A solution to the problem E2716* of the A.M.M.
Category: Mathematics
The Orthoptic Curve of a convex figure
The orthoptic curve K* of the convex curve K is circle. What about K?. Some Inequalities.
The problem (conjecture) of Larman-Zong
A solution for E3
Some Inequalities for a n-simplex
Inequalities between the width, the sum of the sides and the circumradius of a n-simplex.
On Minkowski Geometry
In this note we extend some well known properties of the Euclidean space En to the Minkowski space Mn.
The incircle of a tetrahedron
The incircle of a tetrahedron is a circle of maximum radius inscribed in the tetrahedron for every direction in En.
Inequalities
Some Geometric and Analytic Inequalities.
An inequality in the Cartesian plane.
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.
We found an interesting inequality for the simplex, using barycentric coordinates and then some applications in a triangle.
Inequalities in a triangle
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.