Archive for October, 2006

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.

Art and Geometry

Friday, October 27th, 2006

Opi Zouni

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.

Bistrot

Sunday, October 15th, 2006

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

The tree

Sunday, October 8th, 2006

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

Sunday, October 8th, 2006

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

Monday, October 2nd, 2006

Van den Berg’s Theorem

Monday, October 2nd, 2006

Let Q(z)=z3+a1z2+a2z+a3=0 be a cybic in C and  z1,z2,z3 the roots denoted in the plane by the points A,B,C. The Steiner ellipse in the triangle ABC is denoted by E and F1, F2 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 F1 and F2.