The contribution of mathematics in art and architecture
- 1. 1 | P a g e ‘The Contribution of Mathematics in Art and Architecture’ Name of the Student Name of the University Introduction The tools of mathematics at the maximum applied part has continuously been utilized in an important manner in the formation of art and architecture. The straightedge and the lowly compass since the ancient times augmented by other craftsmen’s tools and simple draftsmen’s tools have been put into use for the creation of attractive projects comprehended in the beautification of cathedrals, fortresses and mosques and also in architecture (Gomez 1983). A testament to the imaginative use of ancient geometric knowledge is the intricate Moorish tessellations in crick, tile and stucco which decorate their structures and also the complex tracery of Gothic interiors and windows. As per the principals of linear perspective, several artists during the Renaissance utilize simple mathematically-based devices and grids so as to portray accurately the scenes in a flat surface. A glimpse of these techniques could be seen in several of the engravings of Durer. During these times, the symbiosis of mathematics and arts developed as the projective geometry and linear perspective and developed as one of the most crucial instance of the mathematics and arts which involved majorly at the same in the fresh directions. Mathematics and Art With digital technology fast becoming a primary choice, present tools of mathematics are more refined. Computers could form art in the hands of an artiste powered by the unseen complex internal process of mathematics which renders their magical capabilities. The means by which a form or image in one space or surface is presented in another is rendered by the mathematical transformations. Transformations are crucial in creation of an illusion as art is regarded as an illusion. Similarities, isometries and affine transformations could transform images with purposeful changes or exactly, it is possible to present 3-D forms on 2-D picture surface with the help of projections. An anamorphic art could be produced with the help of special transformation which could unscramble or distort image. Mathematically, all these
- 2. 2 | P a g e transformation could be explained and it is by computer software that the usage of guiding grids to help in the performance of the transformations has been substituted (Gomez 1983). For the creation of art; rulers, compasses, mechanical devices, grids, keyboard and mouse are physical tools. However, these tools would have little creative power without the power of mathematical processes and relationships. Mathematics generates art In both arts and mathematics, pattern is a chief concept. Artistic patterns could be generated with the help of mathematical pattern. In most of the cases, automatic art could be produced by coloring algorithm which might be aesthetically pleasing or surprising as compared to the ones generated by human hand. The fundamental concepts in both art and mathematics is symmetry and transformations. By means of invariance under a group of transformations, mathematicians define symmetry of objects (matrices, functions, forms or designs in space or on surfaces). The application of a group of transformation on the other hand to spatial objects and simple designs automatically generate beautifully symmetric forms and patterns. Mathematics inspires art To hold the attention of the art viewer; designs, patterns and forms which are the automatic result of the purely mathematical procedure are generally too mechanical, too symmetrical, too precise or too repetitive. They could be fun to create and could be interesting and pleasing, however it lacks spontaneity, subtlety and deviation from the precision which creativity and artistic intuition render (Walton 1994). Mathematically-produced art in the hands of an artiste is only a commencement, a template or a skeleton to which the artists carries training, resourcefulness and individual view which could change the mathematically perfect into a form or an image which is truly inspired. MATHEMATICS AND ARCHITECTURE The golden rectangle in the Greek architecture served as a standard for planning all the architectural designs. It is to at least 300BC that the knowledge of the golden mean goes back, the time when Euclid explained the method of the geometric construction. The golden rectangle is considered pleasing in Western architectural theory which are in the ration of 1:1.618. Symmetry as a guiding principle was used in the Renaissance architecture (Emmer 1982). A
- 3. 3 | P a g e good example is served by the works of Andrea Palladio. Curved and dramatically twisted shaped were used by the Baroque or the later High Renaissance in various contexts like columns, rooms, squares and staircases. In the past, architecture has been a part of mathematics and the two disciplines in many period of the past were vague. Mathematicians were architects in the olden world whose buildings like ziggurats, pyramids, stadia, temples and projects of irrigation are applauded in the present times. The Byzantine emperor Justinian turned to 2 instructors of arithmetic or geometers named Anthemios and Isidoros when he needed an architect so as to build the Hagia Sophia as a structure which outdid the whole lot that was constructed ever before. In the Islamic civilization the tradition continued. Before the western statisticians provided a comprehensive arrangement, the architects of Islam produced a wealth of 2-D tiling arrangements. A strong grasp of geometry is seen in the medieval masons, wherein according to the mathematical principles allowed them to build the huge churches. Dismissing the middle age without mathematics is not entirely fair: instead of being written down, their math is constructed into buildings. During these centuries the unfortunate loss of knowledge was most forcefully not escorted by a proportionate damage of architectural or visual designs. This was because of the fact that patterns reflected procedure which were inherent in the mind of an individual as compared to the theoretical presentation of a printed writing. It is regarded quite useful to differentiate amongst perceivable designs on building walls, frontages and concretes and abstract patterns on a plan. Since the former are and experienced and seen instantaneously, they are the only ones to impact the human beings directly. Although the construction of the building is really an open plaza, the symmetries on the building’s plan are not observable continuously. This is because of the fact that the position, perspective and the size of an individual. The pattern in a usual enclosed building of its strategy is majorly concealed from vision by means of the constructed assembly. Visual patterns, if they are accessible immediately have strongest cognitive and emotional impact. With architectural qualities, proportional ratios might be included which are regarded only in indirect manner. Throughout all of architecture the presence of the Golden ratios (5:3, 8:5) and Golden mean (f= 1.618) and the square root of two proportion could be found.
- 4. 4 | P a g e Moreover, a rich field of study is rendered by this topic. Nonetheless, the effects remains an aesthetic one as no particular mathematical data is provided to the handlers of a façade or a room taking the required inclusive magnitudes (Walton 1994). The fact is that in order to define the coincident scales the proportionate ratios frequently also segments forms and this tend to have a very firm positive impact. Conclusion On the basis of the above discussion we could come to a conclusion that the presence of mathematics has been seen in both art and architecture. The presence has been seen from the medieval period to the current period in all forms of art and architecture. It is believed by many that this presence would continue to be seen in various different forms as mathematics is regarded as an integral part of the overall society. Mathematical proportion and symmetry were deliberately emphasized during the Renaissance architecture. Styles such as the Deconstructivism and modern architecture were seen in the 20th century which explored various geometries to get the desired impacts. References Emmer, M. (1982). ‘Art and Mathematics: The Platonic Solids.’ Leonardo, Vol. 15 N0. 4, pp. 277 – 282. Gomez, A.P. (1983). ‘Architecture and the Crisis of Modern Science’, Cambridge, Massachusetts: MIT Press, pp. 18-39. Walton, K.D. (1994). ‘Albrecht Durer's Renaissance Connections Between Mathematics and Art.’ The Mathematics Teacher, pp. 278-282.