Erdős–Mordell inequality
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In geometry, the Erdős–Mordell inequality states that for any triangle ABC and point O inside ABC, the sum of the distances from O to the sides is less than or equal to half of the sum of the distances from O to the vertices. The inequality was conjectured by Erdős as problem 3740 in the American Mathematical Monthly, 42 (1935). A proof was offered two years later by Mordell and Barrow. These solutions were however not very elementary. Subsequent simpler proofs were then found by Kazarinoff (1957) and Bankoff (1958).
The inequality can be seen as a generalization of the classical Euler inequality, by taking O the circumcenter of the triangle ABC.
[edit] See also
[edit] References
Claudi Alsina and Roger B. Nelsen (2007). "A visual proof of the Erdős-Mordell inequality". Forum Geometricorum 7: 99–102.
[edit] External links
- Erdős-Mordell Theorem at Mathworld.
