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Gauss's original statement of the Theorema Egregium, translated from Latin into English. The theorem is "remarkable" because the definition of Gaussian curvature makes ample reference to the specific way the surface is embedded in 3-dimensional space, and it is quite surprising that the result does not depend on its embedding.
This is an accepted version of this page This is the latest accepted revision, reviewed on 8 January 2025. German mathematician, astronomer, geodesist, and physicist (1777–1855) "Gauss" redirects here. For other uses, see Gauss (disambiguation). Carl Friedrich Gauss Portrait by Christian Albrecht Jensen, 1840 (copy from Gottlieb Biermann, 1887) Born Johann Carl Friedrich Gauss (1777-04-30 ...
Intelligence quotient (IQ) tests do correlate with one another and that the view that the general intelligence factor (g) is a statistical artifact is a minority one. IQ scores are fairly stable during development in the sense that while a child's reasoning ability increases, the child's relative ranking in comparison to that of other ...
Gauss's original statement of the Theorema Egregium, translated from Latin into English. Gauss's Theorema Egregium , the "Remarkable Theorem", shows that the Gaussian curvature of a surface can be computed solely in terms of the metric and is thus an intrinsic invariant of the surface, independent of any isometric embedding in E 3 and unchanged ...
Disquisitiones Arithmeticae (Latin for Arithmetical Investigations) is a textbook on number theory written in Latin by Carl Friedrich Gauss in 1798, when Gauss was 21, and published in 1801, when he was 24. It had a revolutionary impact on number theory by making the field truly rigorous and systematic and paved the path for modern number theory.
For example, Gauss's Theorema Egregium is a deep theorem that states that the gaussian curvature is invariant under isometry of the surface. Another example is the fundamental theorem of calculus [ 8 ] (and its vector versions including Green's theorem and Stokes' theorem ).
Gauss's Theorema egregium (Latin: "remarkable theorem") states that Gaussian curvature of a surface can be determined from the measurements of length on the surface itself. In fact, it can be found given the full knowledge of the first fundamental form and expressed via the first fundamental form and its partial derivatives of first and second ...
The Bell Curve: Intelligence and Class Structure in American Life is a 1994 book by the psychologist Richard J. Herrnstein and the political scientist Charles Murray in which the authors argue that human intelligence is substantially influenced by both inherited and environmental factors and that it is a better predictor of many personal outcomes, including financial income, job performance ...