Cornu spiral
E730640
The Cornu spiral is a graphical representation of Fresnel integrals that forms a characteristic S-shaped curve used to analyze diffraction and wave propagation in optics and engineering.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Cornu spiral canonical | 2 |
| Euler spiral | 1 |
| Fresnel spiral | 1 |
| clothoid | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T8399553 — 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: Cornu spiral Context triple: [Fresnel integrals, usedIn, Cornu 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.
Fermat's spiral
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.
-
C.
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.
-
D.
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.
-
E.
On Spirals
On Spirals is a mathematical treatise by Archimedes in which he systematically studies the properties and applications of spiral curves, especially the Archimedean spiral.
- 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: Cornu spiral Target entity description: The Cornu spiral is a graphical representation of Fresnel integrals that forms a characteristic S-shaped curve used to analyze diffraction and wave propagation in optics and engineering.
-
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.
Fermat's spiral
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.
-
C.
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.
-
D.
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.
-
E.
On Spirals
On Spirals is a mathematical treatise by Archimedes in which he systematically studies the properties and applications of spiral curves, especially the Archimedean spiral.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
graphical representation
ⓘ
mathematical curve ⓘ tool in physical optics ⓘ |
| alsoKnownAs |
Euler spiral
ⓘ
linked to:
Cornu spiral
Fresnel spiral ⓘ
linked to:
Cornu spiral
clothoid ⓘ
linked to:
Cornu spiral
|
| coordinateSystem |
Cartesian coordinates
ⓘ
linked to:
Cartesian coordinate system
|
| definedBy | Fresnel integrals ⓘ |
| domainOfParameter | real numbers ⓘ |
| field |
civil engineering
ⓘ
mathematical physics ⓘ optics ⓘ transportation engineering ⓘ |
| hasParametricEquation |
x(t) = C(t) = ∫₀ᵗ cos(πu²/2) du
ⓘ
y(t) = S(t) = ∫₀ᵗ sin(πu²/2) du ⓘ |
| hasProperty |
approaches asymptotic points as parameter → ±∞
ⓘ
curvature proportional to arc length ⓘ curvature varies linearly with arc length ⓘ passes through the origin ⓘ smoothly varying curvature ⓘ |
| namedAfter | Alfred Cornu ⓘ |
| relatedTo |
Fresnel diffraction theory
ⓘ
Fresnel integrals C(x) and S(x) ⓘ Gaussian beam optics ⓘ spiral easement ⓘ transition curves ⓘ |
| represents | Fresnel integrals ⓘ |
| shape | S-shaped curve ⓘ |
| symmetricAbout |
both coordinate axes
ⓘ
origin ⓘ |
| usedIn |
Fresnel diffraction
ⓘ
linked to:
Fresnel diffraction theory
antenna theory ⓘ aperture diffraction calculations ⓘ computer-aided geometric design ⓘ diffraction analysis ⓘ edge diffraction calculations ⓘ engineering ⓘ highway transition curves ⓘ optical system design ⓘ physical optics ⓘ radio wave propagation ⓘ railway track transition design ⓘ robot path planning ⓘ wave propagation analysis ⓘ |
| usedTo |
construct Fresnel diffraction patterns
ⓘ
determine diffraction field amplitudes ⓘ graphically evaluate Fresnel integrals ⓘ visualize phase and amplitude variations ⓘ |
| visualizationMethod | plot of C(t) versus S(t) ⓘ |
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: Cornu spiral Description of subject: The Cornu spiral is a graphical representation of Fresnel integrals that forms a characteristic S-shaped curve used to analyze diffraction and wave propagation in optics and engineering.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Cornu spiral
linked to: Cornu spiral
linked to: Cornu spiral