The importance of mathematics in aesthetics in architecture

In the ancient Greek, Byzantine, Egyptian, Islamic and Roman societies, mathematicians were architects and architects were mathematical, many of them participated in the construction of large stadium structures, pyramids, temples, irrigation channels and zigurats,

Without mathematics at any historical era, structures would lack the architectural aesthetics or beauty depends largely on mathematics. Architects like Louis Sullivan added ornamental designs to buildings to enhance their beauty. Such designs used symmetry, geometric shapes, fractal and other tapestry patterns that derive from mathematics.

Mathematics can be found in decorative elements, it is enough to place us in front of one of them and contemplate it carefully that the order that is reflected in its architectural image is intimately related to the insertion in the same of geometric figures, and with the existence of relationships between the elements of these.

For a building to have resistance and stability, you must have precise angles, correct lengths of its walls and appropriate measurements for the roof.

Architectural aesthetics or beauty depend largely on mathematics and thanks to this the architect has more freedom of design

It has many practical applications in architecture, geometry is completely essential for architectural design, geometry has important applications for many disciplines and is used to calculate distance, angles and space

In ancient Egypt, ancient Greece, India and the Islamic world, buildings were built that included pyramids, temples, mosques, palaces and mausoleums with specific proportions for religious reasons. In Islamic architecture, geometric shapes and mosaic geometric patterns are used to decorate buildings, both inside and outside.

Some Hindu temples have a structure similar to a fractal where the parts resemble the whole, transmitting a message on infinity in Hindu cosmology. In Chinese architecture, the Tulou in the province of Fujian are circular community defensive structures. In the 21st century, mathematical ornamentation is being used again to cover public buildings.

Architecture is a profession related to the practical issue of building buildings, while mathematics are purely study of the number and other abstract objects

They argue that architects have avoided looking at mathematics in search of inspiration in revival times. This would explain why in revival periods, such as Gothic Renaissance in the 19th century in England, architecture had little connection with mathematics. Similarly, they point out that in times of reaction such as Italian Mannerism of around 1520 to 1580, or the Baroque and Palladian movements of the seventeenth century, mathematics were barely consulted.

On the contrary, the revolutionary movements of the early twentieth century, such as futurism and constructivism, actively rejected the old ideas, adopted mathematics and led to modernist architecture. Towards the end of the 20th century, the architects also quickly took advantage of fractal geometry, as well as the aperioic mosaic, to provide interesting and attractive coatings for buildings.

Architects use mathematics for several reasons, leaving aside the necessary use of mathematics in buildings engineering.

- First, they use geometry because it defines the spatial shape of a building.
- Second, they use mathematics to design forms that are considered beautiful or harmonious. Since the time of the Pythagoreans with their religious philosophy of the numbers, the architects of ancient Greece, the ancient Rome, the Islamic world and the Italian rebirth have chosen the proportions of the built environment: buildings and their designed environment, according to the mathematics and aesthetics and sometimes religious principles.
- Third, they can use mathematical objects such as tesels to decorate buildings.
- Fourth, they can use mathematics in the form of computer models to meet environmental objectives, such as to minimize rotating air currents at the base of high buildings.

They can be used as categories to classify the ways in which mathematics are used in architecture. Firmness covers the use of mathematics to guarantee the construction of a building, hence the mathematical tools used in the design and to support construction, for example to guarantee the stability and performance of the model, resulting from the incorporation of relationships Mathematics in the building; includes aesthetic, sensual and intellectual qualities.

Refers to the application of the concept of minimal surfaces to sculpture design; the second, to the application of the concept of tessellation to hyperbolic spaces, and ultimately, fractal art and coloring algorithms.

The architects Michael Ostwald and Kim Williams, considering the relationships between architecture and mathematics, observe that the fields, as they are commonly understood, seem to be weakly connected, since architecture is a profession related to the practical issue of building buildings , while mathematics are purely study of the number and other abstract objects. But, they argue, the two are strongly connected, and they have been since ancient times. In ancient Rome, Vitruvio described an architect as a man who knew enough about a range of other disciplines, mainly geometry, which allowed him to supervise expert artisans in all other necessary areas, such as masons and carpenters. The same was applied in the Middle Ages, where graduates learned arithmetic, geometry and aesthetics along with the basic grammar, logic and rhetorical program (the trivium) in elegant rooms made by teachers builders who had guided many artisans. A master of works at the top of his profession received the title of architect or engineer. In the Renaissance, the quadrivium of arithmetic, geometry, music and astronomy became an extra expected program of the Renaissance man, such as Leon Battista Alberti. Similarly in England, Sir Christopher Wren, known today as an architect, was first a notable astronomer.

The influential old Roman architect Vitruvio argued that the design of a building as a temple depends on two qualities, proportion and symmetry. The proportion ensures that each part of a building is harmoniously related to any other part. The use of symmetria in vitruvius means somewhat closer to the English term modularity than specular symmetry, since it is again related to the assembly of (modular) parts throughout the building.

In its Basilica of Fano, it uses proportions of small integers, especially triangular numbers (1, 3, 6, 10, …) to divide the structure into modules (vitruvio). Therefore, the width of the basilica is 1: 2; The hall around it is as high as wide, 1: 1; The columns are five feet thick and fifty feet high, 1:10.

One of the surfaces that have been applied most in architecture is the hyperbolic paraboloid. The hyperbolic paraboloid is a specimen already known by the Greeks where the conical curves (the ellipse, the parable and the hyperbole) are for dimension two, in dimension three are the quadric surfaces. The names of these surfaces have to do with the curves that appear as sections with plans. In the hyperbolic paraboloid, one of the quadric surfaces, these sections are parables and hyperbolas.

Mathematics is the basis of architecture. The relationship between mathematics and architecture dates back to the early days of the construction of the man of functional structures. Historically, architecture was part of mathematics, and in many periods of the past, the two disciplines were indistinguishable.

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