Beyond the compasses: the geometry of curves

Studying, drawing, classifying and measuring curved lines has been one of the main concerns of mathematicians, from the straight line and the circle with which geometry began to the complex and rather disquieting shapes of modern fractals.

Curves are above all geometrical shapes and play a delicate role in the mathematical imagination, as a frontier zone where different, and sometimes opposing, activities come together. They remind us of drawing, design, building but together they symbolise gesture and beauty; they are both objects of the imagination and technical instruments.

This exhibition is designed to lead the visitor through this garden of tangible shapes, along a path that links the solidity of the objects and mechanisms to the abstractions of mathematical thought; a path which at the end leads to a web of affinities between geometrical concepts, technical devices and scientific constructions.

The visitor can follow any one of three theoretical tours which are distinct but which interconnect. First there is a conceptual tour where the principal notions of the geometry of curves are described, in their increasing complexity. Overlying this the historical path brings to light the evolution of the concept of curve and the progressive refinement in the relevant mathematical methods. Finally a third itinerary shows how curves and their properties are used at various moments in science and technology.

The items displayed vary from a collection of books which plot the development of geometrical thought, to a series of instruments, some of which can be used freely by the visitor and which illustrate the principal properties of curves, to reproductions of devices which depend on those properties in order to work, to computer experiments to visualise complex situations.