Erlangen Program
E50327
The Erlangen Program is Felix Klein’s influential 1872 framework that classifies and studies geometries based on their underlying symmetry groups and transformation properties.
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
framework for classifying geometries
→
mathematical program → research program in geometry → |
| aimedTo |
clarify relationships between different geometries
→
systematize known geometries → |
| approach |
group-theoretic approach to geometry
→
|
| author |
Felix Klein
→
|
| basedOn |
group theory
→
|
| centralConcept |
group of transformations
→
invariants under a group of transformations → |
| classifies |
Euclidean geometry
→
affine geometry → elliptic geometry → hyperbolic geometry → non-Euclidean geometry → projective geometry → |
| countryOfOrigin |
Germany
→
|
| dateOfLecture |
1872-10-07
→
|
| definesGeometryAs |
study of invariants of a transformation group
→
|
| emphasizes |
equivalence under transformations
→
role of symmetry in geometry → |
| field |
geometry
→
mathematics → |
| focusesOn |
classification of geometries
→
symmetry groups → transformation groups → |
| hasImpactOn |
axiomatic development of geometry
→
foundations of geometry → |
| historicalImportance |
shifted emphasis from objects to transformations
→
unified diverse geometries under a common framework → |
| influencedField |
Lie group theory
→
differential geometry → mathematical physics → modern geometry → topology → |
| namedAfter |
Erlangen
→
|
| originalLanguage |
German
→
|
| originalTitle |
Vergleichende Betrachtungen über neuere geometrische Forschungen
→
|
| presentedAt |
University of Erlangen-Nuremberg
→
|
| proposedBy |
Felix Klein
→
|
| publicationYear |
1872
→
|
| relatedConcept |
Klein geometry
→
|
| relatedTo |
Lie groups
→
homogeneous spaces → |
| timePeriod |
19th century
→
|
Referenced by (4)
| Subject (surface form when different) | Predicate |
|---|---|
|
Felix Klein
→
|
notableIdea |
|
Felix Klein
→
|
notableWork |
|
Erlangen Program
("Vergleichende Betrachtungen über neuere geometrische Forschungen")
→
|
originalTitle |
|
Erlangen Program
("Klein geometry")
→
|
relatedConcept |