Talk:Square packing

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It would be cool to have the images for the first numbers, from 1 to 10. I know how n= 1, 4, and 9 looks, but cannot imagine how 3 or 7 look. — Preceding unsigned comment added by 69.94.46.129 (talk) 09:06, 21 February 2023 (UTC)Reply

Why is there a a table on the Square packing in a square for circle packing in a square, but not for square packing in a square? — Preceding unsigned comment added by 108.24.78.18 (talk) 14:40, 22 February 2023 (UTC)Reply

It appears to me that the numbers ${\displaystyle n}$ where ${\displaystyle n<\lfloor {\sqrt {n}}\rfloor \lceil {\sqrt {n}}\rceil }$ (sequence A189151 in the OEIS) may give the values where packed unit squares in the shortest side square are not orthogonal. Jason Quinn (talk) 08:53, 4 June 2023 (UTC)Reply

The articles describes the problem as being to pack as many quares into a given larger form. Actually it seems to be rather the other way round: How small can the larger form be to pack n squares into it?

This is the way Packing_problems#Packing_of_squares describes it too.

I suggest to adjust the description or at least add an alternative version. Meillo (talk) 12:31, 12 February 2024 (UTC)Reply

These two questions are the same, in the sense that the complete answer to one can be easily translated to give the complete answer to the other. --JBL (talk) 23:55, 13 February 2024 (UTC)Reply

It is known that 11 unit squares cannot be packed in a square of side length less than ${\displaystyle \textstyle 2+2{\sqrt {4/5}}\approx 3.789}$.

Which is more simply expressed as ${\displaystyle \textstyle 2+4/{\sqrt {5}}}$, or ${\displaystyle \textstyle 2+{\sqrt {16/5}}}$. Any reason to prefer the hybrid form? —Tamfang (talk) 04:00, 29 October 2025 (UTC)Reply

It does seem strange to have the numerator half in and half out of the square root. I prefer the first of your two forms but they are both better than what you quoted. —David Eppstein (talk) 05:03, 29 October 2025 (UTC)Reply