LYCOS RETRIEVER 
Archimedes: Square
built 642 days ago
[Note: throughout this proof, Archimedes uses several rational approximations to various square roots. Nowhere does he say how he got those approximations--they are simply stated without any explanation--so how he came up with some of these is anybody's guess.]
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The Stomachion is a puzzle game considered to be from Archimedes. A square with a 12x12 grid is divided in 14 pieces of 3,4 and 5 sided polygons. As the vertices of the polygons are on the grid points their areas, due to Picks theorem, can be expressed as integer ratios to the area of the square.
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Netz wasn't sure whether it would have been feasible for Archimedes to count the number of square tilings that could be made from the puzzle pieces. Was it an easy calculation, he wondered, or something far too difficult to be computed by hand?
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