Archive for the ‘Mathematics’ Category

On Minkowski Geometry

Monday, February 12th, 2007

In this note we extend some well known properties of the Euclidean space En to the Minkowski space Mn.

The incircle of a tetrahedron

Saturday, February 10th, 2007

The incircle of a tetrahedron is a circle of maximum radius inscribed in the tetrahedron for every direction in En.

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.

The applications of Leibniz’s formula in Geometry.

Monday, November 6th, 2006

It is well known from Mechanics that the polar moment of inertia of a system of weighted points is minimum about the centroid. This can be expressed geometrically and very interesting results can be obtained.

A conic classification. Nine-point ellipse.

Saturday, October 28th, 2006

A classification of a conic through three no colinear given points, according the position of its center. Nine point ellipse.

The maximal inscribed and the minimal circumscribed ellipse for a centrally symmetric convex figure.

Tuesday, October 24th, 2006

In this note we study the maximal inscribed and the minimal circumscribed ellipse of a cenrally symmetrc convex figure F and we prove two theorems between the area and the remarcable elements of the figure.

Convex figures with conjugate diameters.

Sunday, October 15th, 2006

The convex figure K has conjugate diameters if and only if its symmetroid K* is an affine image of a Radon curve