The Erdos-Mordell Inequality states that for any point inside a triangle, the sum of that point's distances to the triangle's three vertices is at least twice the sum of its perpendicular distances to the triangle's three sides, with equality exactly when the triangle is equilateral and the point is its center. Named for Paul Erdos, who conjectured it, and Louis Mordell, who along with David Barrow gave the first proof, it is a well known inequality of triangle geometry.
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StatementFor any triangle ABC and point P inside it, the sum of the distances from P to the sides is at most half the sum of the distances from P to the vertices. 2 Classification
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Source Erdos-Mordell inequality, Wikipedia
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1. Wikipedia: Erdős-Mordell inequality
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
In Euclidean geometry, the Erdős-Mordell inequality states that for any triangle A B C and point P inside A B C , the sum of the distances from P to the sides is less than or equal to half of the sum of the distances from P to the vertices.
2. Erdos-Mordell inequality, Wikipedia
Lead, first sentence
In Euclidean geometry, the Erdős-Mordell inequality states that for any triangle ABC and point P inside ABC, the sum of the distances from P to the sides is less than or equal to half of the sum of the distances from P to the vertices.
History paragraph
Erdős (1935) posed the problem of proving the inequality; a proof was provided two years later by Mordell and D. F. Barrow (1937).
- In Branch: Geometry, Lead sentence
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