Category: Mathematics

Every trangle including a unit square in an orthogonal lattice has the lattice point covering property.

Let ABC be a triangle and an interior point M. We denote by AM =x₁, BM = x₂, CM = x₃. The distances of the point M from BC, CA, AB are denoted by p₁, p₂, p₃. Erdos-Mordell inequality asserts:

x₁ + x₂ + x₃ no less than 2[p₁ + p₂ + p₃]

The above problem proposed by P.Erdos in the American Mathematical Monthly in 1935 and solved byI.J.Mordell and D.F.Borrow in 1937. Later many Mathematicians obtained solutions and for a long time the problem was in the air.

For some more solutions you can download my paper on the Erdos-Mordell Inequality.