Degree of equivalence of polygons

Andrew McFarland

Joanna McFarland

James T. Smith

pp. 125-158

in: Andrew McFarland, Joanna McFarland, James T. Smith (eds), Alfred Tarski, Basel, Birkhäuser, 2014

Abstract

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.

Cited authors

Tarski Alfred