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 consequece of his collaboration with Iannis Xenakis, the famous contemporary musician working at that time as engineer in Rue de Sèvres. Xenakis' very deep 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. The idea of a container without an aesthetic claim allowed Le Corbusier to think only about the show; in the meantime he entrusted Xenakis with a "mathematical translation" of his sketches, which represented the volume of a rounded bottle with a stomach-shaped plan. In the Poème Électronic the correspondence between music and architecture is not only a matter of geometry. It was projected by Le Corbusier 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. Architecture played, at the same time, the role of orchestral instrument and of sound box, container and contents.