Fermat's spiral
E620680
Fermat's spiral is a plane curve whose radius grows with the square root of the angle, often used to model naturally occurring spiral patterns such as those in sunflowers and other phyllotactic arrangements.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Fermat spiral | 1 |
| Fermat's spiral canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6801870 — 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: Fermat's spiral Context triple: [Archimedes' spiral, relatedConcept, Fermat's spiral]
-
A.
Archimedes' spiral
Archimedes' spiral is a classical mathematical curve that winds outward from a fixed point at a constant rate as it revolves around that point.
-
B.
Ulam spiral
The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
-
C.
Eratosthenes spiral
The Eratosthenes spiral is a geometric visualization of prime numbers generated by the sieve of Eratosthenes, arranging integers in a spiral so that primes form distinctive radial patterns.
-
D.
Vogel spiral
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.
-
E.
Bernoulli lemniscate
The Bernoulli lemniscate is a figure-eight–shaped algebraic curve that serves as a classic example in the study of complex analysis, elliptic functions, and special constants.
- 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: Fermat's spiral Target entity description: Fermat's spiral is a plane curve whose radius grows with the square root of the angle, often used to model naturally occurring spiral patterns such as those in sunflowers and other phyllotactic arrangements.
-
A.
Archimedes' spiral
Archimedes' spiral is a classical mathematical curve that winds outward from a fixed point at a constant rate as it revolves around that point.
-
B.
Ulam spiral
The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
-
C.
Eratosthenes spiral
The Eratosthenes spiral is a geometric visualization of prime numbers generated by the sieve of Eratosthenes, arranging integers in a spiral so that primes form distinctive radial patterns.
-
D.
Vogel spiral
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.
-
E.
Bernoulli lemniscate
The Bernoulli lemniscate is a figure-eight–shaped algebraic curve that serves as a classic example in the study of complex analysis, elliptic functions, and special constants.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical object
ⓘ
plane curve ⓘ spiral ⓘ |
| belongsTo | family of spirals with power-law radius-angle relation ⓘ |
| classification | algebraic spiral ⓘ |
| comparedTo |
Archimedean spiral
ⓘ
logarithmic spiral ⓘ |
| coordinateRelation | x = r cos θ, y = r sin θ with r = a√θ ⓘ |
| definedInCoordinateSystem | polar coordinates ⓘ |
| differsFrom |
Archimedean spiral where radius grows linearly with angle
ⓘ
logarithmic spiral where radius grows exponentially with angle ⓘ |
| field |
differential geometry
ⓘ
geometry ⓘ mathematical biology ⓘ |
| hasAlternativeName | parabolic spiral ⓘ |
| hasApplication |
computer graphics phyllotaxis algorithms
ⓘ
procedural generation of plant-like patterns ⓘ visualization of uniform point distributions in a disk ⓘ |
| hasAsymptoticBehavior |
radius tends to 0 as θ tends to 0
ⓘ
radius tends to infinity as θ tends to infinity ⓘ |
| hasBranch |
branch for θ ≤ 0
ⓘ
branch for θ ≥ 0 ⓘ |
| hasCurvatureBehavior | curvature decreases as θ increases ⓘ |
| hasEquation |
r = a·√θ
ⓘ
r^2 = a^2·θ ⓘ |
| hasIndependentVariable | θ (polar angle) ⓘ |
| hasParameter | a (scale parameter) ⓘ |
| hasProperty |
arms are equally spaced in angle for constant increments of θ
ⓘ
can generate nearly uniform density of points when combined with golden angle increments ⓘ often combined with golden angle for realistic phyllotaxis models ⓘ two symmetric branches with respect to the origin ⓘ |
| hasSelfIntersection | no self-intersections for θ ≠ 0 ⓘ |
| hasSymmetry | point symmetry about the origin ⓘ |
| namedAfter | Pierre de Fermat ⓘ |
| passesThroughPoint | origin ⓘ |
| powerLawExponent | 1/2 ⓘ |
| radiusGrowthLaw | radius grows with the square root of the angle ⓘ |
| relatedToConcept |
Fibonacci numbers
ⓘ
linked to:
Fibonacci sequence
golden angle ⓘ phyllotactic spirals ⓘ |
| usedInConstruction |
low-discrepancy point sets on the plane
ⓘ
sunflower seed packing models ⓘ |
| usedToModel |
arrangement of leaves
ⓘ
cactus spine patterns ⓘ phyllotaxis ⓘ pinecone scale patterns ⓘ spiral patterns in plants ⓘ sunflower seed patterns ⓘ |
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: Fermat's spiral Description of subject: Fermat's spiral is a plane curve whose radius grows with the square root of the angle, often used to model naturally occurring spiral patterns such as those in sunflowers and other phyllotactic arrangements.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Fermat's spiral