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Erlangen program

In mathematics, the Erlangen program is a method of characterizing geometries based on group theory and projective geometry. It was published by Felix Klein in 1872 as Vergleichende Betrachtungen über neuere geometrische Forschungen. It is named after the University Erlangen-Nürnberg, where Klein worked.

Works, Influence on later work & Abstract returns from the Erlangen program

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Influence on later work

Congruence (geometry)SymmetryPhysicsTopologyHomeomorphism
16 related topics

Abstract returns from the Erlangen program

IsomorphicAutomorphism groupOrientedReflectionsElliptic geometries
29 related topics

The problems of nineteenth century geometry

EuclidEuclidean spacePlane geometrySolid geometryFour or more dimensions
15 related topics

Homogeneous spaces

Homogeneous spacesLie groupsClassical groupsProjective spaceGeneral linear group
11 related topics

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The problems of nineteenth century geometry

Homogeneous spaces

Influence on later work

Abstract returns from the Erlangen program

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Erlangen program

Nodes99
Edges98
Triples60
Avg. degree1.98
Density0.020202
Components1

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Erlangen program

Top relations

related to References · 40
Erlangen program → Also, Athanase Papadopoulos, Cartan's, Complete English Translation, Differential, Differential Geometry, Dover, EMS Press, Encyclopedia, Erlangen, European Mathematical Society Publishing, Felix, Felix Klein, Forschungen, Gesammelte Abh, Heinrich Guggenheimer, Historia Mathematica, History, House, IRMA Lectures
related to Influence on later work · 10
Erlangen program → Books, Coxeter, Erlangen, Euclid, In, Klein, Lie, Of, The, When
related to Abstract returns from the Erlangen program · 8
Erlangen program → Erlangen, Euclidean, It, One, Quite, SO, There, These
is a · 1
Erlangen program → method of characterizing geometries based on group theory and projective geometry

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Important terminology

geometry group geometries klein program projective erlangen groups physics isomorphic spaces euclidean affine mathematics way symmetry example idea felix transformations

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Erlangen programis amethod of characterizing geometries based on group theory and projective geometry0.90text
those by H.S.Minstance ofBooks0.80text
Erlangen programrelated to Abstract returns from the Erlangen programQuite0.60section
Erlangen programrelated to Abstract returns from the Erlangen programThere0.60section
Erlangen programrelated to Abstract returns from the Erlangen programErlangen0.60section
Erlangen programrelated to Abstract returns from the Erlangen programOne0.60section
Erlangen programrelated to Abstract returns from the Erlangen programEuclidean0.60section
Erlangen programrelated to Abstract returns from the Erlangen programSO0.60section
Erlangen programrelated to Abstract returns from the Erlangen programThese0.60section
Erlangen programrelated to Abstract returns from the Erlangen programIt0.60section
Erlangen programrelated to Influence on later workThe0.60section
Erlangen programrelated to Influence on later workErlangen0.60section

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