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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. We have to say that 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.

The Philips Pavilion at the Brussels World Fair is the first of Le Corbusier’s architectural works to connect the evolution of his mathematical thought on harmonic series and modular coordination with the idea of three-dimensional continuity. This propitious circumstance was the consequence of his collaboration with Iannis Xenakis, whose profound interest in mathematical structures was improved on his becaming acquainted with the Modulor, while at the same time Le Corbusier encountered double ruled quadric surfaces. For the Philips Pavilion—the Poeme Electronic—Corbusier entrusted Xenakis with a “mathematical translation” of his sketches, which represented the volume of a rounded bottle with a stomach-shaped plan. The Pavilion was designed as if it were an orchestral work in which lights, loudspeakers, film projections on curved surfaces, spectators’ shadows and their expression of wonder, objects hanging from the ceiling and the containing space itself were all virtual instruments.