On decomposition of point sets into respectively congruent parts (1924)

Andrew McFarland

Joanna McFarland

James T. Smith

pp. 93-123

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

Abstract

This chapter contains an English translation of the paper Sur la décomposition des ensembles de points en parties respectivement congruents, [1924] 2014, by Stefan Banach and Alfred Tarski. It appeared in volume 6 of the journal Fundamenta Mathematicae. This is its first translation. Its best-known result is often called the Banach–Tarski paradox: any two balls with different radii can be decomposed into the same finite number of disjoint, respectively congruent parts.

Cited authors

Tarski Alfred