Relationship of Mathematics and Architecture

Architecture and mathematics seem to have few obvious connections, but despite the apparent differences, the distance between the profession of architecture and the discipline of mathematics, and between an object (of design) and a subject (of study) is far less than many would assume.

In ancient Egypt, ancient Greece, India, and the Islamic world, buildings including pyramids, temples, mosques, palaces and mausoleums were laid out with specific proportions for religious reasons. In Islamic architecture, geometric shapes and geometric tiling patterns are used to decorate buildings, both inside and outside. Some Hindu temples have a fractal-like structure where parts resemble the whole, conveying a message about the infinite in Hindu cosmology. In Chinese architecture, the tulou of Fujian province are circular, communal defensive structures. In the twenty-first century, mathematical ornamentation is again being used to cover public buildings.

In Renaissance architecture, symmetry and proportion were deliberately emphasized by architects such as Leon Battista Alberti, Sebastiano Serlio and Andrea Palladio, influenced by Vitruvius's De architectura from ancient Rome and the arithmetic of the Pythagoreans from ancient Greece. At the end of the nineteenth century, Vladimir Shukhov in Russia and Antoni Gaudí in Barcelona pioneered the use of hyperboloid structures; in the Sagrada Família, Gaudí also incorporated hyperbolic paraboloids, tessellations, catenary arches, catenoids, helicoids, and ruled surfaces. In the twentieth century, styles such as modern architecture and Deconstructivism explored different geometries to achieve desired effects. Minimal surfaces have been exploited in tent-like roof coverings as at Denver International Airport, while Richard Buckminster Fuller pioneered the use of the strong thin-shell structures known as geodesic domes.

Math has various roles in architecture.In math, geometry has a crucial part for for designing.Architects uses geometry to define the spatial form of the buildings.The panning of spaces includes many more shapes and combination of the shapes.

From ancient days, the specific  proportions of the buildings were laid on for various purposes.

The possibility of the form and building orientation depends on it.
Trigonometry is one which decides the angle of the building orientation. So that the building could receive more sunlight or wind flow etc.

The aesthetics of the building can also be done with help of math. From ancient days the tessellations are used for aesthetics in buildings.