In recreational mathematics, a geometric dissection involves cutting a geometric figure into pieces that you can reassemble into another figure. For example, it’s possible to slice a square into four angular pieces that can be rearranged into an equilateral triangle.
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Such puzzles have been around for thousands of years. The problem of dissecting two equal squares to form one larger square using four pieces dates back to at least the time of the Greek philosopher Plato (427 BC–347 BC). In the 10th century, Arabian mathematicians described several dissections in their commentaries on Euclid’s Elements. The 18th-century Chinese scholar Tai Chen presented an elegant dissection for approximating the value of pi–the ratio of a circle’s circumference to its diameter. Others worked out dissection proofs of the Pythagorean theorem. In the 19th century, dissection puzzles were an immensely popular staple of magazine and newspaper columns by puzzlists San Loyd in the United States and Henry E. Dudeney in England.