Geometry Concepts In Architectural Design

The relationship between geometry and architectural design are described and discussed along some examples. Geometry is the fundamental science of forms and their order. Geometric figures, forms and transformations build the material of architectural design. In the history of architecture geometric rules based on the ideas of proportions and symmetries formed fixed tools for architectural design. Proportions were analyzed in nature and found as general aesthetic categories across nature and art. Therefore proportions such as the golden section were seen as the power to create harmony in architecture as well as in art and music. According Pythagoras there were general principles for harmony. They were also applied in architecture and they found a further development especially in the renaissance. Leon Battista Alberti integrated such general harmonic proportion rules in his theory of architecture and realized them in his buildings. To find general principles of harmony in the world were the main research aims of Johannes Kepler in his “Harmonice mundi”. These principles of harmony were based on geometry. Another important branch in the history of architectural design principles was the “golden section” or “divina proportione”. “Modulor” of Le Corbusier is an example of an architectural design and formation concept based on the golden section. The concept of symmetry is combined with the idea of harmony and proportion. Symmetry operations are concerned with motions of figures and shapes. Geometry can be seen also as a structural science. The architectural design is based on geometric structures developed out of the idea of transformations. The symmetry transformations are visible as design concepts through history of architecture. In contemporary architecture there are no fixed rules about design concepts. But there are still relations to geometric space concepts. There is a need of new geometric background for architectural design. Examples of architecture and designing will be presented and discussed in their relationship to geometry. The role of geometry in architectural design processes will be analyzed exemplarily through history of architecture and new fruitful approaches show actual and future perspectives.

The relationship between architectural design and geometry starts with the notion of harmony as the principle for all sciences and creations. The analysis of the antique comprehension of harmony shows the geometrical root and the superior idea of this concept for all sciences and designing disciplines. Today the various sciences and arts are in most cases strongly separated. Therefore there is the risk that the powerful relationship between geometry and architecture gets lost. Steven Holl, who refers in his architectural work to geometry and other sciences, noticed: “For example Johannes Kepler’s Mysterium Cosmographicum united art, science, and cosmology. Today, specialization segregates the fields; yawning gaps prohibit potential cross-fertilization.”.

By remembering the historical relations between geometry and architectural design we help to keep the background of our culture but also to understand the fruitful combination between geometrical thinking and architectural designing. By integrating experiments on using geometric structures for designing in the architecture curriculum we should reflect this relationship and try to develop new impulses for geometrical based designing in architecture. Only few examples were shown here in an overview. There are more efforts necessary in the future to work out this relationship in detail, historical and theoretical, from an architectural and a geometrical point of view as well as to experience and apply it in the practice of architectural design.