Mathematical imagination in architecture

Subtitle of presentation (if needed)

Bruno Autin

3P-Science

Abstract

Unfortunately, in contemporary civilisation, too many buildings are reduced to parallepipedic shapes generating boredom and social trouble in the worst case of big cities outskirts. The obvious arguments for such shapes are low cost and simplicity. Those arguments are justified only within a short sighted project. Here I show that using Geometrica, an application of Mathematica dedicated to geometry, it is not difficult to generate imaginative forms using the concepts of parallel surfaces. In fact, the functions can generate surfaces whose local distance between two points on the same normal line is not only constant (usual definition of parallelism) but may vary as a function of the two parameters of the reference surface. More generally, a group of buildings can be composed from a generic argument as it was sometimes the case at Renaissance times. An example drawn from Piero della Francesca's works will be given.