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
In Branch
Source Wolfram MathWorld: Viviani's Theorem
Principal Result Of
Source Viviani's theorem, Wikipedia
Proved By
Source Viviani's theorem, Wikipedia
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 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.
Proved By: Vincenzo Viviani, Lead 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.
Principal Result Of: Vincenzo Viviani, Lead sentence of the article on the result
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.
View the SourceWolfram MathWorld: Viviani's Theorem
Wolfram MathWorldIn Branch: Geometry, Subject classificationsQuote, In Branch: Geometry, Subject classifications
Geometry Plane Geometry
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