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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.
Gap theorem (computational complexity theory) Gauss's Theorema Egregium (differential geometry) Gauss–Bonnet theorem (differential geometry) Gauss–Lucas theorem (complex analysis) Gauss–Markov theorem ; Gauss–Wantzel theorem ; Gelfand–Mazur theorem (Banach algebra) Gelfand–Naimark theorem (functional analysis)
The crowning result, the Theorema Egregium of Gauss, established that the Gaussian curvature is an intrinsic invariant, i.e. invariant under local isometries. This point of view was extended to higher-dimensional spaces by Riemann and led to what is known today as Riemannian geometry. The nineteenth century was the golden age for the theory of ...
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 ...
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 ...
It is composed of two main dimensions: A) mental visualization and B) perception of the physical world (spatial arrangements and objects). It includes both practical problem-solving as well as artistic creations. Spatial ability is one of the three factors beneath g (general intelligence) in the hierarchical model of intelligence. [21]
The Cattell–Horn–Carroll theory is an integration of two previously established theoretical models of intelligence: the theory of fluid and crystallized intelligence (Gf-Gc) (Cattell, 1941; Horn 1965), and Carroll's three-stratum theory (1993), a hierarchical, three-stratum model of intelligence. Due to substantial similarities between the ...
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.