Vogel spiral
E404063
The Vogel spiral is a mathematical pattern that arranges points in a spiral using the golden angle, often used to model the optimal packing seen in sunflower seed arrangements and other natural phyllotaxis patterns.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Vogel spiral canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3987369 — 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: Vogel spiral Context triple: [Ulam spiral, relatedConcept, Vogel spiral]
-
A.
Triskelion
The Triskelion is a massive high-tech headquarters and command center used by the Marvel Universe intelligence agency S.H.I.E.L.D.
-
B.
Spiral
"Spiral" is a notable work by filmmaker Mark Burg, best known as a producer in the horror and thriller genres.
-
C.
Spiral
Spiral is a distinctive modern architectural complex in Tokyo’s Aoyama district known for its spiral ramp design and role as a cultural and commercial hub.
-
D.
Helix
Helix is a multi-launch steel roller coaster at the Liseberg amusement park in Gothenburg, Sweden, known for its intense inversions and terrain-hugging layout.
-
E.
Vogel
Vogel is a German-origin surname borne by numerous individuals, including figures in sports, arts, science, and public life.
- 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: Vogel spiral Target entity description: The Vogel spiral is a mathematical pattern that arranges points in a spiral using the golden angle, often used to model the optimal packing seen in sunflower seed arrangements and other natural phyllotaxis patterns.
-
A.
Triskelion
The Triskelion is a massive high-tech headquarters and command center used by the Marvel Universe intelligence agency S.H.I.E.L.D.
-
B.
Spiral
"Spiral" is a notable work by filmmaker Mark Burg, best known as a producer in the horror and thriller genres.
-
C.
Spiral
Spiral is a distinctive modern architectural complex in Tokyo’s Aoyama district known for its spiral ramp design and role as a cultural and commercial hub.
-
D.
Helix
Helix is a multi-launch steel roller coaster at the Liseberg amusement park in Gothenburg, Sweden, known for its intense inversions and terrain-hugging layout.
-
E.
Vogel
Vogel is a German-origin surname borne by numerous individuals, including figures in sports, arts, science, and public life.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical pattern
ⓘ
phyllotaxis model ⓘ point distribution model ⓘ |
| angleProperty | α is an irrational multiple of π ⓘ |
| angleRelation | α / 2π = 1 − 1/φ ⓘ |
| coordinateFormula |
r = c · sqrt(n)
ⓘ
θ = n · α ⓘ |
| distributionProperty |
points are quasi-uniformly distributed in a disk
ⓘ
points avoid radial alignment ⓘ points fill space without obvious gaps ⓘ |
| goal |
achieve uniform angular distribution of points
ⓘ
approximate optimal packing in circular regions ⓘ avoid long-range angular correlations ⓘ |
| hasProperty |
no preferred direction
ⓘ
radial density approximately proportional to radius ⓘ rotation-invariant distribution statistics ⓘ |
| mathematicalDomain |
computational geometry
ⓘ
discrete geometry ⓘ dynamical phyllotaxis theory ⓘ |
| models |
optimal packing patterns in nature
ⓘ
phyllotaxis ⓘ plant seed packing ⓘ sunflower seed arrangement ⓘ |
| namedAfter | Hermann Vogel NERFINISHED ⓘ |
| parameter |
c (radial scaling constant)
ⓘ
n (point index) ⓘ α (divergence angle) ⓘ |
| relatedConcept |
Archimedes' spiral
ⓘ
surface form:
Archimedean spiral
Fermat's spiral ⓘ
surface form:
Fermat spiral
low-discrepancy sequences ⓘ quasi-Monte Carlo methods ⓘ sunflower seed packing model ⓘ |
| relatedTo | golden ratio ⓘ |
| typicalAngleValue |
α = 137.5 degrees (approximate)
ⓘ
α = 2π(1 − 1/φ) ⓘ |
| usedIn |
antialiasing sample distributions
ⓘ
computer graphics ⓘ numerical integration point sets ⓘ procedural generation of natural patterns ⓘ sampling on the disk ⓘ visualization of phyllotaxis ⓘ |
| usesAngle | golden angle ⓘ |
| usesIrrationalAngle | true ⓘ |
| visualFeature |
resembles pinecone scale arrangements
ⓘ
resembles sunflower head patterns ⓘ spiral arms appear but are not explicitly constructed ⓘ |
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: Vogel spiral Description of subject: The Vogel spiral is a mathematical pattern that arranges points in a spiral using the golden angle, often used to model the optimal packing seen in sunflower seed arrangements and other natural phyllotaxis patterns.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.