Communications of the
Korean Mathematical Society CKMS

For $n$ random strips chosen so as to meet a fixed bounded convex set $K$ of the plane we let $\nu$ be the number of intersection regions that meet $K$. We develop the integral formula for the mean value of $\nu$ and ${\nu}^2$ involving the area and the perimeter of $K$ and the breadths of the strips. We get some geometric inequalities in way of studying integral geometry.

Keywords: integral geometry, strip, perimeter, density, parallel set

MSC numbers: 53C65, 52A10