Khinchin–Lévy constant
E381487
The Khinchin–Lévy constant is a mathematical constant arising in metric number theory and continued fractions, describing the typical exponential growth rate of the denominators of convergents for almost all real numbers.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Khinchin–Lévy constant canonical | 2 |
| Lévy's constant | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3677823 — 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: Khinchin–Lévy constant Context triple: [Aleksandr Khinchin, notableWork, Khinchin–Lévy constant]
-
A.
Khinchin's constant
Khinchin's constant is a mathematical constant that arises in metric number theory, describing the almost-sure geometric mean of the partial quotients in the continued fraction expansions of real numbers.
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B.
Khinchin–Kolmogorov theorem
The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.
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C.
Khinchin's law of the iterated logarithm
Khinchin's law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuations of partial sums of independent random variables on the scale of the square root of twice the product of their variance and the iterated logarithm of the sample size.
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D.
Khinchin's representation theorem
Khinchin's representation theorem is a result in probability theory that characterizes stationary stochastic processes by representing them in terms of simpler, more fundamental random components.
-
E.
Khinchin
Khinchin is a Russian surname most notably associated with Aleksandr Khinchin, a prominent mathematician known for his contributions to probability theory and number theory.
- 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: Khinchin–Lévy constant Target entity description: The Khinchin–Lévy constant is a mathematical constant arising in metric number theory and continued fractions, describing the typical exponential growth rate of the denominators of convergents for almost all real numbers.
-
A.
Khinchin's constant
Khinchin's constant is a mathematical constant that arises in metric number theory, describing the almost-sure geometric mean of the partial quotients in the continued fraction expansions of real numbers.
-
B.
Khinchin–Kolmogorov theorem
The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.
-
C.
Khinchin's law of the iterated logarithm
Khinchin's law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuations of partial sums of independent random variables on the scale of the square root of twice the product of their variance and the iterated logarithm of the sample size.
-
D.
Khinchin's representation theorem
Khinchin's representation theorem is a result in probability theory that characterizes stationary stochastic processes by representing them in terms of simpler, more fundamental random components.
-
E.
Khinchin
Khinchin is a Russian surname most notably associated with Aleksandr Khinchin, a prominent mathematician known for his contributions to probability theory and number theory.
- F. None of above. chosen
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical constant
ⓘ
number theory constant ⓘ |
| appearsIn |
metric theory of continued fractions
ⓘ
probabilistic properties of continued fractions ⓘ |
| appliesTo | almost all real numbers ⓘ |
| approximateSquare | 10.7350 ⓘ |
| approximateValue |
3.2758
ⓘ
3.275822918721811 ⓘ |
| belongsTo | real numbers ⓘ |
| category |
constants in number theory
ⓘ
constants related to continued fractions ⓘ |
| definition | exp(π² / (12 ln 2)) ⓘ |
| describes | typical exponential growth rate of denominators of convergents ⓘ |
| discoveredBy |
Aleksandr Khinchin
ⓘ
Paul Lévy ⓘ |
| field |
continued fractions
ⓘ
metric number theory ⓘ |
| governs | typical growth rate of q_n in continued fraction expansions ⓘ |
| growthType | exponential growth constant for denominators of convergents ⓘ |
| hasFormula | L = exp(π² / (12 ln 2)) ⓘ |
| hasProperty | independent of the particular real number for almost all reals ⓘ |
| isIrrational | true ⓘ |
| isTranscendental | unknown ⓘ |
| limitProperty | for almost all real x, lim_{n→∞} (q_n)^{1/n} = L where q_n are denominators of convergents of x ⓘ |
| logarithmBase10 | 0.5153205 ⓘ |
| namedAfter |
Aleksandr Khinchin
ⓘ
Paul Lévy ⓘ |
| notEqualTo | Khinchin's constant ⓘ |
| occursIn |
asymptotic behavior of continued fraction denominators
ⓘ
metric Diophantine approximation ⓘ |
| relatedConcept |
ergodic theorem
ⓘ
surface form:
Birkhoff ergodic theorem
Gauss map ⓘ |
| relatedTo |
Gauss–Kuzmin distribution
ⓘ
Khinchin's constant ⓘ continued fraction expansion of real numbers ⓘ denominators of convergents ⓘ ergodic theory of the Gauss map ⓘ |
| symbol | L ⓘ |
| typicalityQualifier | holds for Lebesgue-almost-every real number ⓘ |
| usedIn | probabilistic analysis of continued fraction expansions ⓘ |
| yearOfIntroduction | 1930s ⓘ |
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: Khinchin–Lévy constant Description of subject: The Khinchin–Lévy constant is a mathematical constant arising in metric number theory and continued fractions, describing the typical exponential growth rate of the denominators of convergents for almost all real numbers.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Aleksandr Khinchin
this entity surface form:
Lévy's constant