Introduction

Abstract

The geometry of natural objects ranging in size from the atomic scale to the size of the universe is central to the models we make in order to ‘understand’ nature. The geometry of particle trajectories; of hydrodynamic flow lines, waves, ships and shores; of landscapes, mountains, islands, rivers, glaciers and sediments; of grains in rock, metals and composite materials; of plants, insects and cells, as well as the geometrical structure of crystals, chemicals and proteins — in short the geometry of nature is so central to the various fields of natural science that we tend to take the geometrical aspects for granted. Each field tends to develop adapted concepts (e.g., morphology, four-dimensional spaces, texture, conformation, and dislocations) used intuitively by the scientists in that field. Traditionally the Euclidean lines, circles, spheres and tetrahedra have served as the basis of the intuitive understanding of the geometry of nature.