General Investigations of Curved Surfaces

General Investigations of Curved SurfacesGauss'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

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the text represents the physical model by appropriate mathematical symbols and operators

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Helpful appendixes deal with such mathematical tools as matrices and linear systems (prerequisites include the usual engineering mathematics courses and advanced calculus)

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" and "science" proved highly useful to his successors in the field