How does the Banach-Tarski Paradox work?

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It seems so ridiculously counterintuitive, how could it possibly work?

In: Mathematics

4 Answers

Anonymous 0 Comments

The short answer is that the sphere is split into shapes that are so complex that they don’t have a volume. I don’t mean there volume is 0, I mean there volume just isn’t definable at all.

There is no simple explanation of the proof unfortunately. This paradox isn’t possible in 2D sk any proof must rely on properties of 3D that differ from 2D.

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