’s at one point with the
’s at neighbouring points, and if this mathematical expression remained invariant in value to a change of mesh-system in spite of the variations of the individual
’s which must accompany the change of mesh-system, we should be in the presence of a magnitude which, transcending our choice of a mesh-system, would refer solely to the shape of the surface itself, i.e., to its curvature at the point considered. But before we investigate the nature of Gauss’ discoveries, certain elementary notions must be recalled.
We know that the curvature of a circle at every point of its circumference is a constant given by
, where
