Conoids and Hyperbolic Paraboloids in Le Corbusier’s Philips Pavilion

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 Poème Électronic—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