Erlangen Program

E50327
framework for classifying geometries mathematical program research program in geometry

The Erlangen Program is Felix Klein’s influential 1872 framework that classifies and studies geometries based on their underlying symmetry groups and transformation properties.

Try in SPARQL Jump to: Surface forms Statements Referenced by

All labels observed (4)

Label Occurrences
Erlangen Program canonical 2
Felix Klein's Erlangen program 2
Klein geometry 1

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 space ⓘ
surface form: 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 theory ⓘ
surface form: Lie group theory

differential geometry ⓘ
mathematical physics ⓘ
modern geometry ⓘ
topology ⓘ
namedAfter Erlangen ⓘ
originalLanguage German ⓘ
originalTitle Erlangen Program self-linksurface differs ⓘ
surface form: Vergleichende Betrachtungen über neuere geometrische Forschungen
presentedAt University of Erlangen-Nuremberg ⓘ
proposedBy Felix Klein ⓘ
publicationYear 1872 ⓘ
relatedConcept Erlangen Program self-linksurface differs ⓘ
surface form: Klein geometry
relatedTo Lie group ⓘ
surface form: Lie groups

homogeneous spaces ⓘ
timePeriod 19th century ⓘ

Referenced by (6)

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

Felix Klein → notableWork → Erlangen Program ⓘ
Felix Klein → notableIdea → Erlangen Program ⓘ
Erlangen Program → originalTitle → Erlangen Program self-linksurface differs ⓘ
this entity surface form: Vergleichende Betrachtungen über neuere geometrische Forschungen
Erlangen Program → relatedConcept → Erlangen Program self-linksurface differs ⓘ
this entity surface form: Klein geometry
Theorie der Transformationsgruppen → influencedBy → Erlangen Program ⓘ
this entity surface form: Felix Klein's Erlangen program
"Invariante Variationsprobleme" → relatedTo → Erlangen Program ⓘ
subject surface form: Invariante Variationsprobleme
this entity surface form: Felix Klein's Erlangen program