The geodetic survey of Hanover fuelled Gauss's interest in differential geometry and topology, fields of mathematics dealing with curves and surfaces. This led him in 1828 to the publication of a memoir that marks the birth of modern differential geometry of surfaces, as it departed from the traditional ways of treating surfaces as cartesian graphs of functions of two variables, and that initiated the exploration of surfaces from the "inner" point of view of a two-dimensional being constrained to move on it. As a result, the Theorema Egregium (remarkable theorem), established a property of the notion of Gaussian curvature. Informally, the theorem says that the curvature of a surface can be determined entirely by measuring angles and distances on the surface, regardless of the embedding of the surface in three-dimensional or two-dimensional space.
The geodetic survey of Hanover fuelled Gauss's interest in differential geometry and topology fields of mathematics dealing with curves and surfaces This led him in 1828 to the publication of a memoir that marks the birth of modern differential geometry of surfaces as it departed from the traditional ways of treating surfaces as cartesian graphs of functions of two variables and that initiated the exploration of surfaces from the "inner" point of view of a two-dimensional being constrained to move on it As a result the Theorema Egregium (remarkable theorem) established a property of the notion of Gaussian curvature Informally the theorem says that the curvature of a surface can be determined entirely by measuring angles and distances on the surface regardless of the embedding of the surface in three-dimensional or two-dimensional space