|
gptkbp:instanceOf
|
gptkb:mathematical_concept
|
|
gptkbp:actsOn
|
gptkb:Riemann_sphere
extended complex plane
|
|
gptkbp:alsoKnownAs
|
linear fractional transformations
|
|
gptkbp:application
|
gptkb:geometry
gptkb:hyperbolic_geometry
dynamical systems
mathematical physics
conformal mapping
complex dynamics
|
|
gptkbp:class
|
elliptic
hyperbolic
parabolic
loxodromic
|
|
gptkbp:condition
|
ad - bc ≠ 0
|
|
gptkbp:field
|
complex analysis
|
|
gptkbp:fixes
|
at most two points
|
|
gptkbp:form
|
(az + b)/(cz + d)
|
|
gptkbp:hasSpecialCase
|
translator
dilation
rotation
inversion
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Möbius transformations
|
|
gptkbp:inverseForm
|
(dz - b)/(-cz + a)
|
|
gptkbp:invertible
|
yes
|
|
gptkbp:namedAfter
|
gptkb:August_Ferdinand_Möbius
|
|
gptkbp:parameter
|
a, b, c, d complex numbers
|
|
gptkbp:preserves
|
angles
circles
lines
|
|
gptkbp:relatedGroup
|
gptkb:projective_linear_group_PGL(2,_C)
|
|
gptkbp:relatedTo
|
gptkb:geometry
gptkb:SL(2,_C)
fractional linear transformation
automorphism of the Riemann sphere
|
|
gptkbp:type
|
conformal map
|
|
gptkbp:usedIn
|
gptkb:quantum_field_theory
gptkb:Teichmüller_theory
gptkb:data_visualization
gptkb:stereographic_projection
modular forms
function theory
Kleinian groups
complex projective geometry
mapping of circles and lines
|
|
gptkbp:bfsParent
|
gptkb:Modular_group
gptkb:Poincaré_metric
gptkb:conformal_geometry
gptkb:conformal_transformation
gptkb:Riemann_sphere
|
|
gptkbp:bfsLayer
|
6
|