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Cayley–Klein metric

In mathematics, a Cayley–Klein metric is a metric on the complement of a fixed quadric in a projective space which is defined using a cross-ratio. The construction originated with Arthur Cayley's essay "On the theory of distance" where he calls the quadric the absolute. The construction was developed in further detail by Felix Klein in papers in 1871 and…

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Overview

Foundations

Cross ratio and distance

Disk applications

Special relativity

Affine CK-geometry

History

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Cayley–Klein metric

Nodes69
Edges68
Triples28
Avg. degree1.97
Density0.028986
Components1

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Cayley–Klein metric

Top relations

related to Foundations · 20
Cayley–Klein metric → Another, Beltrami, Cayley, Cayley's, Edmond Laguerre, Euclidean, Eventually, For, In, Indeed, It, Karl, Klein, Laguerre, Poincaré, Similarly, Staudt, Staudt's, The, This
related to Cross ratio and distance · 7
Cayley–Klein metric → Cayley, Furthermore, In, Klein, Ordinarily, Start, The
is a · 1
Cayley–Klein metric → metric on the complement of a fixed quadric in a projective space which is defined using a cross-ratio

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Important terminology

geometry klein cayley metric absolute distance hyperbolic logarithm circle homography projective space ratio invariant line non-euclidean unit real motions disk

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cayley–Klein metricis ametric on the complement of a fixed quadric in a projective space which is defined using a cross-ratio0.90text
Cayley–Klein metricrelated to Cross ratio and distanceCayley0.60section
Cayley–Klein metricrelated to Cross ratio and distanceKlein0.60section
Cayley–Klein metricrelated to Cross ratio and distanceOrdinarily0.60section
Cayley–Klein metricrelated to Cross ratio and distanceStart0.60section
Cayley–Klein metricrelated to Cross ratio and distanceIn0.60section
Cayley–Klein metricrelated to Cross ratio and distanceThe0.60section
Cayley–Klein metricrelated to Cross ratio and distanceFurthermore0.60section
Cayley–Klein metricrelated to FoundationsThe0.60section
Cayley–Klein metricrelated to FoundationsKarl0.60section
Cayley–Klein metricrelated to FoundationsStaudt0.60section
Cayley–Klein metricrelated to FoundationsAnother0.60section

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