One of the possible applications is treated here: https://www.researchgate.net/publication/297167812_Mathematics_and_Architecture_Importance_of_Geometry.
According to Wikipedia, architects use mathematics for several reasons, leaving aside the necessary use of mathematics in the engineering of buildings. Firstly, they use geometry because it defines the spatial form of a building. Secondly, they use mathematics to design forms that are considered beautiful or harmonious. Thirdly, they may use mathematical objects such as tessellations to decorate buildings. Fourthly, they may use mathematics in the form of computer modeling to meet environmental goals, such as to minimize whirling air currents at the base of tall buildings.
Intentionally or unintentionally, architects, builders and other construction experts have been using mathematics and geometry since ancient times as the most basic but nevertheless rather valuable tool in almost all stages of architectural and construction projects. History remembers great builders and architects who were also great mathematicians, and vice versa (Vitruvius, Leonardo Da Vinci,...). Mathematics and architecture have always been close, most of all because of their common aspiration for order and beauty.
Apart from the basics of geometry, trigonometry, some calculus , algebra, and polynomials to solve design, quantities, units of measurement, structural stress problems etc (list is not exhaustive and architects will go to engineers for higher mathematics when needed) , I think the most fascinating mathematics that is applied in architecture is symmetry which is exemplified in Herman Weyl's classic book Symmetry. This book contains some principles of typical symmetries such as reflective or rotational symmetries ( a shape maps to itself when transformed). He goes into how symmetry is employed in architecture eg explaining symmetries of polygons and their mathematical features as used in buildings. Of particular interest is tiling and this is especially important in designing the large office blocks or residential towers or other large public buildings. An unusual (but more mathematical) example of tiling used in architecture has been the use of Prof. Sir Roger Penrose's 'kite and dart' tiling around the courtyard of the Andrew Wiles building - the home of the Oxford Mathematical Institute - also called Penrose paving - an example of aperiodic tiling.
Application of mathematics in architecture is similar to application of chemistry in medicine...
See, e.g., nice applications
(1)IKM94—International conference on the application of computer science and mathematics in architecture and civil engineering: Weimar, Germany, March 16–18, 1994
Journal:Automation in Construction
(2)AIP Conference Proceedings [AIP Publishing LLC APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE'14) - Sozopol, Bulgaria (8–13 June 2014)] - Implementing the finite element analysis with service-oriented architectures and workflows
Mladenov, NikolayYear:2014
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