Post AckR4OCjXfLu9mSYfA by mbonsma@mastodon.social
 (DIR) More posts by mbonsma@mastodon.social
 (DIR) Post #AckR4OCjXfLu9mSYfA by mbonsma@mastodon.social
       2023-12-12T01:23:07Z
       
       1 likes, 1 repeats
       
       We've all been there: it's puzzle time, but once you dump out the pieces and start laying them flat, you realize you don't have enough space on your table. Join me as we use physics to find out ✨HOW BIG A TABLE YOU NEED FOR YOUR JIGSAW PUZZLE ✨https://doi.org/10.48550/arXiv.2312.04588#SciComm
       
 (DIR) Post #AckR4QKxc37alsK9lQ by mbonsma@mastodon.social
       2023-12-12T01:24:26Z
       
       0 likes, 0 repeats
       
       This work was a pandemic collaboration between me and the brilliant Kent Bonsma-Fisher, with assistance from our toddler and cat. The result, in his words, was "the cleanest dataset I have ever collected." Today our results are public on #arXiv!
       
 (DIR) Post #AckR4SOvwFUJAmCMEa by mbonsma@mastodon.social
       2023-12-12T01:24:41Z
       
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       TL;DR: an unassembled jigsaw puzzle takes up an area that is the square root of 3 times the area of the assembled puzzle, or about 1.7 times the assembled area. This is *independent of the number of pieces*.
       
 (DIR) Post #AckR4UHCxwUqzObDTE by mbonsma@mastodon.social
       2023-12-12T01:25:50Z
       
       0 likes, 0 repeats
       
       We derived a theory with a "spherical cow in a vacuum" approach: we approximated each puzzle piece area as a circle, then calculated the area of the circles packed together. Our prediction: the unassembled area is sqrt(3) times the assembled area. Then we took data.
       
 (DIR) Post #AckR4W5aE8O0bvAxd2 by mbonsma@mastodon.social
       2023-12-12T01:27:18Z
       
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       We built 9 puzzles across a variety of total sizes and with piece numbers ranging from 9 to 2000. We laid out all the pieces flat, trying to be realistic by not paying much attention to how they were arranged and not spending time trying to get them closer together.
       
 (DIR) Post #AckR4Xq3ip9m2Lvai0 by mbonsma@mastodon.social
       2023-12-12T01:27:49Z
       
       1 likes, 0 repeats
       
       The results were the most incredible agreement between theory and data I've ever seen in over a decade of being a physicist. I think I gasped when I saw this plot. Without any fitting, our simple theory *very accurately* predicted the unassembled area of all these puzzles.
       
 (DIR) Post #AckR4ZiKkWAJqyKRwe by mbonsma@mastodon.social
       2023-12-12T01:28:37Z
       
       0 likes, 0 repeats
       
       We were surprised that the unassembled area didn't depend on the number of puzzle pieces. The intuition is this: if you have a small number of large pieces, the gaps between pieces are big, but this is multiplied by a small total number of pieces, and vice versa for small pieces.
       
 (DIR) Post #AckR4bY7vRBnXtZKJU by mbonsma@mastodon.social
       2023-12-12T01:28:52Z
       
       0 likes, 0 repeats
       
       So there you have it: you'll need a puzzle table just under twice as big as your assembled puzzle in order to not resort to the box lid or that random side table. Grab a puzzle and impress your relatives this holiday season with your predictive powers!