
Re: Easy problem without primes
Posted:
Dec 31, 2013 1:21 AM


On Mon, 30 Dec 2013 12:57:13 +0000, Port563 wrote: >>>>Peter Percival wrote: >>>>> >>>>>What is the biggest disk that can be covered by 13 unit disks? >>>> quasi wrote: >>>> It's very easy to show 13 unit disks can cover a disk of >>>> radius 2*cos(Pi/13)
> Looking with a sleeprefreshed eye at my arrangement, I am not so sure I > don't have a (tiny) hole or two. Probably safer to approximate it to 2.85 > than to the 2.852.90 range. [...] > In vague terms, I have 4 in the middle and 9 around, but my arrangement has > no axis of symmetry or even vaguely approximate symmetry.
An upper bound on the radius of a 9around arrangement is r = 1/sin(pi/9) = 2.9238..., that is, the radius of a regular nonagon with 2unit sides when each side of the nonagon coincides with a diameter of a unit disk. In this configuration, the clear area inside the ring of 9 disks is about 11.1 or ~ 3.53*pi, which can be covered by 4 disks if they don't overlap anything with more than about half a disk of area (which seems unlikely to happen).
 jiw

