Geometry, together with music, arithmetic and astronomy, constituted the Quadrivium, the four quantitative areas of learning in the ancient Greek world and supported in the Middle Ages as essential for the education of all human beings. Although the educated person would usually have mastered a musical instrument, it was the mathematical and proportional aspect of music that was deemed most relevant. It could be said that the importance of proportions and geometry in architecture and life is a phenomenon that can be seen in nature and also applied to a number of disciplines. Say no to plagiarism. Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an original essay The ancient Greeks were one of the first to apply these concepts, the design of Greek temples was based on strict rules of proportion that governed all parts of the structure. Roman architecture also shared many simple features with Greek architecture, including the portico, use of orders and stepped podium, however it tended to be more ornate and elaborate overall. The main ambition behind the ancient Greeks' use of orders was to discover eternally valid rules of form and proportion, to erect buildings that were human in scale and yet suited to the divinity of their gods, and ultimately to create an architecture classically ideal. Doric temples were a primarily artificial construction rather than a form based on functionality. They were a luminous presence of right angles and sharp geometries. They stood out in the landscape and were monuments of vital abstraction. Orders in Architecture are a specific set of parts subject to already established uniform proportions. Over time, during the Ancient Greek period, the orders underwent major adjustments and changes, as well as which ones were more fashionable or out of fashion. The Hellenistic temple of Apollo in Didyma is a place where there were great changes, especially with the Ionic order which had already developed a lot in the 3rd and 4th centuries. A rejuvenation of the proportions made the Ionic column taller, more slender and the spans wider, influenced by the architects Hermogenes of Albanda and Pythios of Priene. At Didyma the external columns which have a height of 20 meters, being almost 10 times their lower diameter, are the tallest and thinnest of any Greek temple. However, it was the decorative possibilities that made the Ionic order so popular, not its proportions. The more rigid and fixed Doric order was less adaptable, meaning it eventually lost its popularity after its proportions were reduced, in an attempt to make it more modernised. The contrast between the natural and the designed is at the heart of Greek religious architecture. It heralds both the separation of human achievement from the dark forces of the earth and the fulfillment of these divinely controlled forces through the act of building. One of the first mathematical teachings in the form of movement was Pythagoreanism during the 6th century BC, for the Pythagorean number. not only was it the first principle of heaven but also showed its power. Throughout the Egyptian and Greek geometric methods of composition there was the idea that there was a divine relationship between numbers and the human form. The Tetraktys was a triangular figure used as a geometric representation of the fourth triangular number. It was very important to Pythagoreanism and influential on planetary motions. The Pythagorean theorem states that in a right triangle the sum of the squares of two sides is equal to the square of the hypotenuse. When an architect designs a square building or structure, he can divide the square into two triangles and if he knows the length of 2 sides, the third side can beeasily calculated. Using the Pythagorean theorem can make an architect's life easier in determining unknown lengths and shows how mathematics and geometry work important in the world of designIn terms of individuals Vitruvius is the man most commonly known for his discussions of perfect proportions in architecture and in the human body. He stated that 3 conditions of a good building are its usefulness, strength and beauty. Proportion plays a role in all 3 as it provides guidelines for arranging useful spaces, designing structural systems, and creating an aesthetically pleasing environment. Through this we can learn how the appearance of relationships and distances in space creates the basis for all structures. The proportions of a space can radically change how people feel inside it, and the proportions of a facade design can influence whether a building appears welcoming, impressive, or simply neither. The golden ratio was used in ancient Greek architecture to determine aesthetically pleasing ratios between a building's width and its height in terms of dimensions. This would also include things like the size of the porch and even the location of the columns supporting the main structure. The end result is a building that appears completely proportionate. The Second Temple of Hera in Paestum, Italy, is a good example of how the golden ratio is applied. One person famous for focusing his design philosophy on systems of harmony and proportion as well as the golden ratio was the Swiss architect Le Corbusier. His belief in the mathematical order of the universe was closely linked to the Fibonacci series and the golden ratio. He described them as "rhythms evident to the eye and clear in their relations to each other." And these rhythms are at the very root of human activities. They resonate in man with an organic inevitability, the same fine inevitability that causes children, old people, savages and scholars to trace the golden section. “The golden ratio was specifically used in his system for scaling architectural proportions. The system was seen as a continuation of the principles of Vitruvius, the work of Leon Battista Alberti, and many others who used the proportions of the human body to enhance the appearance and function of architecture. He took the concept of the golden ratio in human proportions to the extreme by sectioning the height of his model's human body into several sections divided along many parts of the body. According to these principles buildings should scale down to a size that humans can relate to in order for it to be more appreciated, this theory that we can relate to things close at hand is mostly true as distant things usually seem to us less important. It also provides insight into our relationship with each other, and the scaled universe can greatly change the way we perceive things. It was believed that all buildings should be developed from a standard module, meaning that the dimensions should be proportional to said pre-established module, this rigid structure would allow almost all buildings to have a sense of uniformity and would make the Dimension determination much easier for architects. For some this may be a limiting factor in terms of design restriction, however it is widely accepted that proportions are needed in buildings for them to look good. In 15th century Florence, during the Italian Renaissance period, a change in attitude saw people become more open to new ideas. The current work had a relationship with forms and rulesof antiquity enough to be reused and reinvented when necessary. Mathematical perspective was at a point where it was needed as a way of representing things in space with visual precision and therefore allowed for an ideal level of proportion that generates beauty. In that period Italy had a strong influence on the rest of Europe. The fundamental principles of the Renaissance were symmetry, proportional relationships, the balance of parts, all these things were the basis of construction and contributed to the innate quality of architecture, this was what Alberti knew as “beauty”. Beauty and ornament are seen as the two main elements that determine aesthetic pleasure, the first being natural since it resides in the proportions due to "the harmony and concord of all the parts in such a way that nothing can be added or taken away or altered except for the worst." The renewal of the arts saw a boom in Italian architects and designers who referenced texts, inscriptions and works of art from ancient Rome and Greece. During this period he was aided by a form of mathematical humanism. An increase in research into optics and geometry made linear perspective the main inspiring force in that period. Brunelleschi's use of these studies led to the replacement of Gothic design, which at the time functioned according to an abstract system of proportions. They were only loosely applied, the individual elements of the building had no fixed relationships within themselves or to the overall measurements. Furthermore, many details were improvised or modified on site during the construction process. These Gothic habits were eventually abandoned. Raffaello Bramante and Leonardo da Vinci continued the work of Alberti and Brunelleschi and aimed to stabilize their research by moving towards an abstract ideal perfection. They preferred centrally composed buildings, uniform squares, city forms of immaculate geometry, and rigorously balanced facades on both sides. This shows how proportion and geometry have remained an essential staple in most periods of architectural design, but their importance and use have always changed slightly depending on the values ​​or styles that were most influential in that moment. refinement of our proportions, by musicians who are the greatest masters of this kind of numbers, and by those things in which nature shows itself most excellent and complete” – Leon Battista AlbertiGeometry and beauty in nature can be seen as subjective or in the eyes of the observer, but behind it there are also scientific principles in the form of proportions that can allude to the conclusion that nature is science. The ancient Greeks developed astronomy as a branch of mathematics to a highly sophisticated level, the first three-dimensional geometric models were created to explain the apparent motion of the planets. However, during the 17th century, significant changes occurred in the fields of cosmology and astronomy. John Kepler's discovery that planetary orbits were elliptical and not circular revolutionized the astronomy of the time. Celestial physics connecting forms to God showed how significant geometry was in terms of creating and understanding the universe. Kepler very often emphasized his philosophical approach to the questions he faced. Expressing the concept that God manifests himself not only through the Scriptures but also in the arrangement of the universe and its conformity to our human intellect. Therefore, for Kepler, astronomy represents, if practiced philosophically and correctly, the best path to God. Kepler re-established traditional ideas on creation, giving ancient beliefs a more systematic andquantity responsible for creation. The idea of ​​the Trinity can also be represented geometrically, using the center for the Father, the spherical surface for the Son and the intermediate space for the Holy Spirit. In Kepler's model we are able to reduce all appearances to the straightness and curvature that form the foundation of the geometric structure of the world's vast creations. The first system through which God imagined himself in his creations is quantity. In what quantity was it also introduced to us intellectually in order that this fundamental symmetry could be understood and known scientifically. Inigo Jones, who was an architect during the Stuart and Baroque periods, introduced a style of design based not only on geometry and forms, but also on the theories behind architecture that were fundamental throughout ancient times. He was the first major English architect to showcase Vitruvius' rules of proportion and symmetry in his buildings, as well as introducing Italian Renaissance architecture to Britain. This influence, together with Palladianism, created uniform and well-proportioned buildings. Villa Farnese in Caprarola was a massive Renaissance and Mannerist construction that was one of the finest pieces of architecture of that period. Ornamental decoration was rarely used on the building to achieve proportions and harmony that make it aesthetically pleasing. Therefore, even if the villa dominates its surroundings, its extreme design still integrates with the site. The Mannerist style used in that period was developed as a reaction to the earlier ornate High Renaissance designs of 20 years earlier. Plans were conceived for a pentagon built around a collimated circular courtyard. Another fine example of architecture from that period was the Dome of San Carlo, in Rome, by Francesco Borromini. It has a circular shape with a center of light that opens up to represent God and the distortion applied makes it appear larger and taller than it actually is. The Jones-inspired Chiswick house takes up the Palladian/Italian idea of ​​sequencing rooms where different geometrically shaped rooms are all linked together to provide a range of experiences from different perspectives. Palladian windows were a key feature of the design style and easily recognisable. They were a large three-section window where the central section is arched and larger than the two side sections. This symmetry within them is what makes them distinct and adds more order within the buildings themselves. The Venetian Carlo Lodoli (1690-1761) was an advocate of a radical approach to the way architecture had preceded, his extreme position being that architecture should be thought of as a science and not as a field of artistic imagination governed by beauty rules. He did not agree with the fixed proportions of the orders. Design depended not on ideal models but on (1) function, by which he understood how a building's structure behaves in accordance with the building's use, and (2) representation, "the individual and total expression which results from the idea of ​​the way in which the material is arranged according to geometric-arithmetic-optical rules to achieve the intended purpose”. The ornament could be added once the main functional requirements had been satisfied, but for Lodoli the ornament was not just a decorative cladding: was to be based on scientific laws governing essential building materials Laugier, however, on a similar note did not rule out orders entirely but urged that they behave as functioning parts and not applied as decoration and the decoration of buildings such as columns, pediments and entablatures must,.