THE motion of a perfectly elastic billiard ball upon a convex billiard table is a highly typical system of dynamical systems. Let Γ be the boundary of a billiard table, strictly convex and C^1 smooth. The ball is ass...
If C is any convex dosed curve in plane and P, Q, R are any three points which divide the perimeter of C into three equal parts, then the perimeter of the triangle PQR is never less than half of the perimeter of the c...