Viviani's Theorem states that for any point inside an equilateral triangle, the sum of the perpendicular distances from that point to the triangle's three sides equals the triangle's own height, regardless of where inside the triangle the point lies. Named for Vincenzo Viviani, it is a classical and easily visualized result of elementary geometry, and the constant sum it identifies equals the length of any one of the triangle's altitudes.
Facts
StatementThe sum of the shortest distances from any interior point to the sides of an equilateral triangle equals the length of the triangle's altitude. 2 Classification
Statement Form Connections
Has Statement Form
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.
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.
Sources
1. Wikipedia: Viviani's theorem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
Viviani's theorem, named after Vincenzo Viviani, states that the sum of the shortest distances from any interior point to the sides of an equilateral triangle equals the length of the triangle's altitude.
2. Viviani's theorem, Wikipedia
Lead, first sentenceQuote, Lead, first sentence
Viviani's theorem, named after Vincenzo Viviani, states that the sum of the shortest distances from any interior point to the sides of an equilateral triangle equals the length of the triangle's altitude.
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