Protosurfaces: Mathematical Experiments in Spacial Design

For designers, mathematics presents both the promise of control and the challenge of constraint. The working models presented here are products of an ongoing seminar at the GSD that confronts this productive tension between the freedom of design and the logic of geometry. In particular, these models use automated topological, mathematical, and geometric systems to engage architectural issues such as designed topology, material efficiency, and structural rigidity through geometrical methods. The forms are generalizations of hyperbolic paraboloids called medial or skeletal surfaces. They are prototype spaces, experiments out of which a mathematically synthetic approach to surface design might emerge.

From a diagram of circulation, the surfaces that induce that circulation are calculated automatically. By mathematical definition, all surfaces are subdivided into flat quadrilateral panels, easily buildable with standard sheet material. They introduce few irregular triangles and no superfluous gaps, creating a truly watertight shell. Like hyperbolic shells, these surfaces are mathematically defined for anticlastic curvature, with a remarkable structural rigidity as a natural consequence. Such experiments thus demonstrate the possibility of how multiple constraints of design might be synthesized in the context of mathematical frameworks with provocative spatial results.

Andrew Witt, Lecturer, Architecture, Harvard University