Thales’ theorem
E403439
Thales’ theorem is a fundamental result in Euclidean geometry stating that any angle inscribed in a semicircle is a right angle.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Thales’ theorem canonical | 1 |
| Thales’ theorem in geometry | 1 |
| Theorem of Thales | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3978808 — 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: Thales’ theorem Context triple: [Thales of Miletus, knownFor, Thales’ theorem]
-
A.
Pythagorean theorem
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.
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B.
Pythagoreio
Pythagoreio is a historic coastal town and popular tourist resort on the Greek island of Samos, known for its ancient harbor and archaeological sites.
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C.
Fermat point
The Fermat point is a special point inside a triangle that minimizes the total distance to the triangle’s three vertices.
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D.
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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E.
Tusi couple
The Tusi couple is a geometric device from medieval Islamic astronomy that generates linear motion from the sum of two circular motions, later influencing Copernican models of planetary motion.
- 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: Thales’ theorem Target entity description: Thales’ theorem is a fundamental result in Euclidean geometry stating that any angle inscribed in a semicircle is a right angle.
-
A.
Pythagorean theorem
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.
-
B.
Pythagoreio
Pythagoreio is a historic coastal town and popular tourist resort on the Greek island of Samos, known for its ancient harbor and archaeological sites.
-
C.
Fermat point
The Fermat point is a special point inside a triangle that minimizes the total distance to the triangle’s three vertices.
-
D.
Pythagoras
Pythagoras was an ancient Greek philosopher and mathematician best known for founding the Pythagorean school and for the Pythagorean theorem in geometry.
-
E.
Tusi couple
The Tusi couple is a geometric device from medieval Islamic astronomy that generates linear motion from the sum of two circular motions, later influencing Copernican models of planetary motion.
- F. None of above. chosen
Statements (33)
| Predicate | Object |
|---|---|
| instanceOf |
geometric theorem
ⓘ
result in Euclidean geometry ⓘ |
| angleType | right angle ⓘ |
| appliesTo | all points on a semicircle except the endpoints of the diameter ⓘ |
| condition |
The sides of the angle must pass through the endpoints of a diameter
ⓘ
The vertex of the angle must lie on the circle ⓘ |
| consequence | The diameter of a circle is the hypotenuse of any right triangle inscribed in the circle ⓘ |
| field | Euclidean geometry ⓘ |
| geometricConfiguration | triangle with hypotenuse as diameter of a circle ⓘ |
| hasGeneralization | inscribed angle theorem for arbitrary arcs ⓘ |
| historicalAttribution | traditionally attributed to Thales of Miletus ⓘ |
| implies | If a triangle is inscribed in a circle with one side as a diameter, then the triangle is right-angled ⓘ |
| involvesConcept |
circle
ⓘ
diameter ⓘ inscribed angle ⓘ right triangle ⓘ semicircle ⓘ |
| languageVariant |
Thales’s theorem
ⓘ
Thales’ theorem self-linksurface differs ⓘ
surface form:
Theorem of Thales
|
| level | elementary geometry ⓘ |
| namedAfter | Thales of Miletus ⓘ |
| proofMethod |
can be proved using properties of inscribed angles
ⓘ
can be proved using similar triangles ⓘ |
| relatedTo |
Pythagorean theorem
ⓘ
circle theorems ⓘ inscribed angle theorem ⓘ |
| statement |
Any angle inscribed in a semicircle is a right angle
ⓘ
If A and B are endpoints of a diameter of a circle and C is any other point on the circle, then angle ACB is a right angle ⓘ |
| taughtIn | secondary school mathematics ⓘ |
| timePeriodAttributed | 6th century BCE ⓘ |
| usedFor |
constructing right angles
ⓘ
proving properties of circles ⓘ proving triangles are right-angled ⓘ |
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: Thales’ theorem Description of subject: Thales’ theorem is a fundamental result in Euclidean geometry stating that any angle inscribed in a semicircle is a right angle.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Thales’ theorem in geometry
this entity surface form:
Theorem of Thales