Disquisitiones Generales Circa Superficies Curvas

E157377

Disquisitiones Generales Circa Superficies Curvas is Carl Friedrich Gauss’s foundational 1827 work on differential geometry, in which he developed the intrinsic theory of curved surfaces and introduced concepts such as Gaussian curvature.

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Predicate Object
instanceOf mathematical treatise
scientific work
author Carl Friedrich Gauss
authorBirthYear 1777
authorDeathYear 1855
authorNationality German
centralConcept first fundamental form
geodesics
lines of curvature
metric on a surface
normal curvature
principal curvatures
second fundamental form
surface area element
centralResult Theorema Egregium states that Gaussian curvature is intrinsic
developedTheoryOf curved surfaces
intrinsic curvature
field differential geometry
geometry
hasLaterEdition English translation in the 20th century
hasTopic classification of points on a surface
coordinate systems on surfaces
elliptic, hyperbolic, and parabolic points
geodesic curvature
length of curves on surfaces
normal vectors to surfaces
parametrization of surfaces
historicalSignificance established curvature as an intrinsic invariant
foundational work of intrinsic differential geometry
major milestone in 19th-century mathematics
influenced 19th-century geometry
Bernhard Riemann
the development of general relativity
influencedField Riemannian manifolds
surface form: Riemannian geometry

global differential geometry
modern differential geometry
introducedConcept Gaussian curvature
Theorema Egregium
intrinsic geometry of surfaces
isPartOf collected works of Carl Friedrich Gauss
language Latin
originalPublicationMedium journal article
originalTitle Disquisitiones Generales Circa Superficies Curvas self-link
publicationYear 1827
shows Gaussian curvature is invariant under local isometries
curvature can be determined from the first fundamental form alone
translatedTitle Disquisitiones Generales Circa Superficies Curvas self-linksurface differs
surface form: General Investigations of Curved Surfaces

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Referenced by (5)

Full triples — surface form annotated when it differs from this entity's canonical label.

Theorema Egregium publishedIn Disquisitiones Generales Circa Superficies Curvas
Gauss–Bonnet theorem (early form) documentedIn Disquisitiones Generales Circa Superficies Curvas
this entity surface form: Disquisitiones generales circa superficies curvas
Disquisitiones Generales Circa Superficies Curvas originalTitle Disquisitiones Generales Circa Superficies Curvas self-link
Disquisitiones Generales Circa Superficies Curvas translatedTitle Disquisitiones Generales Circa Superficies Curvas self-linksurface differs
this entity surface form: General Investigations of Curved Surfaces
Gauss’s remarkable theorem publishedIn Disquisitiones Generales Circa Superficies Curvas
this entity surface form: Disquisitiones generales circa superficies curvas