Architecture and geometry share a mutual history, and their relationship
precedes the introduction of digital and computer technologies in
architectural theory and design. Geometry has always been directly related to
the modalities of thinking in architecture through the problems of
conceptualisation, representation, building, technology. Through the
historical overview of these two disciplines, it is possible to perceive
direct influences of geometry on the architectural creative concepts, formal
characteristics of architectural works, structural aspects, and building
methods in architecture. However, the focus of this paper is not on the
representation of historical intertwining of these two disciplines, which is
indisputable, it is on the attempt to represent one specific bond between
topology and architecture, firstly through the explanation of the principle
of continuous deformability, and secondly through the representation of the
models through which the principle occurs in the architectural design
process, as well. The first part of this work will introduce and analyse the
transition of concepts of continuity and deformability, from mathematical
topology through philosophy to architecture, while the second part of the
work will explain two models in detail, formal and systematic, through which
the principle of continuous deformation is applied in certain architectural
design practices. Overall, this work deals with the interpretation of the
principle of continuous deformation in architecture and it shows in which way
the architectural discourse changes the meaning of a
mathematical-philosophical notion and turns it into a design methodology of
its own. The subtlety of the question Bernard Tschumi asks about space
illustrates the need to thoroughly investigate interdisciplinary relation
between architecture, philosophy, and mathematics: ?Is topology a mental
construction toward a theory of space?? (Tschumi, 2004, p.49)