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Theorem

Heron's Formula

Geometry

Heron's Formula gives the area of a triangle purely from the lengths of its three sides, as the square root of the triangle's semiperimeter multiplied successively by the semiperimeter minus each of the three sides in turn. Named for Heron of Alexandria, who recorded it in his work Metrica, it lets a triangle's area be found without first computing an angle or an altitude, and some historians attribute an equivalent form of the result to Archimedes at an earlier date.

Facts
Classification
Statement Form
Identity or Equation 1
Proof Year
60 1
Connections

Has Statement Form

Equation, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Identity, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

In Branch

Source Heron's formula (Wikipedia)
Sources
1. Heron's formula (Wikipedia)
  • History section
    The formula is credited to Heron (or Hero) of Alexandria (fl. 60 AD), and a proof can be found in his book Metrica.
  • In Branch: Geometry, Lead sentence
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