Unearthing the Banach–Tarski paradox

Article Type

Research Article

Publication Title

Resonance

Abstract

Greeks used the method of cutting a geometric region into pieces and recombining them cleverly to obtain areas of figures like parallelograms. In such problems, the boundary is ignored. However, in our discussion, we will take every point of space into consideration. The human endeavour to compute lengths, areas, and volumes of irregular complicated shapes and solids created the subject of ‘measure theory’. The paradox of the title can be informally described as follows. Consider the earth including the inside stuff. It is possible to decompose this solid sphere into finitely many pieces and apply three-dimensional rotations to these pieces such that the transformed pieces can be put together to form two solid earths! The whole magic lies in the word ‘pieces’. The pieces turn out to be so strange that they cannot be ‘measured’.

First Page

943

Last Page

953

DOI

10.1007/s12045-017-0554-2

Publication Date

10-1-2017

This document is currently not available here.

Share

COinS