MathDB
Unit square cut into m quadrilaterals inequality

Source: Baltic Way 2009

November 27, 2010
inequalitiesgeometrygeometry proposed

Problem Statement

A unit square is cut into mm quadrilaterals Q1,…,QmQ_1,\ldots ,Q_m. For each i=1,…,mi=1,\ldots ,m let SiS_i be the sum of the squares of the four sides of QiQ_i. Prove that S1+…+Sm≥4S_1+\ldots +S_m\ge 4
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