Application of Mathematics in Architecture: a Research

In this 'Mathematics in Architecture' essay, the researcher delves into the question if it is possible for architecture to stand alone without the help of mathematics? This research paper will also determine how Mathematics is related in Architecture. The subject areas of this term paper are the following:

• The concept of Architecture;
• The concept of Mathematics;
• The concept of Mathematics in relation to Architecture.

The researcher came up with the idea of having this topic as a research paper in order to help the readers know more about the importance of mathematics in everything that people see; specifically, its importance in the field of Architecture.

One of the purposes of this research is to identify if whether Architecture can still be possible without Mathematics. Another purpose is, if not possible, this research should be able to identify how important Mathematics is in the field of Architecture. The statement of purpose of this study will be later on discussed in the Literature and Factual Review.

Literature and Factual Review

Ziegler has stated in a book entitled An Invitation to Mathematics, in one of his chapters, the preface, in which he used Wikipedia as an example; in which it was stated in there that “Mathematics is the study of quantity, structure, space and change.” He then defined Mathematics as something that could not be defined by a single answer, for he said that, “Mathematics in the 21st century is a huge body of knowledge and a very diverse area of study,” indeed.

According to Bianco, overtime, the definition of architecture has changed. As a result of Bianco’s study in 2017, Architecture was then defined for the Academics as a functional space fit for human needs developed through dialogue between human activities and the environment.

Salvadori then stated that, “I must agree with you that the relationships between Mathematics and architecture are so many and so important that, if mathematics had not been invented, architects would have had to invent it themselves.” Based on a lot of articles, it has also shown that Geometry is the most involved branch of Mathematics in Architecture. Choudhary, et. al., stated that even from years ago, Geometry was present in Architecture. He stated that, “The whole architecture of that time was based on “occult geometry system,” for geometry involves space and shapes, which are needed in complying with spatial needs. He described the “occult geometry system” as a system that involves measurements, dimensions, and proportions. That is the reason why the Greeks were able to come up with columns, and with through proportion and visual effects, according to the dimensions of the columns, the main concept of the building was achieved.

O'Connor, J. J., & Robertson, E. F., stated in their published article on the web, entitle Mathematics and Architecture that, “The first definite mathematical influence on architecture we mention is that Pythagoras.” Stating also that, what Pythagoras has said about “all things are number,” it was indeed true, as it has a significance for architecture. For Pythagoras, number had to do something about geometrical properties, as well, and besides this, the Pythagoreans were able to develop a notion of aesthetics based on proportion. As an additional statement from O’Connor and Robertson, geometrical regularity expressed beauty and harmony and this was applied to architecture with the use of symmetry, as they took the Parthenon as an example of symmetry and proportion. More theories and Principles were later on discovered, for a lot of well-known mathematicians were able to contribute to architecture from the time of Brunelleschi.

Discussion

In correlation to how Ziegler used Wikipedia’s definition, in which it was stated that Mathematics is the study of structure, is there a possibility that Architecture can stand alone without Mathematics? Salvadori answered this with a statement similar to this that without mathematics being invented, or without its existence, architecture will not exist as well.

The argument of Salvadori was backed up by O’Connor and Robertson, as they were able to determine how the concept of architecture came from mathematics. They used examples in their article, such as the Parthenon, in which its lengths correlate to the mathematical principles of proportions of the Pythagoreans. Basically, it is saying that Pythagoras was the first to discover about Mathematics, and until now, even though it was far beyond time that he discovered or came up with theories and principles, it is still applicable until now.

Mathematics is essential in architecture, especially which the main principles of architectural design are made up of scale, proportion, balance, emphasis, unity, rhythm, harmony, and contrast. All of these are in need of mathematics.

Conclusions

Based on the supporting articles, that have been used as evidence as well, without Mathematics, Architecture would not be possible. To put it to something that can be comprehended more, architecture without mathematics is impossible.

Architecture may be composed of drawings and aesthetics, but it is not possible to come up with drawing or sketches, without proper measurements, even though measurements are not shown in a drawing, it still not possible for someone to come up with a drawing of a structure that is not balanced nor proportion, as one will not be able to put this into life nor reality without Mathematics. Even on scale models, this is not possible. One will not be able to test a scale model’s structure’s stability and endurance, without measuring nor calculating how it will be balanced and proportion.

Architecture doesn’t just deal with the factor of art and beauty, but it also deals with the structure and stability. Without Mathematics in Architecture, would you imagine a world filled with buildings, skyscrapers, houses, infrastructures, in which every time that you pass by these structures, you would feel like they will fall on you, because it is not stable? Without Mathematics being applied on Architecture, how will one be able to calculate how strong the foundation of the structure is? How will one be able to determine how long will the building stand? That is why Salvadori’s statement is highly agreeable, because without Mathematics, how can Architecture exist?

References:

• Ziegler, G. M. (2011). Preface: What is Mathematics? An Invitation to Mathematics. Retrieved February 27, 2019, from https://www.springer.com/gp/book/9783642195327
• Salvadori, M. (2015). Can There Be Any Relationships Between Mathematics and Architecture? Architecture and Mathematics from Antiquity to the Future, 28-28. Retrieved February 27, 2019, from https://www.springer.com/gp/book/9783319001364
• Bianco. (2017). DEFINING ARCHITECTURE: A QUALITATIVE RESEARCH. UACG, 51(1). Retrieved February 27, 2019, from https://uacg.bg/UserFiles/File/UACEG_Annual/2018/Брой 1/7(1).pdf.
• Choudhary, A., Maheshwari, S., & Dogne, N. (2014). Mathematics and Architecture: Importance of Geometry (Vol. 1). Gwalio, India: NCAMAET-2014.
• O'Connor, J. J., & Robertson, E. F. (2002, February). Mathematics and Architecture. Retrieved February 28, 2019, from http://www-history.mcs.st-and.ac.uk/HistTopics/Architecture.html