beautiful rectangles were those whose sides have a numerical relationship to music. More popular was the one whose sides are made using the golden ratio. The Pythagorean tradition was able to develop the most detailed and coherent mathematical foundations for musical study, the philosophy being founded on a notion of universal (numerical) harmony. A famous legend tells us about Pythagoras' discovery of the mathematical basis of musical proportions. Therelegend tells of Pythagoras' walk through the city. He was passing a blacksmith's shop when he heard several tones made by the hammers hitting the anvils. It is said that he then thought that the different weight of the hammers was the reason why the pitches were different and led him to experiment with musical ratios. The Pythagoreans discovered that the speed of vibration and the size of the body producing the sound were the factors in music that were governed by numbers. An octave scale could therefore be expressed as variable methods of dividing the single string of this instrument, divisions described in terms of mathematical proportions. Ratios are usually based on geometric sequences. The one who created an architectural system based on ratios such as 2:1 and 3:1, just as Alberti based himself on these ratios in music. He was using the idea given by Plato's Timaeus who said "what is pleasing to the ear should be pleasing to the eye". In music, harmony is conceived and perceived as a pleasant union of different sounds. Alberti refers to the number 1,2,3,4 to establish the harmonic intervals of 2:3 (fifth), 3:4 (fourth), 1:2 (octave) among others (Calter, 2006, p.28) . Harmonic musical intervals could be expressed as pure mathematical ratios and thus could be applied to geometry. The octave falls into the haul tone form of the pitch structure. There is a casual link between physical dimensions and harmonious sounds. The sound of the stretched string divided in half corresponds exactly to the distance of an octave: the ear is able to discern with surprising precision, from its exactness to its deviation. There is a great temptation to link these measures to vision. Alberti's words are strictly proportional to the musical analogy and no one will doubt their quality. Inspired by the mathematical order and beauty found in nature, Alberti establishes rules of distance, size and proportion. Alberti attached the utmost importance to three means and those are arithmetic, geometric and harmonic. Aesthetics and beauty were closely linked in mathematics. Since all sciences and arts were assumed to have moved away from mathematics, musical harmonies were determined by mathematical calculations. Alberti then applied the harmonic proportions used in the music of the time to the design of his buildings, obtaining the right balance and harmony with the environment. Palladio used mathematical tools as devices to aid his designs: concepts such as symmetry and proportion are fundamental to understanding Palladio's architecture. It is generally accepted that the theory and practice of applying musical proportions to architecture during the Renaissance was a way of giving the building cosmic harmony. In addition to using harmonious proportions in design, Paladio also proposed several methods to be used to determine the height of rooms so that they are proportionate to the width and length. The height of rooms with flat ceilings would be equal to their width. The height of square rooms with vaulted ceilings would be one third greater than their width. (Calter, 2006, p.16) In architecture, geometry plays a role in quantitatively controlling the harmony of buildings, so much so that its lack would make the building vague and not clearly defined. Another number-based system is the golden ratio. The Golden Number is very close to the 5:8 ratio which is the one used by Le Corbusier. His theories based on the 11th century mathematician Fibonacci take credit for reducing the Golden Number to rational numbers applicable to architecture. The Modulor is a geometric proportion grid based on the human form (Calter, 2006, p.55). He created an architectural system based on2:1 and 3:1 ratios suggested by Plato's Timaeus in ancient Greece and based on the musical scale. The same from the challenge of placing the human form within three interconnected squares. The challenge came in the placement of the third square. Le Corbusier solved the problem using the relation of φ and the introduction of a right angle. But modular wasn't very successful until now. Stability, harmony and dynamics have become key issues. The problem now was to find some rule that would allow the building to be based on the surface. The idea of ​​the Golden Ratio was born. It's about maintaining the proportions between the sides of a rectangle. The golden ratio was obtained by dividing a line into two parts so that the total length divided by the length of the longer side is equal to the length of the long side divided by the length of the short side. Many buildings have been based on this rule. The adaptation of this rule was adapted to the circular facades of the building. The architecture itself was purely mathematical and precise. It was commonly believed that beauty was somehow linked to numbers (mathematics) – as Plato stated. Architects perceived architecture as mathematics translated into spatial units. A similar idea was developed by the Greeks when they thought that music was geometry translated into sound. For architects, it is assumed that the sense of balance is based on visual appreciation and sight; symmetry is the most obvious known form of that balance (Meiss, 1992, p.66). Symmetry can be identified in geometric figures, in nature among plants and animals, also in the spacing of the body's organs, in construction, in art, in craftsmanship, practically everywhere, because symmetry is a structural necessity of organisms . Using symmetry in architecture, weight can be properly distributed on more solid things with supports. In Greek art each part is a whole in itself, but at the same time it is part of something bigger, it is the rule of multiplicity in unity. This is why even the ruins of ancient Greece seem beautiful to us. The beauty of architecture is measured through balanced proportions, calculated mathematically. (Osinska, p.41) Palladio thought that symmetry was necessary for harmony. In axial symmetry it is common to avoid the center of the building. Until the 18th century this type of symmetry was only used in religious constructions. Later the use of axial symmetry began to become more common in other places such as homes and factories. A symmetry can also be noted in Gothic. The mathematics of Gothic architecture is present in several ways. One of these is one of the many ways to obtain the effect desired by the architect, other times it can be a rule of work and beauty. Mathematics as the first way appears in architecture as any type of calculation that allows the building to be stable and resistant. From a casual person's point of view, these calculations are not important at all. They belong to the technical aspect of the object, which the author cares a lot about. What matters to the audience is how it looks in the end, no matter how it was made. To meet the aesthetic needs of design, a system of proportions has been implemented and used throughout the history of architecture. The key principles of this system were to ensure that the key relationship was maintained throughout the design, the building had to be able to be easily divided into different parts and it had to be adaptable to the technical means of the architect. Many well-known architects have developed this system throughout the history of architecture and among them are Vitruvius, Alberti and Le Corbusier. Symmetry in Gothic architecture was seen as a good way to resolve projection. It was seen in the prospectuses.