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

# Month: October 2006

## Art and Geometry

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

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.

## Bistrot

## Convex figures with conjugate diameters.

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

## The tree

## The triangle of minimum perimeter circumscribed to a smooth closed compact convex curve (c) in the plane.

**Theorem**

For the triangle T of a minimum perimeter circumscribed to a convex figure (c) the excircles of T are tangent to (c).

## The bird

## Van den Berg’s Theorem

Let Q(z)=z^{3}+a_{1}z^{2}+a_{2}z+a_{3}=0 be a cybic in C andÂ z_{1},z_{2},z_{3} the roots denoted in the plane by the points A,B,C. The Steiner ellipse in the triangle ABC is denoted by E and F_{1}, F_{2} the foci. Van den Berg’s theorem asserts that the roots of the derivate Q'(z) are the complex numbers defined in C by the points F_{1} and F_{2}.