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 sea gull
The applications of Leibniz’s formula in Geometry.
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.
The fishing-boat
A conic classification. Nine-point ellipse.
A classification of a conic through three no colinear given points, according the position of its center. Nine point ellipse.
Art and Geometry
Opi Zouni
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
