Random Curves
E831067
Random Curves is a mathematics book by Neal Koblitz that explores probabilistic and heuristic methods in number theory and algebraic geometry, particularly in relation to elliptic curves and cryptographic applications.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Random Curves canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9931759 — 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: Random Curves Context triple: [Neal Koblitz, authorOf, Random Curves]
-
A.
Peano curve
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.
-
B.
Bezier curves
Bézier curves are mathematically defined parametric curves widely used in computer graphics and digital design to model smooth, scalable shapes and paths.
-
C.
Page curve
The Page curve is a theoretical prediction in black hole physics that describes how the entanglement entropy of Hawking radiation should rise and then fall over time if black hole evaporation is ultimately unitary.
-
D.
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.
-
E.
"On types of knotted curves"
"On types of knotted curves" is a 1926 mathematical paper by J. W. Alexander and G. B. Briggs that introduced a systematic classification and notation for mathematical knots.
- 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: Random Curves Target entity description: Random Curves is a mathematics book by Neal Koblitz that explores probabilistic and heuristic methods in number theory and algebraic geometry, particularly in relation to elliptic curves and cryptographic applications.
-
A.
Peano curve
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.
-
B.
Bezier curves
Bézier curves are mathematically defined parametric curves widely used in computer graphics and digital design to model smooth, scalable shapes and paths.
-
C.
Page curve
The Page curve is a theoretical prediction in black hole physics that describes how the entanglement entropy of Hawking radiation should rise and then fall over time if black hole evaporation is ultimately unitary.
-
D.
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.
-
E.
"On types of knotted curves"
"On types of knotted curves" is a 1926 mathematical paper by J. W. Alexander and G. B. Briggs that introduced a systematic classification and notation for mathematical knots.
- F. None of above. chosen
Statements (31)
| Predicate | Object |
|---|---|
| instanceOf | mathematics book ⓘ |
| author | Neal Koblitz ⓘ |
| countryOfPublication |
United States
ⓘ
linked to:
United States of America
|
| explores |
connections between number theory and cryptography
ⓘ
random models for curves over finite fields ⓘ |
| field |
algebraic geometry
ⓘ
cryptography ⓘ number theory ⓘ |
| focusesOn |
applications to cryptographic security
ⓘ
heuristics for elliptic curve behavior ⓘ probabilistic models in number theory ⓘ |
| genre | non-fiction ⓘ |
| hasAuthor | Neal Koblitz ⓘ |
| hasFormat |
ebook
ⓘ
print ⓘ |
| intendedAudience |
graduate students
ⓘ
researchers ⓘ |
| language | English ⓘ |
| publisher | Springer ⓘ |
| series | Universitext ⓘ |
| subjectArea |
applied number theory
ⓘ
mathematical cryptography ⓘ mathematics ⓘ |
| topic |
Diophantine equations
ⓘ
computational number theory ⓘ congruences ⓘ distribution of rational points ⓘ elliptic curve cryptography ⓘ elliptic curves ⓘ heuristic methods ⓘ probabilistic methods ⓘ |
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: Random Curves Description of subject: Random Curves is a mathematics book by Neal Koblitz that explores probabilistic and heuristic methods in number theory and algebraic geometry, particularly in relation to elliptic curves and cryptographic applications.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.