Disk covering problem

The disk covering problem asks for the smallest real number

Dually, for a given radius ε, one wishes to find the smallest integer n such that n disks of radius ε can cover the unit disk.

One of the covering disks is placed central and the remaining five in a symmetrical way around it.

While this is not the best layout for r(6), similar arrangements of six, seven, eight, and nine disks around a central disk all having same radius result in the best layout strategies for r(7), r(8), r(9), and r(10), respectively.

[2] The corresponding angles θ are written in the "Symmetry" column in the above table.