Archive for January, 2007

Inequalities

Monday, January 15th, 2007

Some Geometric and Analytic Inequalities.

An inequality in the Cartesian plane.

Tuesday, January 9th, 2007

Let A(1,0), B(-1,0), C(0,1), D(0,-1) be points in the Cartesian plane and P so that OP is no less than 1. Then, it holds:

|AP-BP|+|CP-DP| is no less than 2.

Inequalities for a simplex and a triangle.

Tuesday, January 9th, 2007

We found an interesting inequality for the simplex, using barycentric coordinates and then some applications in a triangle.

Inequalities in a triangle

Tuesday, January 9th, 2007

Let ABC be a triangle and M an interior point. We denoted by RM the sum of the distances of the point M from the vertices of ABC and by rM the sum of the distances of the point M from the sides. We found the inequalities between RM and rM for M=O,G,I,H that is the pericenter the centroid the incenter and the orthocenter respectively.