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Dissection of a Square to a Parallelogram with the Same Base

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Two polygons of the same area are said to be equivalent. In [1], Tarski defines the degree of equivalence of two equivalent polygons and as the smallest natural number for which there exists a dissection of to using pieces. The function is denoted as .

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Later he defines , where is a unit square and is a parallelogram with the same base and altitude with angle . He states that and leaves the proof as an exercise for the readers.

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Contributed by: Izidor Hafner (May 2017)
Open content licensed under CC BY-NC-SA

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[1] A. McFarland, J. McFarland and J. Smith, eds., Alfred Tarski: Early Work in Poland—Geometry and Teaching, Basel: Birkhäuser, 2014 pp. 156–158.

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