Erdős–Mordell inequality


Erdős–Mordell inequality

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".

See also

* Barrow's inequality

References

cite journal
author = Claudi Alsina and Roger B. Nelsen
title = A visual proof of the Erdős-Mordell inequality
journal = Forum Geometricorum
volume = 7
pages = 99–102
year = 2007

External links

* [http://mathworld.wolfram.com/Erdos-MordellTheorem.html Erdős-Mordell Theorem] at Mathworld.


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