## 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