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. Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position The inequality was conjectured by Erdős as problem 3740 in the American Mathematical Monthly, 42 (1935). Paul Erdős ( Hungarian: Erdős Pál, in English occasionally Paul Erdos or Paul Erdös, March 26, 1913 &ndash The American Mathematical Monthly ( is a mathematical journal founded by Benjamin Finkel in 1894. A proof was offered two years later by Mordell and Barrow. Louis Joel Mordell ( 28 January 1888 - 12 March 1972) was a British mathematician known for pioneering research in Number theory. 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. In Geometry, Euler's theorem, named after Leonhard Euler, states that the distance d between the Circumcentre and Incentre of a
See also
References
Claudi Alsina and Roger B. In Geometry, Barrow's inequality states the following Let P be a point inside the Triangle ABC, U, V, and W Nelsen (2007). "A visual proof of the Erdős-Mordell inequality". Forum Geometricorum 7: 99–102.
External links
- Erdős-Mordell Theorem at Mathworld.
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