Post #2672385
2026-01-22 17:34 UTC
A note on notation: what we care about is the relative proportions of our rectangles and our square -- we could treat it all as happening in a 1x1 unit square and label the rectangles with fractional lengths (filling a 1x1 square with two 1/2x1 rectangles), but it's just as good to say we're filling a 2x2 square with two 1x2 rects. I don't want to keep writing fractions so I'll just use whole number proportions in my illustrations.
Replies (1)
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@joshmillard@mastodon.social 2026-01-22 17:51
So, quick summary of what the video covers: there is *no* solution for n=1 (can't fill a square with one rectangle half its size), and also none for n=3 or n=4. (Try it!) So after n=2 our next solution is for n=5: take one of the rectangles and divide it into four smaller rectangles, voila! For n=6, we also have a solution: wrap four larger rectangles around a core of two smaller rectangles, voila!