Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
Conformal map |
| gptkbp:alsoKnownAs |
Linear fractional transformation
|
| gptkbp:application |
gptkb:geometry
Mathematical physics Complex dynamics |
| gptkbp:category |
Rational function
|
| gptkbp:composition |
gptkb:Möbius_transformation
|
| gptkbp:definedIn |
Extended complex plane
|
| gptkbp:designer |
gptkb:Möbius_transformation
|
| gptkbp:field |
Complex analysis
|
| gptkbp:form |
f(z) = (az + b) / (cz + d)
|
| gptkbp:hasSpecialCase |
translator
Inversion Rotation Dilation |
| https://www.w3.org/2000/01/rdf-schema#label |
Möbius transformation
|
| gptkbp:mapType |
Extended complex plane to itself
|
| gptkbp:namedAfter |
gptkb:August_Ferdinand_Möbius
|
| gptkbp:parameter |
a, b, c, d ∈ ℂ, ad - bc ≠ 0
|
| gptkbp:preserves |
gptkb:Angles
Circles Lines |
| gptkbp:relatedGroup |
gptkb:Projective_linear_group_PGL(2,_ℂ)
|
| gptkbp:relatedTo |
gptkb:Riemann_sphere
Automorphism Fractional linear transformation |
| gptkbp:bfsParent |
gptkb:modular_group
|
| gptkbp:bfsLayer |
5
|