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Topic: Easy problem without primes
Replies: 33   Last Post: Dec 31, 2013 9:22 AM

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 James Waldby Posts: 308 Registered: 1/27/11
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

> Looking with a sleep-refreshed 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 2.85-2.90 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 9-around arrangement is
r = 1/sin(pi/9) = 2.9238..., that is, the radius of a regular
nonagon with 2-unit 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

Date Subject Author
12/29/13 Port563
12/29/13 Robin Chapman
12/29/13 Port563
12/29/13 quasi
12/29/13 Peter Percival
12/29/13 Port563
12/30/13 quasi
12/30/13 quasi
12/30/13 quasi
12/30/13 Port563
12/30/13 quasi
12/30/13 Port563
12/30/13 Phil Carmody
12/30/13 Port563
12/30/13 quasi
12/30/13 Port563
12/30/13 fom
12/31/13 David Bernier
12/31/13 James Waldby
12/31/13 Port563
12/30/13 Phil Carmody
12/30/13 Peter Percival
12/30/13 Port563
12/30/13 Wizard-Of-Oz
12/30/13 Peter Percival
12/30/13 Wizard-Of-Oz
12/30/13 fom
12/30/13 Phil Carmody
12/30/13 quasi
12/30/13 Port563
12/29/13 Port563
12/30/13 Dr J R Stockton
12/30/13 Port563
12/29/13 Steffen Schuler