Research problems (Q5916465)

The author calls attention to the problem of covering a parallel strip of width w with unit circles as thinly as possible. In one arrangement in which the circles cover the strip in n parallel linked rows, the `density' of the covering is given by \(d_ n(w)=\pi n(n+1)/[2w\sqrt{\{(w+2)(2n-3)}\}].\) However for certain domains of w lower densities can be achieved by certain non-linked rows. The author ends with a conjectured inequality for the density.