Topological architecture

Topology [gr. topos - place, logos - study] is a branch of mathematics that determines and studies the fundamental properties of certain types of spaces. Robert ^Bruner1 argues that topology is, in fact, one of the primary forms of geometry, which, although a distinct field, is used in almost all branches of mathematics in one form or another. The features of topology differ from those of Euclidean geometry. Whereas Euclidean geometry is based on measurable quantities such as distances, areas, angles, topology works with abstract structures whose common feature is continuity, one of the basic properties of space. When we talk about abstract structures, we are referring to those types of non-orientable spaces whose properties do not change with deformation and which use invariants such as connectivity and solidity.

The best known topological structure was discovered in 1858 by the German mathematician August Ferdinand Möbius. This is the Möbius strip, the first example of a non-orientable surface whose faces are indistinguishable. If we follow a linear trajectory on the central axis of this strip, we end up back where we started, realizing that the strip is a single continuous surface.

But how can topology be applied to architectural practice? Because of the invariants with which it works, the application of topology to fields other than mathematics or computer science becomes an abstract procedure. Since the main characteristics of topological structures are flexibility and adaptability, mathematicians are not convinced about the applicability of topology in architecture. In the case of architecture we are dealing with concrete materiality, as buildings are characterized by rigidity and stability, which are the opposite properties of topology. However, architects who adopt the topological approach try to find solutions to eliminate the rigidity of the built object so that, depending on certain factors, it can adapt and cope with different situations.

The introduction of the notion of topology in architecture took place in the early 1960s with the formulation of the principles of oblique function by Claude Parent and Paul ^Virilio2, founding members of the Architecture Principe group. Their intention was to go beyond orthogonality and move towards an architecture based on non-Eeuclidean geometry. The oblique function was an attempt to apply topology to architecture, which used oblique surfaces to create unity and fluidity between the architectural object and its context, facilitating a livable circulation. Beyond the aesthetic aspect, the oblique function led to a destabilization of the modern object through radical abstraction, representing a critique of verticality and horizontality in architecture and urbanism of that time. One of Parent and Virilio's first proposals along these lines was the Charleville Exhibition^Palace3 of 1966, a program involving a complex mix of cultural and commercial activities. In the case of this project, the authors sought to promote other kinds of connections, establishing a new, artificial relationship with the relief and the surrounding space. They sought to define a new way of traversing space, encouraging new directions and new ways of using surfaces.

Read the full text in issue 6/2014 of Arhitectura magazine

NOTES:

1 Robert Bruner works as a professor of mathematics at Wayne State University.

2 The work of Parent (architect) and Virilio (theorist) between 1963 and 1968 represented a challenge to post-war modernism, both as a formal language and as a sociomoral discourse. They rejected all that was fashionable and explored through design, constantly searching for new possibilities and construction techniques.

3 Large-scale building, conceived as a concrete shell and located on the Meuse; the project was never realized.