Abstract
Here a complete answer is not known, but Laczkovich [2] has shown that a square cannot be dissected into 30?-60?-90? triangles. In fact, he proved that a square cannot be dissected into a finite number of triangles all of whose angles (measured in degrees) are even. (These two types of dissection problems form the content of chapters 5 and 6 of Stein and Szabo's recent book [510 Now, suppose a square is dissected into Pythagorean triangles?right triangles with integer sides:
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