13.18. What is the least number of strips of width 1 required to cover a circle of diameter $d$?
13.18. When solving this problem, we will use the fact that the area of a strip cut on a sphere of diameter $d$ by two parallel planes, the distance between which is $h$, equals $\pi d h$ (see problem 4.24).

Let a circle of diameter $d$ be covered by $k$ strips of width 1. Consider a sphere for which this circle serves as the equator. By drawing planes through the edges of the strips, perpendicular to the equator, we obtain spherical strips on the sphere, each of which has an area equal to $\pi d$ (more precisely, does not exceed $\pi d$, since one boundary of the original strip may not intersect the circle). The spherical strips also cover the entire sphere, so their area is not less than the area of the sphere, i.e., $k \pi d \geqslant \pi d^2$ or $k \geqslant d$. Thus, if $k \geqslant d$, then $k$ strips can cover a circle of diameter $d$.