Geometry in architecture
Geometry in architecture is like a bridge to the transcendental.
The prevailing view in contemporary architecture argues that a break from Euclidean geometry is necessary to express a new paradigm that reflects the complex, dynamic conditions of the contemporary world. Euclidean geometry, which traditionally connects man and space through simple, fixed relationships, is seen as limiting architectural expression and adaptability in contemporary digital design, which now obeys new geometric forms, such as non-Euclidean curvatures and organic, biomimetic surfaces. In this perspective, space is not static, but a fluid field that is constantly reshaped, with the emphasis on morphogenesis and the process of producing space, rather than adherence to fixed shapes.
However, the traditional geometric principles remain central but also misunderstood for the understanding of architecture as a spiritual and philosophical art. Geometry in architecture is not simply a tool for constructing functional and aesthetically imposing buildings; it embodies, instead, profound philosophical principles that shape the very concept of space. From antiquity to today, geometric relationships and proportions have been imbued with a notion of cosmic order that is not accidental but an expression of the sacred. Under this perspective, which is most often overlooked, architecture takes on a spiritual dimension, embodying a space filled with deep and almost mystical meaning.
Geometric relationships and proportions are not simply technical properties; they are characterized by a proportionality that approaches the limits of the dogmatic. This is demonstrated by their uninterrupted immortality in time. These structures reveal a transcendent world where architecture is based on philosophical and theological foundations. Mathematics functions as a theoretical substance, the most appropriate medium for accessing the invisible world, with architecture implementing these theoretical concepts in the physical environment. The geometric foundation, then, is not only a technical issue; it also ensures the spiritual integrity of the space. The importance of this idea is first revealed in the ancient Greek philosophers, such as Pythagoras and Plato. They were the first to establish the conception of geometry not merely as a means of measurement, but as a path to understanding the harmony of the universe. For the Pythagoreans, mathematics was the language of nature, and numerical relations such as the golden ratio offered aesthetic perfection. The Parthenon, for example, is an indisputable example of applying this harmony, capturing the concept of timeless beauty and spirituality.
The Renaissance reintroduced this philosophical relationship between geometry and architecture, deepening the ideas of the Platonic world of ideas. Leonardo da Vinci and Filippo Brunelleschi were pioneers in the study of proportion and symmetry, applying these principles to give their buildings a sense of divine harmony and spiritual uplift. For example, the mathematical relationships in Bruneleski’s works seek to evoke not only visual pleasure but also spiritual uplift. In religious architecture, the use of geometry symbolizes the connection between man and the divine. The Gothic cathedrals of Europe, with their bold vertical lines and ornate proportions, are designed to direct the gaze to the sky, offering an experience that enhances the religious mood of the believer. However, geometry in architecture transcends the boundaries of Christian tradition. Islamic geometric art, for example, expresses the order of the universe through compositional patterns that reflect the eternal nature of God. Geometry in architecture is not only about aesthetics or structural strength. On the contrary, it is a fundamental element of the human endeavour to express the sacred, providing spaces that inspire a sense of eternal harmony. This philosophical approach shows how architecture can give deeper meaning to the experience of space, enriching it on a secular and spiritual level.
