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Mathematics has been a fundamental tool in the design process. Right from drawing or making plans, execution till finalization of building projects, architects, builders, and construction experts use it intentionally or unintentionally. If we peek into history, mathematicians were architects and vice-versa. One of the famously known mathematicians, Vitruvius, was also a well-known architect. Pythagoras readings were then used in the building proportions. Leonardo Da Vinci, who worked and used the golden ratio widely, was also an architect. The importance and presence of mathematics in architecture can be seen right from site analysis to the final facade design. The two are inseparable.

Mathematics, though a technical science, is a crucial part of architectural design. One can never realize its enormous extent unless employed and worked upon. It can be beautifully applied both artistically and practically while generating a design proposal. Mathematics has a two-fold function, firstly it serves as the economic factors relevant to the proposed design solution. Through this method, one can decide the budget for the construction and maintenance with the help of floor area, heights, materials, and developments.

The second role, which can be stated as the key segment of the design, includes size, proportions, and area division of the designed spaces are based on mathematical relations.

Mathematics plays an equally vital role, whether the design is a renovation or new construction or an extension to the existing building. Size and scale definitely affect the user’s perspective and can create the atmosphere required. It is maths, which also helps in monitoring the construction maintenance to achieve a cost-effective design, as construction could turn out to be an expensive venture.

Dramatically, it can be stated that mathematics, an essential factor in the architectural design process, remains behind the scene many times. And comes to notice when a piece of bad news or wrong solutions are highlighted when they face some issues. Wise and faithful use of mathematics in the process from the beginning will foster the project for potential success.

Mathematics, as much as is beneficial in ensuring design practicality, also adds an intangible element to the design in the form of beauty. The architectural design provides a basis, and mathematics supplements a design with beauty, life, and imagination. There have been numerous architects and designers who keep this thought close to their hearts. Despite the complexities involved in mathematics, its ultimate intention to create visual simplicity and satisfaction cannot be stressed enough.

Christopher Alexander, a British-American architect and design theorist, firmly believes that mathematical analysis of various architectural details yields an objective interpretation of the beauty of any structure. He states further that the architectural beauty directly correlates to 15 these mathematical properties:

1) Level of scale

2) Strong centers

3) Boundaries

4) Alternating repetition

5) Positive space

6) Good shape

7) Local symmetries

8) Deep interlock and ambiguity

9) Contrast

11) Roughness

12) Echoes

13) The void

14) Simplicity and inner calm

15) Not-separateness

His work, The Nature of Order – a 4-volume work, consolidates his views on how the inclusion of these 15 properties becomes important in adding life to any space. As a result, a structure naturally feels appealing to its audience and makes it easy for them to appreciate it.

Bertrand Russell, an influential personality in the field of mathematics, logic, philosophy, and history, also expresses his take on mathematical beauty. While the design is as subjective as its creator and masses, mathematics holds nothing but the truth when approached rightly. Its ability to convey the supreme beauty, without possessing the innate beauty of any piece of art or musical overture, is just pure. He adds mathematical visualizations hold a hint of happiness, delight, and a feeling of beyond, as powerful as poetry.

In the architectural world, we acknowledge an unsaid pleasure in geometric regularity of shape and form. Our history is evidence of many architectural marvels that strike us with awe. On the one hand, we agree on the importance of mathematics in architecture. Still, on the other, it is crucial to realize that it is not capable of defining architectural beauty ultimately. It is also noteworthy to know the relation of these mathematical expressions in human perception. Alexander believes contemporary architecture sometimes might differ from the 15 traditional building design tools. This says a lot about historic and modern buildings’ architecture. Hence, with the changing times, the use and method of mathematics in architecture may change, but it still holds its position tight.

Tanvi Saraf, an architect who believes that every space has a story, waiting to be narrated. Always looking to make a tiny effort to connect the dots through experiences.