Love a jigsaw but struggle finding the best-sized surface to lay out ALL your pieces? Well, now scientists have the answer (and no, it’s NOT just buying a bigger table!)
- Often a table is too small for your puzzle, but experts may have a solution
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It's the time of year when families spending days together at home often begin a challenging new puzzle.
But many households fall at the first hurdle because they fail to find the right size surface to put all the puzzle pieces on.
Now they never have to do that again, as a research paper helpfully reveals the best table size – just under twice the size of the assembled puzzle.
Data scientist Dr. Madeleine Bonsma-Fisher and her husband, quantum physicist Dr. Kent Bonsma-Fisher, constructed nine jigsaw puzzles, with a number of pieces ranging from nine to 2,000, to solve the tricky problem.
They found that an unassembled puzzle occupies an area approximately 1.7 times larger than the assembled area.
Discovering too late that your table is too small for your jigsaw puzzle is a common source of frustration, but scientists may finally have a solution (file photo)
Dr. Madeleine Bonsma-Fisher wrote on social media site
“Pick up a puzzle and impress your family with your predictive powers this holiday season!”
The researchers laid the pieces of each puzzle flat in an oval shape, or a rectangle for two of the large puzzles, and then calculated their length and width.
They tried to arrange the pieces as naturally as possible, instead of placing them artificially close together.
They then painstakingly completed each puzzle, determining the length and width of the composite image.
To their surprise, a simple theory predicted the surface area needed for the puzzle pieces.
An unassembled puzzle took up an area equal to the square root of three times the area of the assembled puzzle.
Simply put, the pieces required an area approximately 1.7 times the size of the completed puzzle.
Dr. Explaining why they conducted the experiment at home, Madeleine Bonsma-Fisher wrote on . make sure there is enough space on your table.'
The researchers laid the pieces of each puzzle flat in an oval shape, or a rectangle for two of the large puzzles, and then calculated their length and width.
Because the pieces were randomly oriented before assembly, the experts assumed that on average they behave like circles with a diameter equal to the diagonal of the square (shown here)
The mathematical theory worked regardless of the number of pieces in a puzzle.
That's because with a small number of large pieces, the gaps between the pieces are larger, but this area is multiplied by a small number of pieces.
Meanwhile, for a large number of small pieces, the distance is smaller, but there are more pieces, so more space in total.
Dr. Madeleine Bonsma-Fisher, from the University of Toronto, said she “gasped” when she discovered the simple theory for putting together a puzzle.
“The results were the most incredible agreement between theory and data that I have ever seen in my more than a decade as a physicist,” she said.