The Banach–Tarski Paradox

Stan Wagon ()
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Stan Wagon: Macalester College, Department of Mathematics and Computer Science

Chapter 19 in Mathematica in Action, 2010, pp 491-504 from Springer

Abstract: Abstract The Banach—Tarski paradox is one of the most shocking results of mathematics. In this chapter we show how tilings of the hyperbolic plane can help us visualize the paradox. The images shown here display three congruent subsets of the hyperbolic plane. In the left image, the congruence is evident. The right image changes the viewpoint a little and changes the green to a blue shade; it is evident that the red set is congruent to its complement. Thus these sets are, simultaneously, one half and one third of the hyperbolic plane.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-387-75477-2_20

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DOI: 10.1007/978-0-387-75477-2_20

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