Synopses & Reviews
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 "Theorema Egregium." It consists of his penetrating definition of the concept of surface curvature and the theorem that the "Gauss curvature" 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.
Synopsis
A masterpiece by an influential mathematician, this work defines the concept of surface curvature and presents the important theorem stating that the Gauss curvature is invariant under arbitrary isometric deformation of a curved surface.
Synopsis
Long regarded as a masterpiece in content and form, this work defines the concept of surface curvature and presents the important theorem stating that the "Gauss curvature" is invariant under arbitrary isometric deformation of a curved surface. This edition of Gauss's classic features a new introduction, bibliography, and notes by science historian Peter Pesic. 1902 edition.
Table of Contents
Introduction to the Dover Edition
Historical Background
Part I. General Investigations of Curved Surfaces (1827)
Gauss's Abstract
Notes
Part II. New General Investigations of Curved Surfaces (1825)
Notes
Part III. Additional Notes
Appendix: Basic Formulas of Spherical Trigonometry
Bibliography
Index