Thales’ theorem

E403439

geometric theorem result in Euclidean geometry

Thales’ theorem is a fundamental result in Euclidean geometry stating that any angle inscribed in a semicircle is a right angle.

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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.
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
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 ⓘ Theorem of Thales ⓘ linked to: Thales’ theorem
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

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Thales of Miletus → knownFor → Thales’ theorem ⓘ

Thales of Miletus → attributedDiscovery → Thales’ theorem in geometry ⓘ

linked to: Thales’ theorem

Thales’ theorem → languageVariant → Theorem of Thales ⓘ