Topologic Multi-faceted Structures

‘Topology’ is defined as study of intrinsic, qualitative forms that are not normally affected by changes in size or shape, which remain invariant through continuous transformation of elastic deformation, such as stretching or twisting. Greg Lynn’s essay (1993) on ‘architectural curvilinearity’ is one of the first examples of the new topological approach to design that moves away from the dominant deconstructivist ‘logic of conflict and contradiction’ to develop a ‘more fluid logic of connectivity’ and manifested by continuous highly curvilinear surfaces.

Non-Euclidean Geometry

Since the last few years of 20th century, digital media is used as tool for visualization and representation but also as a generative tool to design architecture forms. The traditional way of designing is becoming obsolete and replaced by digitally driven design process. The plan no longer ‘generates’ the design and sections, but are attain in a purely digital process. Complex curvilinear geometries can now be produced with the ease as Euclidean geometries of planar shapes, cylindrical, spherical and topological forms (Kolaveric 2005).

Architecture throughout the past centuries was based on Euclidean geometry. On Dan Pedoe’s book ‘Geometry and the Visual Arts’ it was postulated that Gauss (1830) obtained the theorems and later discovered the existence of non-Euclidean geometry. The work of Gauss showed that space is not only curve but also multi-dimensional spaces. One of the interesting theories is the concept of ‘curvatures of space’ and the ‘space of positive and negative curvature’. As architectural conceptions of space move from the three dimensions of the Cartesian space to fourth-dimensional continuum of interactions between space and time, other dimensions and other conceptions of space begin to open new possibilities for architectural thought.