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If you think taking up architecture will get you rid of Mathematics, then my friend, you are standing on the wrong side of the fence! While both subjects don’t seem to have the same standards, it is their inspiration from natural concepts bringing them together. However, for an architect, it can be only little to take. In conventional practice, basic math can suffice to execute an architectural project. It only gets complex as one is willing to experiment with the endless possibilities architecture and construction can bring.

Whether its function is to hold, cover or block, any piece of architecture will serve a purpose thanks to the way its parts are carefully calculated and placed

(Raval, 2020)

Mathematics, in literal words, plays its roles in architecture by being the Seen and the Unseen. The Planning and Designing stage is when math contributes directly and where it can be seen visually. The Unseen has to do with the calculation of structures, material usage, costing and wages. The Unseen validates the drawings and helps translate the design to reality. Yet, what is talked about or discussed is the part which is ‘Seen’.

Covering a 2d surface, with polygons or tiles of more than one shape, leaving no gaps on the surface is known as tessellation. Examples like these can be labelled as Seen.

## The Journey so far | Architecture and Construction

According to history, architecture was pursued by mathematicians, which is why their construction, the pyramids, temples, ziggurats and stadiums, stand firm in their statement. The 19th century saw a change of attitude, which led to a separation in people’s minds of the scientific and the artistic. (O’Connor and Robertson, 2002).

In design, aesthetics respond to visual and emotional needs. Design principles like Symmetry, Proportion, Rhythm, Pattern etc., define a design aesthetically and functionally. Each principle relates to a value handled purely by numbers. Symmetry is by division, the proportion is by ratio, and pattern relates to simple and complex formulae. Whereas Geometry, algebra, trigonometry, and calculus help design structural elements. Symmetry comes from the ancient Greek architectural term “symmetria”, which indicates the repetition of shapes and ratios from the minor parts of a building to the whole structure. (O’Connor and Robertson, 2002)

## Architecture, Math & Nature

The application of mathematical concepts can sometimes demand the designers to use them. It is crucial to acknowledge concepts like the Golden Ratio and fractal geometry, among the most common principles known for their occurrence in everyday life, e.g. mountains, waves, DNA, crystals etc.

The below image shows a portion of Lake Nasser in Egypt, one of the largest artificial lakes in the world. These fractals appeared over a period of time as a natural phenomenon. This phenomenon has been adopted in Urban planning and incremental housing. Frank Lloyd’s Palmer house is an example of fractals of triangles applied in residential design. Charles Correa’s Belapur total housing is also inspired by fractal growth.

The overall layout of the settlement is the layout of the individual houses. From the entrance to the rear end of the settlement, the homes increase in their size and maintain the proportion of the house plan. The bigger houses are reserved for families of higher social statuses. (Raval, 2020)

## Construction

There is a lot of everyday practical arithmetic and mathematics in construction, from setting out a building on site to calculating quantities and costs, from determining floor space ratios to ordering materials. Consider the Great Pyramid of Giza, the largest pyramid structure in the world, circa 2550 B.C. The pyramid’s base is a polygon, the triangles being the sides having a shared vertex, forming a polyhedron. The principles of right angle triangles, accurate corners and many more theories prove the construction was purely based on math and geometrical knowledge.

## The New Mathematics of Architecture | Architecture and Construction

The architects of recent years have taken up not only complexity theory but also the underlying principles of complexity and fractal geometry directly in the generation of systems.

Access to electronic computational power, together with accessible graphical interaction with virtual space, has brought mathematical creativity in architecture.

(Burry and Burry, 2012)

The book, The New Mathematics of Architecture, by Jane Burry and Mark Burry, is a compiled explanation of notable projects that represents the use of Math in non-Cartesian form, contrary to the conventional practice. The six chapters discussed in this book give an idea of how architects befriend maths, giving a whole new outlook on construction and structures.

i)Mathematical surfaces and seriality.

ii)Chaos, Complexity and Emergence.

iii)Packing and Tiling.

iv)Optimization.

v)Topology.

vi)Datascapes and Multi-dimensionality.

Let us understand one of the chapters from the above list, Topology. As the word means, the principle has to do with the surfaces; two dimensional manifolds embedded in three dimensions. In simple words, consider the vertical and horizontal surfaces as the same, modified and suited to the function as intended. The Metropolitan Opera House, by Toyo Ito, has continuous surfaces, with fluid-like infinite spaces interrupted by a bounding box.

This complex structure was built onsite using concrete, taking around 2.5 years to complete. Architecture in practical works with numbers, numbers that validate and denote the attainment of a design, be it structural or non-structural. Access to electronic computational power, together with accessible graphical interaction with virtual space, has brought mathematical creativity to architecture. (Burry and Burry, 2012)

References:

• Burry, J. and Burry, M. (2012). The new mathematics of architecture. London: Thames & Hudson.
• Raval, C. (2020). Exploring The Mathematics Behind Architecture. [online] The Architects Diary. Available at: https://thearchitectsdiary.com/exploring-the-mathematics-behind-architecture/
• O’Connor, J.J. and Robertson, E.F. (2002). Mathematics and Architecture. [online] Maths History. Available at: https://mathshistory.st-andrews.ac.uk/HistTopics/Architecture/
•  Eglash, R. (2005). African fractals: modern computing and indigenous design. New Brunswick, N.J.: Rutgers University Press.

Book

• Burry, J. and Burry, M. (2012). The new mathematics of architecture. London: Thames & Hudson.