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.
All labels observed (6)
| Label | Occurrences |
|---|---|
| Descartes circle | 1 |
| Descartes' circle theorem | 1 |
| Descartes' theorem on four mutually tangent circles | 1 |
| Soddy circle canonical | 1 |
| Soddy line | 1 |
| inner Soddy circle | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T8453085 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Soddy circle Context triple: [Frederick Soddy, knownFor, Soddy circle]
-
A.
Conway circle theorem
The Conway circle theorem is a geometric result in triangle geometry that identifies a special circle associated with a triangle and certain constructed points, revealing notable collinearities and concyclicity relationships.
-
B.
Malfatti
Malfatti is an Italian-origin surname notably associated with Brazilian modernist painter Anita Malfatti.
-
C.
Fermat point
The Fermat point is a special point inside a triangle that minimizes the total distance to the triangle’s three vertices.
-
D.
Cartesian circle
The Cartesian circle is a famous alleged circular reasoning in René Descartes’ Meditations, where his proof of God’s existence and his justification of clear and distinct perceptions appear to depend on each other.
-
E.
Several Circles
Several Circles is an abstract painting by Wassily Kandinsky that explores pure geometric forms and color relationships through a dynamic composition of overlapping circles.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Soddy circle Target entity description: 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.
-
A.
Conway circle theorem
The Conway circle theorem is a geometric result in triangle geometry that identifies a special circle associated with a triangle and certain constructed points, revealing notable collinearities and concyclicity relationships.
-
B.
Malfatti
Malfatti is an Italian-origin surname notably associated with Brazilian modernist painter Anita Malfatti.
-
C.
Fermat point
The Fermat point is a special point inside a triangle that minimizes the total distance to the triangle’s three vertices.
-
D.
Cartesian circle
The Cartesian circle is a famous alleged circular reasoning in René Descartes’ Meditations, where his proof of God’s existence and his justification of clear and distinct perceptions appear to depend on each other.
-
E.
Several Circles
Several Circles is an abstract painting by Wassily Kandinsky that explores pure geometric forms and color relationships through a dynamic composition of overlapping circles.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
circle
ⓘ
configuration of circles ⓘ geometric object ⓘ |
| appearsIn |
Apollonian circle packings
ⓘ
Descartes' theorem on four mutually tangent circles ⓘ
linked to:
Soddy circle
|
| canBe |
inner Soddy circle
ⓘ
linked to:
Soddy circle
outer Soddy circle ⓘ |
| definedAs | one of the four circles in a configuration of four mutually tangent circles ⓘ |
| definedBy | Descartes' circle equation for curvatures ⓘ |
| fieldOfStudy |
complex analysis (via circle inversions)
ⓘ
discrete geometry ⓘ geometry ⓘ mathematics ⓘ |
| hasAlternativeName |
Descartes circle
ⓘ
linked to:
Soddy circle
kissing circle in a Descartes configuration ⓘ |
| hasContext |
Euclidean geometry
ⓘ
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
ⓘ
linked to:
Apollonian circle packings
|
| isSolutionOf | problem of finding a circle tangent to three given mutually tangent circles ⓘ |
| namedAfter | Frederick Soddy ⓘ |
| occursWith |
Descartes configuration
ⓘ
three given mutually tangent circles ⓘ |
| relatedTo |
Apollonian gasket
ⓘ
Descartes' circle theorem ⓘ
linked to:
Soddy circle
Soddy hexlet ⓘ Soddy line ⓘ
linked to:
Soddy circle
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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Soddy circle Description of subject: 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.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Soddy circle
linked to: Soddy circle
linked to: Soddy circle
linked to: Soddy circle
linked to: Soddy circle