Peano curve
E403670
The Peano curve is a space-filling fractal curve that continuously maps a one-dimensional interval onto a two-dimensional area, demonstrating that a line can completely fill a square.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Peano curve canonical | 2 |
| Lebesgue space-filling curve | 1 |
| Sierpiński curve | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3995509 — 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: Peano curve Context triple: [Giuseppe Peano, notableWork, Peano curve]
-
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.
Jordan curve theorem
The Jordan curve theorem is a fundamental result in topology stating that any simple closed curve in the plane divides the plane into exactly two distinct regions, an "inside" and an "outside."
-
D.
Menger sponge
The Menger sponge is a classic three-dimensional fractal object characterized by infinite surface area and zero volume, constructed by recursively removing cubes from a larger cube.
-
E.
Weierstrass function
The Weierstrass function is a classic example in mathematical analysis of a continuous function that is nowhere differentiable, illustrating the counterintuitive behavior possible in real-valued functions.
- 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: Peano curve Target entity description: The Peano curve is a space-filling fractal curve that continuously maps a one-dimensional interval onto a two-dimensional area, demonstrating that a line can completely fill a square.
-
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.
Jordan curve theorem
The Jordan curve theorem is a fundamental result in topology stating that any simple closed curve in the plane divides the plane into exactly two distinct regions, an "inside" and an "outside."
-
D.
Menger sponge
The Menger sponge is a classic three-dimensional fractal object characterized by infinite surface area and zero volume, constructed by recursively removing cubes from a larger cube.
-
E.
Weierstrass function
The Weierstrass function is a classic example in mathematical analysis of a continuous function that is nowhere differentiable, illustrating the counterintuitive behavior possible in real-valued functions.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
continuous surjection
ⓘ
curve in the plane ⓘ fractal curve ⓘ mathematical object ⓘ space-filling curve ⓘ |
| cardinalityOfFibers | uncountable for many points in the square ⓘ |
| codomain | [0,1]×[0,1] with the Euclidean topology ⓘ |
| demonstrates |
that a one-dimensional interval can be mapped continuously onto a two-dimensional area
ⓘ
that there exists a continuous surjection from [0,1] onto [0,1]×[0,1] ⓘ that topological dimension differs from intuitive geometric dimension ⓘ |
| dimension | 1 ⓘ |
| domain | [0,1] with the usual topology ⓘ |
| field |
fractal geometry
ⓘ
real analysis ⓘ set theory ⓘ topology ⓘ |
| hasConstruction |
iterative subdivision of the unit square into 3×3 grids
ⓘ
limit of a sequence of polygonal paths ⓘ |
| hasProperty |
fills a two-dimensional region
ⓘ
has self-intersections ⓘ image has nonempty interior ⓘ image has positive Lebesgue measure ⓘ image is compact ⓘ image is connected ⓘ image is locally connected ⓘ is a continuous surjection between compact metric spaces ⓘ is a counterintuitive example in topology ⓘ is not injective ⓘ preserves compactness ⓘ |
| introducedBy | Giuseppe Peano ⓘ |
| is |
a continuous mapping from [0,1] onto the unit square
ⓘ
a surjective mapping from [0,1] onto the unit square ⓘ nowhere differentiable almost everywhere ⓘ |
| isExampleOf |
continuous surjection that is not a homeomorphism
ⓘ
curve whose image has higher topological dimension than its domain ⓘ path whose image is a Peano continuum ⓘ |
| mapsFrom | closed interval [0,1] ⓘ |
| mapsTo | unit square [0,1]×[0,1] ⓘ |
| namedAfter | Giuseppe Peano ⓘ |
| relatedTo |
Hilbert curve
ⓘ
Peano curve self-linksurface differs ⓘ
surface form:
Lebesgue space-filling curve
Peano continuum ⓘ space-filling curves ⓘ |
| topologicalDimensionOfImage | 2 ⓘ |
| usedAs |
example in courses on fractal geometry
ⓘ
example in courses on real analysis ⓘ example in courses on topology ⓘ |
| yearProposed | 1890 ⓘ |
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: Peano curve Description of subject: The Peano curve is a space-filling fractal curve that continuously maps a one-dimensional interval onto a two-dimensional area, demonstrating that a line can completely fill a square.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Sierpiński curve
this entity surface form:
Lebesgue space-filling curve