The projections on the coordinate planes of a convex body. The Loomis-Whitney inequality.

In our generalization we have found intermediate terms between the two

parts of the Chebyshev inequality

Greek Mythology. Aegeus, king of Athens and father of Theseus, falls into the sea after he saw Theseaus's boat. They had prearranged that if Theseus would die, the ship would come back wearing black sails. Theseus did not die but forgot to change the sails to white. So, Aegeus died in vain.

The idea relative to simplex seems to simplify some propositions and theorems

about to John's matrix.

We prove an interesting theorem in Topology similar to the Helly type theorem in Convexity.

R.J.Gardner, S.Kwapien and D.P.Laurie working on a conjecture of B.Grunbaum, reached two elegant conjectures including inequalities about ovals. Here is an interesting solution.

Theorems and inequalities on simplices

A solution to the problem E2716* of the A.M.M.

The orthoptic curve K_* of the convex curve K is circle. What about K?. Some Inequalities.