The application models of the topological principle of continuous deformation in the architectural design process

Abstract

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).

Arhitektura i geometrija dele zajedničku istoriju, a njihov odnos prethodi pojavi digitalnih i kompjuterskih tehnologija u arhitektonskoj teoriji i stvaralaštvu. Geometrija je oduvek bila u direktnoj vezi sa modalitetima promišljanja u arhitekturi, kroz pitanja konceptualizacije, prikazivanja, građenja, tehnologije. Istorijskim pregledom odnosa ovih disciplina moguće je sagledati direktne uticaje geometrije na arhitektonske stvaralačke koncepte, formalne karakteristike arhitektonskih dela, konstruktivne aspekte, uticaj na metode građenja u arhitekturi. Međutim, fokus ovog rada nije na prikazu istorijskog prepleta ovih disciplina, koji je neosporan, već je pokušaj da se prikaže jedna specifična veza između topologije i arhitekture, najpre kroz objašnjenje principa kontinuirane deformabilnosti, a zatim i prikazom modela pomoću kojih se princip pojavljuje u projektantskom procesu. U prvom delu rada će se prikazati i analizirati tranzicija pojmova kontinuiteta i deformabilnosti od matematičke topologije, preko filozofije do arhitekture, dok će se u drugom delu detaljnije objasniti dva modela, formalni i sistemski, pomoću kojih se principi kontinualne deformacije apliciraju u pojedinim projektantskim praksama. Uopšteno, rad se bavi tumačenjem principa kontinualne deformacije u arhitekturi i prikazuje na koji način arhitektonski diskurs menja značenje jednog matematičko-filozofskog pojma i pretvara ga u spostvenu projektantsku metodologiju. Suptilnost pitanja o prostoru koje postavlja Bernard Tschumi najbolje govori o potrebi da se detaljno istraži interdisciplinarni odnos između arhitekture, filozofije i matematike:"Da li je topologija samo mentalna konstrukcija bliska teoriji prostora?"(Tschumi, 2004, p.49).