• Thumbnail for Theorema Egregium
    Gauss's Theorema Egregium (Latin for "Remarkable Theorem") is a major result of differential geometry, proved by Carl Friedrich Gauss in 1827, that concerns...
    6 KB (685 words) - 19:24, 29 August 2024
  • Thumbnail for Differential geometry of surfaces
    located in the ambient Euclidean space. The crowning result, the Theorema Egregium of Gauss, established that the Gaussian curvature is an intrinsic...
    127 KB (17,444 words) - 03:32, 17 October 2024
  • Thumbnail for Gaussian curvature
    the content of the Theorema egregium. Gaussian curvature is named after Carl Friedrich Gauss, who published the Theorema egregium in 1827. At any point...
    19 KB (2,612 words) - 22:21, 7 August 2024
  • Thumbnail for Differential geometry
    the Earth's surface onto a flat plane, a consequence of the later Theorema Egregium of Gauss. The first systematic or rigorous treatment of geometry using...
    46 KB (5,912 words) - 17:02, 17 October 2024
  • two theorems of Carl Friedrich Gauss: Theorema Egregium, "Remarkable Theorem", best-known example Aureum Theorema, "Golden Theorem", better-known as quadratic...
    669 bytes (113 words) - 13:25, 7 December 2019
  • cylinder, which is a consequence of Gaussian curvature and Gauss's Theorema Egregium. A familiar example of this is a floppy pizza slice, which will remain...
    19 KB (2,925 words) - 11:22, 13 October 2024
  • geometry. One of the oldest such discoveries is Carl Friedrich Gauss's Theorema Egregium ("remarkable theorem") that asserts roughly that the Gaussian curvature...
    100 KB (9,886 words) - 03:41, 24 August 2024
  • Thumbnail for Carl Friedrich Gauss
    two-dimensional being constrained to move on it. As a result, the Theorema Egregium (remarkable theorem), established a property of the notion of Gaussian...
    182 KB (18,159 words) - 14:58, 4 November 2024
  • Thumbnail for World map
    world map changes Mappa mundi Maps of the world Rhumbline network Theorema Egregium Time zone Large-Scale Distortions in Map Projections Archived 16 February...
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  • Gauss equation, as it may be viewed as a generalization of Gauss's Theorema Egregium. For general Riemannian manifolds one has to add the curvature of...
    10 KB (1,454 words) - 20:34, 18 January 2024
  • Thumbnail for Bernhard Riemann
    differential geometry of surfaces, which Gauss himself proved in his theorema egregium. The fundamental objects are called the Riemannian metric and the...
    26 KB (2,959 words) - 22:11, 20 October 2024
  • Thumbnail for Riemannian manifold
    surface (the first fundamental form). This result is known as the Theorema Egregium ("remarkable theorem" in Latin). A map that preserves the local measurements...
    59 KB (8,680 words) - 10:03, 21 October 2024
  • Thumbnail for Equal-area projection
    change apparent density of the phenomenon being mapped. By Gauss's Theorema Egregium, an equal-area projection cannot be conformal. This implies that an...
    8 KB (801 words) - 21:45, 22 September 2024
  • Thumbnail for Mathematical beauty
    unexpected insights into mathematical structures. For example, Gauss's Theorema Egregium is a deep theorem that states that the gaussian curvature is invariant...
    32 KB (3,734 words) - 05:39, 2 November 2024
  • L, M, and N are the coefficients of the second fundamental form. Theorema egregium of Gauss states that the Gaussian curvature of a surface can be expressed...
    6 KB (1,137 words) - 16:36, 14 September 2024
  • Curvature Radius of curvature Osculating circle Curve Fenchel's theorem Theorema egregium Gauss–Bonnet theorem First fundamental form Second fundamental form...
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  • – Originally described something that was remarkably good (as in Theorema Egregium). The word is from the Latin egregius "illustrious, select", literally...
    26 KB (3,043 words) - 08:46, 8 July 2024
  • Thumbnail for List of things named after Carl Friedrich Gauss
    Gauss map in differential geometry Gaussian curvature, defined in his Theorema egregium Gauss circle problem Gauss–Kuzmin–Wirsing constant, a constant in...
    14 KB (1,124 words) - 14:42, 31 July 2024
  • Thumbnail for Shape of the universe
    paradoxes – List of statements that appear to contradict themselves Theorema Egregium – Differential geometry theorem—The "remarkable theorem" discovered...
    30 KB (3,840 words) - 21:17, 12 September 2024
  • Thumbnail for Corrugated galvanised iron
    a layer of paint. Chattel house Metal roof Nissen hut Quonset hut Theorema Egregium, for more information on why corrugation increases strength Tin tabernacle...
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  • Thumbnail for List of geometers
    projective geometry; Gergonne point Carl Friedrich Gauss (1777–1855) – Theorema Egregium Louis Poinsot (1777–1859) Siméon Denis Poisson (1781–1840) Jean-Victor...
    14 KB (1,126 words) - 04:18, 9 October 2024
  • the Riemannian metric of the surface. This is Gauss's celebrated Theorema Egregium, which he found while concerned with geographic surveys and mapmaking...
    44 KB (6,461 words) - 20:22, 15 October 2024
  • Thumbnail for Manifold
    consider abstract spaces as mathematical objects in their own right. His theorema egregium gives a method for computing the curvature of a surface without considering...
    68 KB (9,505 words) - 23:59, 2 November 2024
  • Darboux frame Toponogov (2006) This equation is the basis for Gauss's theorema egregium. Gauss 1828. (Kline 1972, p. 885). Peterson (1853) Ivanov 2001. Terminology...
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  • projection be conformal. This is also a consequence of Carl Gauss's 1827 Theorema Egregium [Remarkable Theorem]. A conformal parameterization of a disc-like...
    11 KB (1,211 words) - 00:36, 1 September 2024
  • Thumbnail for Scale (map)
    points on the map to a bar scale on the map. As proved by Gauss’s Theorema Egregium, a sphere (or ellipsoid) cannot be projected onto a plane without...
    35 KB (5,382 words) - 07:35, 22 June 2024
  • Thumbnail for Map projection
    differences are reduced to imperceptibility. Carl Friedrich Gauss's Theorema Egregium proved that a sphere's surface cannot be represented on a plane without...
    59 KB (6,478 words) - 00:47, 19 September 2024
  • Thumbnail for Sphere
    constant Gaussian curvature at each point equal to 1/r2. As per Gauss's Theorema Egregium, this curvature is independent of the sphere's embedding in 3-dimensional...
    41 KB (5,327 words) - 20:13, 25 October 2024
  • Thumbnail for List of important publications in mathematics
    introducing the notion of Gaussian curvature and Gauss's celebrated Theorema Egregium. Bernhard Riemann (1854) Publication data: "Über die Hypothesen, welche...
    97 KB (10,409 words) - 10:05, 2 September 2024
  • theorem (vector calculus) Gamas's Theorem (multilinear algebra) Gauss's Theorema Egregium (differential geometry) Gauss–Bonnet theorem (differential geometry)...
    73 KB (6,030 words) - 15:22, 20 October 2024