VIDEO: Banach–Tarski Paradox

The Banach-Tarski Paradox is a theorem in geometry which states that:

“It is possible to decompose a ball into five pieces which can be reassembled by rigid motions to form two balls of the same size as the original.”

It was first stated in 1924, and is called a paradox as it contradicts basic geometric intuition.

An alternate version of this theorem tells us that:

“It is possible to take a solid ball the size of a pea, and by cutting it into a finite number of pieces, reassemble it to form a solid ball the size of the sun.”

Below is an awesome video explaining how this paradox works:

 

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2 comments

  1. This is one of my favorite theorems, just because it so defies all intuition. It would be at least reasonable if you could turn one thing into two by splitting it infinitely many times and then reassembling the pieces, because it’s natural that when you let infinity get involved everything gets weird. But five? Five is too mundane a number for a result that crazy to turn up. It’s wonderful.

    Liked by 1 person

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