Mathematics is the abstract science of number, quantity, and space, either as abstract concepts (pure mathematics), or as applied to other disciplines such as physics and engineering (applied mathematics).
• When engineering buildings
Maths describes the shapes of the structures to be built, the physical features to be understood and forms the basis for every step of modeling process
• Geometry: to define the spatial form of a building
Geometry concerns with questions of shape, size, relative position of figures, and the properties of space.
• Aesthetic and religious principles
Vaastu Shastra, the ancient Indian canons of architecture and town planning, employs symmetrical drawings called mandalas. Complex calculations are used to arrive at the dimensions of a building and its components. The designs are intended to integrate architecture with nature, the relative functions of various parts of the structure, and ancient beliefs utilizing geometric patterns (yantra), symmetry and directional alignments.
• To decorate buildings with mathematical objects such as tessellations
o Tesselation: an arrangement of shapes closely fitted together, especially of polygons in a repeated pattern without gaps or overlapping.
o Islamic buildings are often decorated with geometric patterns which typically make use of several mathematical tessellations, formed of ceramic tiles that may themselves be plain or decorated with stripes.
o Symmetries such as stars with six, eight, or multiples of eight points are used in Islamic patterns. Some of these are based on the 'Khatem Sulemani' or Solomon's seal motif, which is an eight-pointed star made of two squares, one rotated 45 degrees from the other on the same centre.
The complex geometry and tilings of the muqarnas vaulting in the Sheikh Lotfollah Mosque, Isfahan, 1603–1619
• To meet environmental goals, such as to minimise wind speeds around the bases of tall buildings
"The Gherkin" for its cucumber-like shape, is a solid of revolution designed using parametric modelling. Its geometry was chosen not purely for aesthetic reasons, but to minimise whirling air currents at its base.
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