Talk:Circle packing in a square

Packing of two equal circles; the second of which may be cut.

What is the minimum size of the enclosing square if 0-cut; 1-cut, 2-cut, 3-cut, 4-cut, 5-cut etc ?

Is there a general pattern to one result based on the previous ?

Does it make a difference if circle-1 is placed in the corner, in the middle-edge or at the centre or freely.

0-cut	the result is the simple 2-circle packing of [2+sqrt(2)] = 3.414r
1-cut	two semicircles which result in an enclosing square of 3r.
2-cut	small improvement to approximately 2.93r
3-cut	into 4 segments results in a square of sqrt(4r) ie 2.828r (with the circle in the centre surrounded by 4 quadrants); with the circle at the corner, the enclosing square is approximately 2.865r.
....
6 cuts	into 7 segments results in a square of approximately 8r/3

and the trend is to a final (infinitely sliced) figure of sqrt(2pi) =c 2.5066 Nojoking (talk) 07:27, 23 October 2011 (UTC)[reply]

I took the liberty of reformatting your list into a table to make the 'columns' clearer. But I don't understand what you mean by 'cut' – it could mean so many different things! —Tamfang (talk) 23:52, 11 December 2011 (UTC)[reply]

Use of unit circle vs unit square.

The main references for this page use a unit square and adjust the radii, the difference isn't all that important but I'm curious why the unit circle was chosen. — Preceding unsigned comment added by 8BitTRex (talk • contribs) 19:18, 23 April 2014 (UTC)[reply]

Using WolframAlpha

For those with interest, WA handles related queries such as: pack circles of radius 1 in a square of side 7. Above a certain side length the results are estimated (and unfortunately not taken to an integer ).--Billymac00 (talk) 01:59, 3 September 2020 (UTC)[reply]

Infinite plane

We should somehow mention that the densest packing in the infinite plane is the honeycomb/hex pattern, and that alle the deviations from such a pattern in the finite cases may be seen as edge effects. E.g., the square lattice mentioned for small square numbers is eventually replaced by a honeycomb pattern (or a slightly modified one?) for large square numbers. I do not have a source, though. Of course, the infinite case as such is easy to source, but it's the transistion that makes it relevant here. Nø (talk) 14:03, 23 February 2023 (UTC)[reply]