Re: Q: surrounding a sphere

On 25 Sep., 11:53, David W. Cantrell <DWCantr...@xxxxxxxxxxx> wrote:
Karelk <K.Knech...@xxxxxxxxx> wrote:
Hello all,

A small question, maybe someone knows the answer?

I have a sphere of radius one.
I would like to put 5 other spheres (of all the same radius, but
larger than sphere one) in contact with the first sphere, effectively
covering the first sphere with one layer. What can be the maximal
radius of the five spheres?

For 4 and six surrounding spheres I can calculate it since those
situations result in symmetrical configurations, but for five
surrounding spheres I cannot figure it out.

Does anyone know the answer?

I think that the result for 5 surrounding spheres is the same as the result
for 6 surrounding spheres, which you've already worked out. See the second
and third rows of the table at
<http://www.research.att.com/~njas/packings/index.html>.

David

The number of equal shortest distances between neighbors in the
optimal configurations is given in
http://www.research.att.com/~njas/sequences/A080866
See also the visualizations at the link given in the sequence.

Hugo Pfoertner

.

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