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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.
In 1827 Gauss presented to the Royal Society of Göttingen his important paperon the theory of surfaces, which seventy-three years afterward the eminent Frenchgeometer, 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 finishedand useful introduction to the study of infinitesimal geometry. This memoir maybe called: General Investigations of Curved Surfaces, or the Paper of 1827, todistinguish it from the original draft written out in 1825, but not publisheduntil 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 intoGerman. The paper was originally published in Latin under the title: Ia. Disquisitiones generales circa superficies curvasauctore Carolo Friderico Gauss.Societati regiæ oblatæ D. 8. Octob. 1827,
General Investigations of Curved Surfaces of 1827 and 1825 by Carl Friedrich Gauss
Intended for juniors and seniors majoring in mathematics, as well as anyone pursuing independent study, this book traces the historical development of four different mathematical concepts by presenting readers with the original sources. Each chapter showcases a masterpiece of mathematical achievement, anchored to a sequence of selected primary sources. The authors examine the interplay between the discrete and continuous, with a focus on sums of powers. They then delineate the development of algorithms by Newton, Simpson and Smale. Next they explore our modern understanding of curvature, and finally they look at the properties of prime numbers. The book includes exercises, numerous photographs, and an annotated bibliography.
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.