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)
| Label | Occurrences |
|---|---|
| Disquisitiones Generales Circa Superficies Curvas canonical | 2 |
| Disquisitiones generales circa superficies curvas | 2 |
| General Investigations of Curved Surfaces | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1382029 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
Target entity: Disquisitiones Generales Circa Superficies Curvas Context triple: [Theorema Egregium, publishedIn, Disquisitiones Generales Circa Superficies Curvas]
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A.
Theorema Egregium
Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
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B.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
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C.
Elementa curvarum linearum
Elementa curvarum linearum is a 17th-century mathematical treatise by Johan de Witt that systematically studies the geometry and properties of linear curves.
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D.
Treatise on Demonstration of Problems of Algebra
Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
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E.
Commentary on the Difficulties of Certain Postulates of Euclid
Commentary on the Difficulties of Certain Postulates of Euclid is a mathematical treatise by Omar Khayyam in which he critically examines and attempts to resolve issues in Euclid’s postulates, especially the parallel postulate, laying early groundwork for later developments in geometry.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: Disquisitiones Generales Circa Superficies Curvas Target entity description: 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.
-
A.
Theorema Egregium
Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
-
B.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
-
C.
Elementa curvarum linearum
Elementa curvarum linearum is a 17th-century mathematical treatise by Johan de Witt that systematically studies the geometry and properties of linear curves.
-
D.
Treatise on Demonstration of Problems of Algebra
Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
-
E.
Commentary on the Difficulties of Certain Postulates of Euclid
Commentary on the Difficulties of Certain Postulates of Euclid is a mathematical treatise by Omar Khayyam in which he critically examines and attempts to resolve issues in Euclid’s postulates, especially the parallel postulate, laying early groundwork for later developments in geometry.
- F. None of above. chosen
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 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
|
How these facts were elicited
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Subject: Disquisitiones Generales Circa Superficies Curvas Description of subject: 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.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.