Thinking Architecture in Four Dimensions

In mathematics, it is quite easy to define four dimensional geometry. With their equations, in fact, mathematicians work without any difficulty with any “n” dimension. From this point of view, it is also quite easy to describe what shape in our 3d word a hypercube, for example, can assume, taking advantage of projections of the geometric figure in the lower dimension. Architects are accustomed to draw the space they imagine through orthogonal projections and therefore to see the 3d space through its 2d projection in plan and section. As part of a research on the design theory and related analysis of the compositional process, as well as related changings of paradigms in Architecture, the paper presents the geometric consistency of multidimensional characteristics of a number of architectures, in which the concept and the image of multidimensional geometry interpret the architectural thought of the XXI century, are investigated.