THE CURVATURE OF CHEMICAL STRUCTURES

Abstract
It can be demonstrated by many examples that in an universal sense, the adaption of local structures to a collective order finds a natural solution through curvature. This is based on the balance between the rigidity of the individuals and the force of the collective law, in other words it is the principal of the optimal form, which obviously connects science with mathematics, art, architecture and also sociology. The structural chemistry of molecules and solids substantiates the consequences of this principle and its general importance for the organization of individuals. In general, the symmetry of individuals and collectives don't fit well together. In small aggregates (molecules) this strain is released by the formation of bent bonds, however not without loss of the usual meaning of bond distances and bond angles. In large collectives (crystals), space partitioners, which in general are curved surfaces, representing the symmetry of the collective, essentially determine the organization of the parts to the whole. Apparently, also in crystals a hierarchy for the organization of "organisms" exists, from which one can conclude evolution and selection even in the inanimated nature.