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(2014) Alfred Tarski, Basel, Birkhäuser.
The elementary approach to the theory of area, described in section 4.1, includes definitions of polygonal region, of equivalence of a pair V, W of regions under decomposition into the same finite number n of respectively congruent subregions with disjoint interiors, and of the area of a polygonal region. It includes the Bolyai–Gerwien theorem: polygonal regions are equivalent if and only if they have the same area. The 1924 papers of Alfred Tarski and Stefan Banach, translated in chapters 5 and 6, extended that theory to include analogous results with a different, set-theoretic, definition of equivalence.
Publication details
DOI: 10.1007/978-1-4939-1474-6_7
Full citation:
McFarland, A. , McFarland, J. , Smith, J.T. (2014)., Degree of equivalence of polygons, in A. Mcfarland, J. Mcfarland & J. T. Smith (eds.), Alfred Tarski, Basel, Birkhäuser, pp. 125-158.
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