Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
Photogrammetry
Conformal mappings Perspective drawing Harmonic division |
| gptkbp:defines |
Four collinear points
|
| gptkbp:field |
gptkb:Mathematics
gptkb:Projective_geometry |
| gptkbp:form |
(AC/BC) / (AD/BD)
|
| gptkbp:generalizes |
Ratio of distances
|
| gptkbp:hasInvariant |
gptkb:Projective_transformations
|
| https://www.w3.org/2000/01/rdf-schema#label |
Cross-ratio
|
| gptkbp:introduced |
gptkb:August_Ferdinand_Möbius
|
| gptkbp:notation |
CR(A, B; C, D)
|
| gptkbp:property |
Permutation of points gives six possible values
Remains unchanged under projective maps Takes real or complex values Takes value -1 for harmonic conjugate quadruple Takes value 1 for harmonic quadruple |
| gptkbp:relatedTo |
gptkb:Möbius_transformation
Projective line Harmonic conjugate |
| gptkbp:symbol |
(A, B; C, D)
|
| gptkbp:used_in |
gptkb:geometry
Computer vision Complex analysis |
| gptkbp:bfsParent |
gptkb:Linear_Fractional_Transformation
gptkb:Möbius_Transformation |
| gptkbp:bfsLayer |
8
|