Integral Formulas for Strips
Commun. Korean Math. Soc. 1997 Vol. 12, No. 4, 985-998
Yong Il Kim
Sung Kyun Kwan University
Abstract : 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
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