Gauss’s constant
E29371
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Gauss's constant | 2 |
| G for Gauss's constant | 1 |
| Gauss’s constant canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T228961 — 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: Gauss’s constant Context triple: [Carl Friedrich Gauss, hasConceptNamedAfter, Gauss’s constant]
-
A.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
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B.
Newtonian gravitational constant G
The Newtonian gravitational constant G is the fundamental physical constant that quantifies the strength of gravitational attraction between masses in classical and relativistic theories of gravity.
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C.
Carl Friedrich Gauss
Carl Friedrich Gauss was a German mathematician and physicist whose foundational contributions to number theory, geometry, statistics, and electromagnetism earned him the title "Prince of Mathematicians."
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D.
Aitken
Aitken is a Scottish-origin surname notably borne by Max Aitken, 1st Baron Beaverbrook, a prominent Canadian-British newspaper magnate and politician.
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E.
Levine-Fricke Field
Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
- 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: Gauss’s constant Target entity description: Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
-
A.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
-
B.
Newtonian gravitational constant G
The Newtonian gravitational constant G is the fundamental physical constant that quantifies the strength of gravitational attraction between masses in classical and relativistic theories of gravity.
-
C.
Carl Friedrich Gauss
Carl Friedrich Gauss was a German mathematician and physicist whose foundational contributions to number theory, geometry, statistics, and electromagnetism earned him the title "Prince of Mathematicians."
-
D.
Aitken
Aitken is a Scottish-origin surname notably borne by Max Aitken, 1st Baron Beaverbrook, a prominent Canadian-British newspaper magnate and politician.
-
E.
Levine-Fricke Field
Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
- F. None of above. chosen
Statements (36)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical constant
ⓘ
number-theoretic constant ⓘ |
| appearsIn |
arithmetic–geometric mean identities
ⓘ
theory of elliptic integrals ⓘ theory of theta functions ⓘ |
| approximateValue |
0.8346268
ⓘ
0.834626841674073186281429732799046808 ⓘ |
| catalogCode | OEIS A064988 ⓘ |
| context |
classical analysis
ⓘ
elliptic curves over the complex numbers ⓘ modular forms ⓘ |
| definedAs |
1/(2^{1/4}·K(1/√2))
ⓘ
2^{-1/4}·K(1/√2)^{-1} ⓘ |
| definedVia |
arithmetic–geometric mean identities
ⓘ
surface form:
arithmetic–geometric mean
|
| field |
complex analysis
ⓘ
elliptic function theory ⓘ number theory ⓘ theory of the lemniscate ⓘ |
| hasType | transcendental constant (conjectured) ⓘ |
| namedAfter | Carl Friedrich Gauss ⓘ |
| namedInHonorOf | Carl Friedrich Gauss ⓘ |
| occursIn |
special values of elliptic integrals
ⓘ
special values of modular functions ⓘ |
| property |
dimensionless quantity
ⓘ
positive real number ⓘ |
| relatedCurve | Bernoulli lemniscate ⓘ |
| relatedFunction | complete elliptic integral of the first kind ⓘ |
| relatedTo |
arithmetic–geometric mean identities
ⓘ
surface form:
Gaussian arithmetic–geometric mean
arithmetic–geometric mean of 1 and √2 ⓘ elliptic modulus k = 1/√2 ⓘ lemniscatic constant ⓘ lemniscatic elliptic functions ⓘ singular modulus of order 4 ⓘ |
| symbol | G ⓘ |
| usedIn |
evaluation of certain definite integrals
ⓘ
evaluation of periods of the lemniscate ⓘ |
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: Gauss’s constant Description of subject: Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Gauss's constant
this entity surface form:
Gauss's constant
this entity surface form:
G for Gauss's constant