The Pyramid of the Sun in today’s Mexico City, built by the pre-Aztec Teotihuacános around 150 CE, was then home to lavish spiritual and ritualistic ceremonies and pageants. Like the ancient Egyptian burial tombs and royal complexes, the Mesoamerican temple was fashioned in the form of a pyramid, but with an additional small structure at the top.

The ancient Egyptians who constructed the astonishing Giza pyramids as divine burial chambers in 2,700 BCE and the pre-Aztec South American peoples are temporally apart over two millennia. However, their comprehension of stable geometric forms is clearly visible in these material legacies.

The Pre-Aztec natives must have carried 2.5 million tons worth of stone and rubble to create an East-West aligned structure without the use of wheels. The location also corresponds precisely with the position of the Pleiades constellation in the night sky. A mathematically accurate understanding of building massive forms is visible here, as applied geometry has been used for maximum functional output. At the same, that geometrical precision also symbolically represents divinity and beauty in numerous architectural structures throughout the world.

Since the dawn of the third 3rd century BCE, distinct versions of Buddhist temples sprung up in India and later in East Asia. The Great Stupa at Sanchi, India, was constructed during the reign of the influential Ashoka of the Mauryan dynasty, who exercised significant political influence over his people through the commissioning of Buddhist stupas and pillars.

Geometrical precision in architectural constructions through the history of world cultures is more than just pleasing to the eyes. It often represented spirituality and harmony

The Sanchi Stupa is a simple hemispherical structure that contains various relics associated with the enlightened Buddha. The spherical structure of the Stupa is simple yet quite effective, as the form allows for multiple rounds of chanting while circumambulating by Buddhist devotees. The stupa is visually balanced by four vertical pillars or toranas that contain extensive carving, depicting scenes from the life and wisdoms of the Buddha. The four toranas also symbolise earth, fire, air, and the sky.

The ancient Greeks prioritised principles of symmetry, beauty and balance and their avid interest in mathematically harmonious spaces that are fit for worship is fully embodied in their temples. The Parthenon in Athens from 432 BCE is built sculpturally — the outer columns are thicker and situated closer to neighbouring columns to compensate for the sunlight behind them that would make them appear thinner.

The Doric columns themselves are thicker in the middle and work like an illusion to visually unify the endeavour. The architects of the Parthenon used geometric forms to their advantage while creating a space that is eloquent and fit for rigorous worship and for offerings to their gods and goddesses.

Spherical domes with windows were perfected by the Europeans, as seen in the Pantheon in Rome completed in 126 CE. Dedicated to the Roman gods, the magnificent concrete dome with an oculus at the top was a symbol of divine presence that poured from the skies above.

The methods of building domes were lost in mediaeval times. However, this valuable knowledge was rediscovered and improved upon during the Renaissance in Europe in the 15th century, where the clergy and ruling monarchies spent enormous sums of money to build beautiful places of worship that advanced their political regimes as well.

Islamic places of worship have achieved this epitome of geometric sophistication. Aesthetically appealing and majestically sized domes in various mosques throughout the world, built under Islamicate cultures, allow a plethora of lighting to wash through the interiors, infusing the spaces with mystical energy, sound and glow. Geometric structures and proportional patterns have been linked to an intelligent and spiritual way of understanding the cosmos in Islamic mysticism.

The Dome of the Rock in Jerusalem (Umayyads, 692), The Blue Mosque in Turkey (Ottoman, 1616) and the Badshahi Mosque (Mughal, 1673) helped advance the political might and military power of the ruling governments while also presenting some of the most beautiful and geometrically pleasing structures.

In numerous buildings throughout the world, including the very tall mediaeval Gothic cathedrals, mid-centuries Renaissance churches and Hindu rock-cut temples, geometry has been held sacred and mystical. The patrons of these buildings have held common goals: to use mathematical proportions to visually elevate tangible structures toward perfection, timelessness and divine appeal.

Published in Dawn, EOS, June 5th, 2022