construction of the regular 17-gon with straightedge and compass
E29366
classical geometry problem
constructible polygon problem
geometric construction
straightedge-and-compass construction
The construction of the regular 17-gon with straightedge and compass is a classical geometric achievement, first shown possible by Carl Friedrich Gauss, that exemplifies the link between constructible polygons and number theory.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Gauss–Wantzel theorem | 1 |
| construction of the regular 17-gon with straightedge and compass canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T228927 — 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: construction of the regular 17-gon with straightedge and compass Context triple: [Carl Friedrich Gauss, notableWork, construction of the regular 17-gon with straightedge and compass]
-
A.
Mathematical Bridge
The Mathematical Bridge is a famous wooden footbridge at Queens' College, Cambridge, known for its elegant arch that is constructed entirely from straight timbers.
-
B.
Levine-Fricke Field
Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
-
C.
Carl Friedrich Gauss
Carl Friedrich Gauss was a German mathematician and physicist whose foundational contributions to number theory, geometry, statistics, and electromagnetism earned him the title "Prince of Mathematicians."
-
D.
Pascal's triangle
Pascal's triangle is a triangular array of numbers in which each entry is the sum of the two directly above it, widely used in combinatorics, algebra, and probability.
-
E.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
- 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: construction of the regular 17-gon with straightedge and compass Target entity description: The construction of the regular 17-gon with straightedge and compass is a classical geometric achievement, first shown possible by Carl Friedrich Gauss, that exemplifies the link between constructible polygons and number theory.
-
A.
Mathematical Bridge
The Mathematical Bridge is a famous wooden footbridge at Queens' College, Cambridge, known for its elegant arch that is constructed entirely from straight timbers.
-
B.
Levine-Fricke Field
Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
-
C.
Carl Friedrich Gauss
Carl Friedrich Gauss was a German mathematician and physicist whose foundational contributions to number theory, geometry, statistics, and electromagnetism earned him the title "Prince of Mathematicians."
-
D.
Pascal's triangle
Pascal's triangle is a triangular array of numbers in which each entry is the sum of the two directly above it, widely used in combinatorics, algebra, and probability.
-
E.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
classical geometry problem
ⓘ
constructible polygon problem ⓘ geometric construction ⓘ straightedge-and-compass construction ⓘ |
| hasAngleMeasure |
central angle 360°/17
ⓘ
interior angle 15·180°/17 ⓘ |
| hasConstructionType | exact construction ⓘ |
| hasEducationalUse |
example in advanced Euclidean geometry courses
ⓘ
example in algebra and number theory courses ⓘ illustration of constructible numbers ⓘ |
| hasFieldExtensionDegree | degree 8 over ℚ ⓘ |
| hasFirstProofYear | 1796 ⓘ |
| hasHistoricalSignificance |
first new regular n-gon constructible in many centuries
ⓘ
influenced development of Galois theory ⓘ revived interest in Euclidean constructions ⓘ |
| hasKeyProperty |
cos(2π/17) is a constructible number
ⓘ
sin(2π/17) is a constructible number ⓘ |
| hasKeyQuantity |
cos(2π/17)
ⓘ
sin(2π/17) ⓘ |
| hasNumberOfSides | 17 ⓘ |
| hasPolygonType | regular 17-gon ⓘ |
| hasRelatedPolygon |
regular 257-gon
ⓘ
regular 3-gon ⓘ regular 5-gon ⓘ regular 65537-gon ⓘ |
| hasRelatedResult | classification of constructible regular polygons ⓘ |
| hasStepType | angle division via algebraic relations ⓘ |
| hasSymbolicMeaning |
bridge between classical geometry and modern algebra
ⓘ
symbol of Gauss's mathematical genius ⓘ |
| isConstructible | true ⓘ |
| isDescribedIn |
Disquisitiones Arithmeticae
ⓘ
surface form:
Gauss's Disquisitiones Arithmeticae
|
| isExampleOf |
construction of the regular 17-gon with straightedge and compass
self-linksurface differs
ⓘ
surface form:
Gauss–Wantzel theorem
|
| isLinkedTo |
Galois theory
ⓘ
Gaussian periods ⓘ constructible numbers ⓘ cyclotomic fields ⓘ cyclotomic polynomial Φ₁₇(x) ⓘ number theory ⓘ roots of unity ⓘ |
| reliesOnProperty |
17 = 2^(2^2) + 1
ⓘ
17 is a Fermat prime ⓘ |
| satisfiesCriterion | n is product of a power of 2 and distinct Fermat primes ⓘ |
| usesOperation |
nested square roots
ⓘ
successive quadratic extensions ⓘ |
| usesTool |
compass
ⓘ
straightedge ⓘ |
| wasProvedPossibleBy | Carl Friedrich Gauss ⓘ |
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: construction of the regular 17-gon with straightedge and compass Description of subject: The construction of the regular 17-gon with straightedge and compass is a classical geometric achievement, first shown possible by Carl Friedrich Gauss, that exemplifies the link between constructible polygons and number theory.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
Carl Friedrich Gauss
→
notableWork
→
construction of the regular 17-gon with straightedge and compass
ⓘ
construction of the regular 17-gon with straightedge and compass
→
isExampleOf
→
construction of the regular 17-gon with straightedge and compass
self-linksurface differs
ⓘ
this entity surface form:
Gauss–Wantzel theorem