golden ratio
E337571
The golden ratio is an irrational mathematical constant, approximately 1.618, that appears in geometry, art, nature, and number theory due to its unique proportional properties.
All labels observed (5)
| Label | Occurrences |
|---|---|
| Golden Section | 1 |
| divine proportion | 1 |
| golden mean | 1 |
| golden ratio canonical | 1 |
| golden section | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3214178 — 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: golden ratio Context triple: [Fibonacci sequence, limitOfRatioOfConsecutiveTerms, golden ratio]
-
A.
Fibonacci sequence
The Fibonacci sequence is an infinite series of numbers where each term is the sum of the two preceding ones, widely used in mathematics, art, and design due to its connection with the golden ratio and natural growth patterns.
-
B.
the golden one
"The golden one" refers to El Dorado, a legendary figure or city in South American lore believed to be fabulously rich in gold and treasures.
-
C.
GOLD
GOLD is the radio call sign historically used by the British royal yacht HMY Britannia.
-
D.
Pi
Pi is a 1998 psychological thriller film directed by Darren Aronofsky that explores obsession, mathematics, and mysticism through the story of a reclusive number theorist.
-
E.
Section d'Or
Section d'Or was an influential early 20th-century French artistic group that expanded and theorized Cubism, bringing together painters, sculptors, and writers to develop and promote the movement.
- 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: golden ratio Target entity description: The golden ratio is an irrational mathematical constant, approximately 1.618, that appears in geometry, art, nature, and number theory due to its unique proportional properties.
-
A.
Fibonacci sequence
The Fibonacci sequence is an infinite series of numbers where each term is the sum of the two preceding ones, widely used in mathematics, art, and design due to its connection with the golden ratio and natural growth patterns.
-
B.
the golden one
"The golden one" refers to El Dorado, a legendary figure or city in South American lore believed to be fabulously rich in gold and treasures.
-
C.
GOLD
GOLD is the radio call sign historically used by the British royal yacht HMY Britannia.
-
D.
Pi
Pi is a 1998 psychological thriller film directed by Darren Aronofsky that explores obsession, mathematics, and mysticism through the story of a reclusive number theorist.
-
E.
Section d'Or
Section d'Or was an influential early 20th-century French artistic group that expanded and theorized Cubism, bringing together painters, sculptors, and writers to develop and promote the movement.
- F. None of above. chosen
Statements (67)
| Predicate | Object |
|---|---|
| instanceOf |
algebraic number
ⓘ
irrational number ⓘ mathematical constant ⓘ ratio ⓘ real number ⓘ |
| appearsIn |
architecture
ⓘ
art ⓘ geometry ⓘ nature ⓘ number theory ⓘ pentagon geometry ⓘ pentagram geometry ⓘ phyllotaxis ⓘ quasicrystals ⓘ |
| continuedFraction | [1; 1, 1, 1, …] ⓘ |
| decimalExpansionStartsWith | 1.6180339887498948482 ⓘ |
| defines |
golden rectangle
ⓘ
golden section ⓘ golden spiral ⓘ |
| hasAlternativeName |
golden ratio
ⓘ
surface form:
divine proportion
golden ratio ⓘ
surface form:
golden mean
golden ratio ⓘ
surface form:
golden section
|
| hasAlternativeSymbol | Φ ⓘ |
| hasApproximateFraction |
13/8
ⓘ
21/13 ⓘ 8/5 ⓘ |
| hasApproximateValue |
1.618
ⓘ
1.6180339887 ⓘ |
| hasConjugate | (1 - √5) / 2 ⓘ |
| hasConjugateName | silver ratio (in some contexts) ⓘ |
| hasExactValue | (1 + √5) / 2 ⓘ |
| hasNameOrigin | Greek letter phi ⓘ |
| hasProperty | most irrational number (in sense of continued fractions) ⓘ |
| hasReciprocal | φ - 1 ⓘ |
| hasSymbol | φ ⓘ |
| isAlgebraic | true ⓘ |
| isFixedPointOf |
x ↦ 1 + 1/x
ⓘ
x ↦ 1/(x - 1) ⓘ |
| isGreaterRootOf | x^2 - x - 1 = 0 ⓘ |
| isGreaterThan | 1 ⓘ |
| isIrrational | true ⓘ |
| isLessThan | 2 ⓘ |
| isLimitOfRatioOfConsecutiveTerms | Fibonacci sequence ⓘ |
| isMonotonicFunctionOf | square root of 5 ⓘ |
| isPositive | true ⓘ |
| isRatioOf |
diagonal to side of a regular pentagon
ⓘ
side to smaller segment in golden section division ⓘ |
| isRelatedTo |
Fibonacci sequence
ⓘ
surface form:
Binet's formula
Fibonacci sequence ⓘ
surface form:
Fibonacci numbers
Lucas numbers ⓘ plastic number ⓘ silver ratio ⓘ |
| isSolutionOf | x^2 - x - 1 = 0 ⓘ |
| isTranscendental | false ⓘ |
| isUsedAs |
example in Diophantine approximation
ⓘ
example in dynamical systems ⓘ example of worst-approximable irrational number by rationals ⓘ |
| isUsedIn |
aesthetic proportion theories
ⓘ
design ⓘ financial market technical analysis ⓘ logo design ⓘ visual arts composition ⓘ |
| reciprocalEquals | φ - 1 ⓘ |
| satisfiesEquation |
φ = 1 + 1/φ
ⓘ
φ^2 = φ + 1 ⓘ |
| simpleContinuedFraction | 1 + 1/(1 + 1/(1 + 1/(…))) ⓘ |
| squareEquals | φ + 1 ⓘ |
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: golden ratio Description of subject: The golden ratio is an irrational mathematical constant, approximately 1.618, that appears in geometry, art, nature, and number theory due to its unique proportional properties.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Golden Section
this entity surface form:
divine proportion
this entity surface form:
golden mean
this entity surface form:
golden section