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. It is named after Paul Erdős and Louis Mordell. posed the problem of proving the inequality; a proof was provided two years later by Mordell and D. F. Barrow (). This solution was however not very elementary. Subsequent simpler proofs were then found by , , and .

Property Value
dbo:abstract
• 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. It is named after Paul Erdős and Louis Mordell. posed the problem of proving the inequality; a proof was provided two years later by Mordell and D. F. Barrow (). This solution was however not very elementary. Subsequent simpler proofs were then found by , , and . Barrow's inequality is a strengthened version of the Erdős–Mordell inequality in which the distances from P to the sides are replaced by the distances from P to the points where the angle bisectors of ∠APB, ∠BPC, and ∠CPA cross the sides. Although the replaced distances are longer, their sum is still less than or equal to half the sum of the distances to the vertices. (en)
dbo:thumbnail
dbo:wikiPageID
• 13006855 (xsd:integer)
dbo:wikiPageLength
• 6738 (xsd:integer)
dbo:wikiPageRevisionID
• 926095193 (xsd:integer)
dbp:first
• D. F. (en)
dbp:last
• Barrow (en)
• Mordell (en)
dbp:title
• Erdős-Mordell Theorem (en)
dbp:urlname
• Erdos-MordellTheorem (en)
dbp:wikiPageUsesTemplate
dbp:year
• 1937 (xsd:integer)
dct:subject
rdf:type
rdfs:comment
• 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. It is named after Paul Erdős and Louis Mordell. posed the problem of proving the inequality; a proof was provided two years later by Mordell and D. F. Barrow (). This solution was however not very elementary. Subsequent simpler proofs were then found by , , and . (en)
rdfs:label
• Erdős–Mordell inequality (en)
owl:sameAs
prov:wasDerivedFrom
foaf:depiction
foaf:isPrimaryTopicOf
is dbo:knownFor of
is dbo:wikiPageDisambiguates of
is dbo:wikiPageRedirects of