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    Erdős-Mordell Theorem

    Statement

    The Erdős-Mordell theorem states that if P is a pedal point inside a triangle ΔABC and P_A, P_B, and P_C are the feet of the perpendiculars from P upon the respective sides BC, CA, and AB, then PA + PB + PC>=2(PP_A + PP_B + PP_C).

    Alternate name

    Erdős-Mordell inequality

    History

    formulation date | 1935 (90 years ago) formulator | Paul Erdős status | proved proof date | 1937 (2 years later) (88 years ago) provers | Louis Joel Mordell | David Francis Barrow additional people involved | Donat Kazarinoff | Leon Bankoff

    Associated equation

    PA + PB + PC>=2(PP_A + PP_B + PP_C)

    Current evidence

    Elementary proofs were obtained by Kazarinoff and Bankoff.

    Classes

    solved mathematics problems | mathematics theorems

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