This is a list of Göbel square packings, shown alongside their alternative packings or rearrangements. For the main list, see Squares in Squares.

Where the word "alternative" is used, this designates an alternative packing, which is enclosed within the same-sized bounding square as another packing, but cannot be reached by continuously translating and/or rotating the squares in that packing. When the packing can be reached by such continuous transformations, the word "rearrangement" is used.

For more information on each packing, view its SVG's source code.

Generalizing from Frits Göbel's findings, if $a,b \in \mathbb{Z}^+$ satisfy $a\!-\!1 \lt {1\over 2}b\sqrt 2 \lt a\!+\!1$, then $n = 2(a\!+\!1)a\!+\!b^2$ unit squares can be packed inside a square of side $s = a\!+\!1\!+\!{1\over 2}b\sqrt 2$. This is accomplished by placing a $b\!×\!b$ square of squares at a $45°$ angle in the center, surrounded by four "staircases" each having $a$ steps. This is better than a trivial packing iff $s \lt \bigl\lceil \sqrt{n} \bigr\rceil$.

David Ellsworth found that the arrangement in which all four corner squares of the $b\!×\!b$ square are unrotated is attainable iff $0 \, \le \, {1\over 2}b\sqrt 2 - a \, \le \, 2\sqrt 2-2$, and is an alternative packing iff $4 - b + (a - {5\over 4})\sqrt 2 - {1\over 2}\sqrt 5 \lt 0$, which is the case for $s(28)$, $s(1544)$, $s(4009)$, $s(9465)$, $s(14716)$, $s(32149)$, $s(41340)$, $s(56308)$, $s(68285)$, $s(101956)$, etc.

For more details, see Erich Friedman's paper on the subject: Packing Unit Squares in Squares: A Survey and New Results (or David Ellsworth's edit).