Gauss's theory of surfaces is among the purely mathematical achievements inspired by ideas that arose in connection with surveys of the surface of the earth. Long regarded as a masterpiece in content and form, this work features one of the author's most original contributions to mathematics--the discovery that Gauss termed the "e;Theorema Egregium."e; It consists of his penetrating definition of the concept of surface curvature and the theorem that the "e;Gauss curvature"e; is invariant under arbitrary isometric deformation of a curved surface. The profound effects of these concepts were soon generalized by Bernhard Riemann, and subsequent development included the important role of the Gauss-Riemann concept of curvature in modern relativity theory.This edition of Gauss's classic work features a new introduction, bibliography, and notes by science historian Peter Pesic. In addition, an informative appendix offers historical background.
