My grandparents left me several Arabic/Persian inlay boxes: made from mosaics of many small wooden tiles; triangular, square, and other shapes. It occurred to me that if you were constructing one of these boxes and needed to fill in a larger triangular or square area, then it would not take you long to know how many small tiles it was going to take. Knowing that a^2 and b^2 added up to c^2 would be empirical knowledge for a box maker. Easy to re-discover.
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