Archimedes' spiral
E156204
Archimedes' spiral is a classical mathematical curve that winds outward from a fixed point at a constant rate as it revolves around that point.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Archimedean spiral | 4 |
| Archimedes' spiral canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1358742 — 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: Archimedes' spiral Context triple: [Archimedes, knownFor, Archimedes' spiral]
-
A.
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.
-
B.
Crescent
Crescent is a long-distance Amtrak passenger train that runs between New York City and New Orleans, serving major cities along the U.S. East Coast and Deep South.
-
C.
Arago ring
The Arago ring is a faint, narrow planetary ring encircling Neptune, named after the French astronomer François Arago.
-
D.
Cone
Cone is a surname most notably associated with David Cone, a former Major League Baseball pitcher and five-time World Series champion.
-
E.
Spiral (album)
Spiral is a 1977 electronic music album by Greek composer Vangelis, known for its synthesizer-driven, space-themed soundscapes and innovative use of electronic instrumentation.
- 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: Archimedes' spiral Target entity description: Archimedes' spiral is a classical mathematical curve that winds outward from a fixed point at a constant rate as it revolves around that point.
-
A.
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.
-
B.
Crescent
Crescent is a long-distance Amtrak passenger train that runs between New York City and New Orleans, serving major cities along the U.S. East Coast and Deep South.
-
C.
Arago ring
The Arago ring is a faint, narrow planetary ring encircling Neptune, named after the French astronomer François Arago.
-
D.
Cone
Cone is a surname most notably associated with David Cone, a former Major League Baseball pitcher and five-time World Series champion.
-
E.
Spiral (album)
Spiral is a 1977 electronic music album by Greek composer Vangelis, known for its synthesizer-driven, space-themed soundscapes and innovative use of electronic instrumentation.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical curve
ⓘ
plane curve ⓘ spiral ⓘ |
| appearsIn | classical Greek mathematics ⓘ |
| category |
curves defined by polar equations
ⓘ
spiral curves ⓘ |
| contrastedWith | logarithmic spiral ⓘ |
| definedIn | polar coordinates ⓘ |
| hasCoordinateRepresentation |
x(θ) = (a + bθ) cos θ
ⓘ
y(θ) = (a + bθ) sin θ ⓘ |
| hasIndependentVariable | θ (polar angle) ⓘ |
| hasParameter |
a (radial offset)
ⓘ
b (growth rate of radius with angle) ⓘ |
| hasPolarEquation |
r = a + bθ
ⓘ
r = kθ ⓘ |
| hasProperty |
angle between radius vector and tangent varies with θ
ⓘ
can be traced by a point moving with constant linear speed in radial direction and constant angular speed ⓘ curvature varies with angle ⓘ distance between successive turns equals 2πb ⓘ distance between successive turns is constant ⓘ equidistant spiral ⓘ not self-intersecting for θ in a monotone interval ⓘ passes through origin when θ = 0 for r = kθ ⓘ radius increases linearly with angle ⓘ unbounded curve ⓘ |
| hasSpecialCase | r = θ ⓘ |
| hasSymmetry | rotational symmetry about its pole ⓘ |
| liesIn |
Euclidean plane
ⓘ
linked to:
Euclidean geometry
|
| namedAfter |
Archimedes of Syracuse
ⓘ
linked to:
Archimedes
|
| relatedConcept |
Fermat's spiral
ⓘ
equiangular spiral ⓘ hyperbolic spiral ⓘ |
| studiedBy | Archimedes ⓘ |
| usedFor |
squaring the circle (classical constructions)
ⓘ
trisecting an angle (classical constructions) ⓘ |
| usedIn |
cam design
ⓘ
graphical design and art ⓘ mathematical analysis of spirals ⓘ mechanical engineering ⓘ optical devices ⓘ path planning and motion control ⓘ phonograph recording technology ⓘ scroll compressors ⓘ spiral antennas ⓘ |
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: Archimedes' spiral Description of subject: Archimedes' spiral is a classical mathematical curve that winds outward from a fixed point at a constant rate as it revolves around that point.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Archimedes' spiral
linked to: Archimedes' spiral
linked to: Archimedes' spiral
linked to: Archimedes' spiral