'GAUSS' THEOREMA EGREGIUM FOR TRIANGULATED SURFACES

Abstract

The paper deals with fundamental geometric assumptions of the static-kinematic analysis of triangulated surfaces. First. intrinsic and extrinsic properties of triangulated surfaces as analogues of those of smooth surfaces are introduced, then static-kinematic analogies between triangulated surfaces and pin-jointed single-layer space grids are dealt with. It is shown that Gaussian curvature of smooth surfaces cannot be interpreted for triangulated surfaces. and space grids. however, statements of Gauss' Theorema Egregium can be replaced for statements concerning simple and useful connections between their intrinsic and extrinsic measures.