Project SherlockEst. Knowledge

Book

1828

General Investigations of Curved Surfaces

Carl Friedrich Gauss

Proves the Theorema Egregium: a surface's curvature can be measured from within the surface itself, without reference to the space it sits in — which is what makes intrinsic geometry possible.

Before you start

FreeAdvancedlink checked 17 Sept 2026

Groundwork for

Works in the library that name this one as a prerequisite.

A Treatise on the Differential Geometry of Curves and SurfacesLuther Pfahler Eisenhart, 1909Develops the geometry of a surface entirely from its first and second fundamental forms, treating Gauss's Theorema Egregium as the fact that curvature is intrinsic and geodesics as the resulting generalisation of a straight line.

Filed under Geometry in Mathematics.