RESEARCH OF GEOMETRY IN THE ARCHITECTURE OF ANTONIO GAUDI
Authors:   Odessa State Academy of Civil Engineering and Architecture, Perperi A.A. , Yavorskaya N.M. ,   Odessa State Academy of Civil Engineering and Architecture, Yavorskyy P.V. ,   Odessa State Academy of Civil Engineering and Architecture
Published: April 2021

Exploring the work of Antonio Gaudi and his knowledge in descriptive geometry, which develops a spatial imagination, we notice the use of lines, shapes, volumetric geometric images in architectural creativity. In his early work, Antonio Gaudi designs buildings under the influence of the Moorish style, using geometric shapes and lines that emphasize Arabic motifs in the patterns. So in the house of Vissenty, made in the style of modernism, he applied the idea of a self-repeating element of a simple form toa more complex one. In a fragment of the gallery of the city park Guell, which is an example of the urban style, Gaudi used the transformation of one surface to another, while showing the smoothness of lines and the accuracy of surface construction and without violating their regularity.Combining various forms in one building or structure, Gaudi perfectly mastered the geometry of the curved lines of the second and third order in space. To achieve a similar effect of shaping, scientists tried in the 60s of the XX century by constructing curved lines and Bezier surfaces. Gaudi achieved a similar effect of shaping in a practical way.n his work, he used cylindrical, conical and spherical surfaces that smoothly passed one into another, as well as the surfaces of Catalan: a hyperbolic paraboloid, conoid, cylindroid. In creating volumetric interior plastic, the curved lines with a kinematic movement created bizarre shapes of the ceiling, smoothly turning into other geometric shapes of the walls.The staircasein one of the towers of the Sagrada Familia is a geometric image of a helicoid, where a complex geometric shape is taken as the generatrix, and the guides are two helises -cylindrical helical lines of different radii.In the geometric construction of a direct or inclined helicoid, it is necessary to have two guides and a movement step, which can be set mathematically. In any case, such a surface remains one of the most unique in nature because the helicoid is a minimal surface.Park Guell is located in Barcelona on the Carmel hill, an area of 17.2 hectares. It was built in the first half of the last century. The customer, who was Eusebi Güell.He huge park complex includes a territory with residential buildings and comfortable relaxation areas, amazing picturesque gardens, quaint shady alleys, multi-tiered terraces, colorful flower arrangements, winding grottoes and gazebos.Working on a park project, Gaudi was inspired by the beauties of the surrounding nature of the Carmel Upland and its picturesque landscapes. In the project, walking paths stretched across the entire park, the mountains were not specially cut from the terrain to emphasize the natural landscape of nature.Necessary for the construction of the elements of the park: poles and beams, were decorated under palm trees. Despite the fact that the height difference was 60 meters, the master skillfully beat the landscape with bizarre forms, emphasizing the desire of a person from simple to sublime.If you delve into history, you can see that the construction work is divided into three stages: the strengthening of hills and slopes with the arrangement of terraces for curved paths and the erection of walls; the construction of a colonnade, a market and mansions; building a bench in the shape of a snake. To date, all the facilities of the complex have been preserved in their original form. At the entrance to the park there are two houses resembling fabulous gingerbread houses, the walls of which arelined with ceramic fragments. The facade of eachhouse is decorated with a medallion with the inscription “Park Guell”. In Gaudi’s work, the “hundred columns” hall, which is inscribed in the landscape of the hill, is a terrace with 86 columns of 6 meters each. These columns support a ceiling with a bizarre shape of complex geometric surfaces of revolution. The plastic of the ceiling vault is made of modern concrete of the time, the decoration of which is made of ceramic in the form of a mosaic. In practical work, Antonio Gaudi took a self-repeating algorithm that developed in space in the form necessary for his design. Gaudi perfectly mastered the skills and knowledge of the discipline called Descriptive Geometry. Developing the spatial imagination, this discipline offers us all kinds of lines, geometric shapes and three-dimensional bodies, for the embodiment of the ideas of masters of architecture, one of which is Antonio Gaudi.