<p>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.<br>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.</p>

General Investigations of Curved Surfaces: Edited with an Introduction and Notes by Peter Pesic (Dover Books on Mathematics)

Science & Math

Karl Friedrich Gauss

Mathematics

Dover Publications

Excerpt from General Investigations of Curved Surfaces: Of 1827 and 1825In 1827 Gauss presented to the Royal Society of Gottingen his important paper on the theory of surfaces, which seventy-three years afterward the eminent French geometer, who has done more than any one else to propagate these principles, characterizes as one of Gauss's chief titles to fame, and as still the most finished and useful introduction to the study of infinitesimal geometry. This memoir may be called: General Investigations of Curved Surfaces, or the Paper of 1827, to distinguish it from the original draft written out in 1825, but not published until 1900. A list of the editions and translations of the Paper of 1827 follows. There are three editions in Latin, two translations into French, and two into German. The paper was originally published in Latin under the title:I a. Disquisitiones generales circa superficies curvasauctore Carolo Friderico GaussSocietati regise oblatse D. 8. Octob. 1827,and was printed in: Commentationes societatis regise scientiarum Gottingensis recentiores, Commentationes classis mathematicse. , Tom. VI. (ad a. 1823-1827). Gottingse, 1828, pages 99-146. This sixth volume is rare; so much so, indeed, that the British Museum Catalogue indicates that it is missing in that collection. With the signatures changed, and the paging changed to pages 1-50, Ia also appears with the title page added:I b. Disquisitiones generales circa superficies curvasauctore Carolo Friderico Gauss.Gottingse. Typis Dieterichianis. 1828.II. In Monge's Application de l'analyse a la géométrie, fifth edition, edited by Liouville, Paris, 1850, on pages 505-546, is a reprint, added by the Editor, in Latin under the title: Recherches sur la thorie genrale des surfaces courbes; Par M. C. -F. Gauss.

General Investigations of Curved Surfaces of 1827 and 1825: Translated With Notes and a Bibliography (Classic Reprint)

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