Soddy circle
E734966
A Soddy circle is one of the circles in a configuration of four mutually tangent circles, central to the geometric problem described by Descartes' circle theorem.
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
circle
ⓘ
configuration of circles ⓘ geometric object ⓘ |
| appearsIn |
Apollonian circle packings
NERFINISHED
ⓘ
Descartes' theorem on four mutually tangent circles NERFINISHED ⓘ |
| canBe |
inner Soddy circle
NERFINISHED
ⓘ
outer Soddy circle ⓘ |
| definedAs | one of the four circles in a configuration of four mutually tangent circles ⓘ |
| definedBy | Descartes' circle equation for curvatures NERFINISHED ⓘ |
| fieldOfStudy |
complex analysis (via circle inversions)
ⓘ
discrete geometry ⓘ geometry ⓘ mathematics ⓘ |
| hasAlternativeName |
Descartes circle
NERFINISHED
ⓘ
kissing circle in a Descartes configuration ⓘ |
| hasContext |
Euclidean geometry
NERFINISHED
ⓘ
circle packing theory ⓘ plane geometry ⓘ |
| hasEquationForm | (x - a)^2 + (y - b)^2 = r^2 in Cartesian coordinates ⓘ |
| hasGeneralization | higher-dimensional analogs in sphere packings ⓘ |
| hasHistoricalNote | studied by Frederick Soddy in the context of Descartes' circle theorem ⓘ |
| hasMeasure |
curvature
ⓘ
radius ⓘ |
| hasPart |
center point
ⓘ
circumference ⓘ |
| hasProperty |
center lies at intersection of two solution points from Descartes' theorem
ⓘ
curvature satisfies Descartes' circle equation ⓘ determined by three given mutually tangent circles ⓘ mutually tangent to three other circles in the configuration ⓘ part of a set of four mutually tangent circles ⓘ |
| hasSymmetry | invariant under Möbius transformations preserving the configuration ⓘ |
| isElementOf | Apollonian circle packing NERFINISHED ⓘ |
| isSolutionOf | problem of finding a circle tangent to three given mutually tangent circles ⓘ |
| namedAfter | Frederick Soddy NERFINISHED ⓘ |
| occursWith |
Descartes configuration
NERFINISHED
ⓘ
three given mutually tangent circles ⓘ |
| relatedTo |
Apollonian gasket
NERFINISHED
ⓘ
Descartes' circle theorem NERFINISHED ⓘ Soddy hexlet NERFINISHED ⓘ Soddy line NERFINISHED ⓘ kissing circles problem ⓘ |
| satisfies | k1^2 + k2^2 + k3^2 + k4^2 = 1/2 (k1 + k2 + k3 + k4)^2 ⓘ |
| usedIn |
circle packing problems
ⓘ
construction of Apollonian gasket ⓘ inversive geometry ⓘ |
| visualizedAs | one of four circles each tangent to the other three ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.