Author: Carl Friedrich GaussPublisher:
ISBN:
Category : Surfaces
Languages : en
Pages : 144
Book Description
General Investigations of Curved Surfaces of 1827 and 1825
Author: Carl Friedrich GaussPublisher:
ISBN:
Category : Surfaces
Languages : en
Pages : 144
Book Description
General Investigations of Curved Surfaces of 1827 and 1825
Author: Carl Friedrich GaussPublisher: Createspace Independent Publishing Platform
ISBN: 9781548653491
Category :
Languages : en
Pages : 154
Book Description
General Investigations of Curved Surfaces of 1827 and 1825 by Carl Friedrich Gauss
General Investigations of Curved Surfaces of 1827 and 1825
Author: Karl Friedrich GaussPublisher:
ISBN:
Category :
Languages : en
Pages : 126
Book Description
General Investigations of Curved Surfaces
Author: Karl Friedrich GaussPublisher: Courier Corporation
ISBN: 0486154815
Category : Mathematics
Languages : en
Pages : 146
Book Description
This influential 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. 1902 edition.
General Investigations of Curved Surfaces
Author: Karl Friedrich GaussPublisher:
ISBN: 9780243657148
Category :
Languages : en
Pages :
Book Description
General Investigations of Curved Surfaces of 1827 and 1825
Author: Karl Friedrich GaussPublisher: Forgotten Books
ISBN: 9780428690816
Category : Mathematics
Languages : en
Pages : 136
Book Description
Excerpt from General Investigations of Curved Surfaces of 1827 and 1825: Translated With Notes and a Bibliography Recently the eighth volume of Gauss's Works has appeared. This contains on pages 408 - 442 the paper which Gauss wrote out, but did not publish, in 1825. This paper may be called the New General Investigations of Curved Surfaces, or the Paper of 1825, to distinguish it from the Paper of 1827. The Paper of 1825 shows the manner in which many of the ideas were evolved, and while incomplete and In some cases inconsistent, nevertheless, when taken in connection with the Paper of 1827, shows the development of these ideas in the mind of Gauss. In both papers are found the method of the spherical representation, and, as types, the three important theorems: The measure of curvature is equal to the product of the reciprocals of the principal radii of curvature of the surface, The measure of curvature remains unchanged by a mere bending of the surface, The excess of the sum of the angles of a geodesic triangle is measured by the area of the corresponding triangle on the auxiliary sphere. But in the Paper of 1825 the first six sections, more than one-fifth of the whole paper, take up the consideration of theorems on curvature in a plane, as an introduction before the ideas are used in space; whereas the Paper of 1827 takes up these ideas for space only. Moreover, while Gauss introduces the geodesic polar coordinates In the Paper of 1825, in the Paper of 1827 he uses the general coordinates, p, 9, thus introducing a new method, as well as employing the principles used by Monge and others. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
General Investigations of Curved Surfaces of 1827 And 1825; Tr. With Notes And a Bibliography by James Caddall Morehead And Adam Miller Hiltebeitel.
Author: Carl Friedrich GaussPublisher: Scholarly Pub Office Univ of
ISBN: 9781418163877
Category : Mathematics
Languages : en
Pages : 140
Book Description
General Investigations of Curved Surfaces of 1827 and 1825
Author: Karl Friedrich GaussGeneral investigations of curved surfaces
Author: Karl Friedrich GaussPublisher: BoD - Books on Demand
ISBN:
Category : Mathematics
Languages : en
Pages : 145
Book Description
INTRODUCTION In 1827 Gauss presented to the Royal Society of Göttingen 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 andusefulintroductiontothestudyofinfinitesimalgeometry.∗ Thismemoirmay 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: Ia. Disquisitiones generales circa superficies curvas auctore Carolo Friderico Gauss. Societati regiæ oblatæ D. 8. Octob. 1827, and was printed in: Commentationes societatis regiæ scientiarum Gottingensis recentiores, Commentationes classis mathematicæ. Tom. VI. (ad a. 1823–1827). Gottingæ, 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: Ib. Disquisitiones generales circa superficies curvas auctore Carolo Friderico Gauss. Gottingæ. Typis Dieterichianis. 1828. II. In Monge’s Application de l’analyse à 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 théorie générale des surfaces courbes; Par M. C.-F. Gauss. IIIa. A third Latin edition of this paper stands in: Gauss, Werke, Her- ausgegeben von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Vol. 4, Göttingen, 1873, pages 217–258, without change of the title of the original paper (Ia). IIIb. The same, without change, in Vol. 4 of Gauss, Werke, Zweiter Abdruck, Göttingen, 1880. IV. A French translation was made from Liouville’s edition, II, by Captain Tiburce Abadie, ancien élève de l’École Polytechnique, and appears in Nouvelles Annales de Mathématique, Vol. 11, Paris, 1852, pages 195–252, under the title: Recherches générales sur les surfaces courbes; Par M. Gauss. This latter also appears under its own title. Va. Another French translation is: Recherches Générales sur les Surfaces Courbes. Par M. C.-F. Gauss, traduites en français, suivies de notes et d’études sur divers points de la Théorie des Surfaces et sur certaines classes de Courbes, par M. E. Roger, Paris, 1855.
General Investigations OF Curved Surfaces
Author: Karl Friedrich GaussPublisher:
ISBN: 9781677953820
Category :
Languages : en
Pages : 120
Book Description
In 1827 Gauss presented to the Royal Society of Göttingen 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, todistinguish 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: Ia. Disquisitiones generales circa superficies curvas auctore Carolo Friderico Gauss.