Pythagorean theorem
E121353
The Pythagorean theorem is a fundamental principle of geometry stating that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Pythagorean theorem canonical | 8 |
| In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1056962 — 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: Pythagorean theorem Context triple: [Euclidean space, satisfies, Pythagorean theorem]
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A.
Pythagoras
Pythagoras was an ancient Greek philosopher and mathematician best known for founding the Pythagorean school and for the Pythagorean theorem in geometry.
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B.
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.
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C.
Pythagoras of Rhegion
Pythagoras of Rhegion was an ancient Greek sculptor renowned for his realistic bronze statues and is traditionally credited with creating the famous Charioteer of Delphi.
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D.
Pyramid
Pyramid is a lightweight, flexible Python web framework designed to scale from small applications to large, complex systems while offering great configurability and extensibility.
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E.
Fibonacci sequence
The Fibonacci sequence is an infinite series of numbers where each term is the sum of the two preceding ones, widely used in mathematics, art, and design due to its connection with the golden ratio and natural growth patterns.
- 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: Pythagorean theorem Target entity description: The Pythagorean theorem is a fundamental principle of geometry stating that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
-
A.
Pythagoras
Pythagoras was an ancient Greek philosopher and mathematician best known for founding the Pythagorean school and for the Pythagorean theorem in geometry.
-
B.
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.
-
C.
Pythagoras of Rhegion
Pythagoras of Rhegion was an ancient Greek sculptor renowned for his realistic bronze statues and is traditionally credited with creating the famous Charioteer of Delphi.
-
D.
Pyramid
Pyramid is a lightweight, flexible Python web framework designed to scale from small applications to large, complex systems while offering great configurability and extensibility.
-
E.
Fibonacci sequence
The Fibonacci sequence is an infinite series of numbers where each term is the sum of the two preceding ones, widely used in mathematics, art, and design due to its connection with the golden ratio and natural growth patterns.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
geometric theorem
ⓘ
mathematical theorem ⓘ |
| appliesTo | right triangle ⓘ |
| assumes | flat (Euclidean) geometry ⓘ |
| category | fundamental theorem of elementary geometry ⓘ |
| condition | triangle must be right-angled ⓘ |
| defines | relationship between legs and hypotenuse of a right triangle ⓘ |
| dimension | 2D geometric relationship ⓘ |
| failsIn | general non-Euclidean geometries ⓘ |
| field |
Euclidean geometry
ⓘ
geometry ⓘ |
| generalizedBy |
Pythagorean identity in trigonometry
ⓘ
Pythagorean theorem in n dimensions ⓘ law of cosines ⓘ |
| hasProofCount | hundreds of known proofs ⓘ |
| historicallyAttributedTo |
Pythagoras of Samos
ⓘ
linked to:
Pythagoras
|
| holdsIn | Euclidean space ⓘ |
| hypotenuseDenotedBy | c ⓘ |
| implies |
area of square on hypotenuse equals sum of areas of squares on legs
ⓘ
c is the longest side of a right triangle ⓘ |
| knownTo |
Babylonian mathematicians
ⓘ
linked to:
Babylonians
ancient Chinese mathematicians ⓘ ancient Indian mathematicians ⓘ |
| legDenotedBy |
a
ⓘ
b ⓘ |
| proofType |
algebraic proofs
ⓘ
dissection proofs ⓘ geometric proofs ⓘ similarity-based proofs ⓘ |
| relatedConcept |
Pythagorean triple
ⓘ
distance formula ⓘ inner product ⓘ orthogonality ⓘ |
| relates | sides of a right triangle ⓘ |
| standardForm | a^2 + b^2 = c^2 ⓘ |
| statement |
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
ⓘ
linked to:
Pythagorean theorem
|
| symbolicForm | c^2 = a^2 + b^2 ⓘ |
| usedFor |
checking if a triangle is right-angled
ⓘ
computing length of a side of a right triangle ⓘ deriving Euclidean distance formula ⓘ distance calculation in the plane ⓘ |
| usedIn |
analytic geometry
ⓘ
computer graphics ⓘ engineering ⓘ navigation ⓘ physics ⓘ surveying ⓘ trigonometry ⓘ vector calculus ⓘ |
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: Pythagorean theorem Description of subject: The Pythagorean theorem is a fundamental principle of geometry stating that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
Referenced by (9)
Full triples — surface form annotated when it differs from this entity's canonical label.
Pythagorean theorem
→
statement
→
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
ⓘ
linked to: Pythagorean theorem