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.

All labels observed (3)

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Statements (47)

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 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 ⓘ
publicationYear 1827 ⓘ
shows Gaussian curvature is invariant under local isometries ⓘ
curvature can be determined from the first fundamental form alone ⓘ
translatedTitle General Investigations of Curved Surfaces ⓘ

How these facts were elicited

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 ⓘ
linked to: Disquisitiones Generales Circa Superficies Curvas
Disquisitiones Generales Circa Superficies Curvas → originalTitle → Disquisitiones Generales Circa Superficies Curvas ⓘ
Disquisitiones Generales Circa Superficies Curvas → translatedTitle → General Investigations of Curved Surfaces ⓘ
linked to: Disquisitiones Generales Circa Superficies Curvas
Gauss’s remarkable theorem → publishedIn → Disquisitiones generales circa superficies curvas ⓘ
linked to: Disquisitiones Generales Circa Superficies Curvas