What is Banach–Tarski paradox?
{{No sources|date=January 2021}}[[File:Banach-Tarski Paradox.svg|thumb]] The '''Banach–Tarski paradox''' is a [[theorem]] in [[mathematics]] that says that any [[solid]] shape can be reassembled into any other solid shape. It was made by mathematicians Stefan Banach and Alfred Tarski. For example, a [[sphere]] can be split up into a limited number of parts which can then be put back together again to make two identical copies of the original sphere. The Banach–Tarski [[paradox]] can also be used to turn a small sphere into a huge sphere. It is important when thinking about this to realize that the parts that the solid shape is being split into are not solid shapes themselves; they are [[infinite]] sets of points spread around the solid shape. For the Banach–Tarski paradox to work, you need to use the [[axiom of choice]]. This is called a paradox because no stretching or bending of the parts takes place and no new [[material]] is added, yet by the end the [[volume]] can be doubled. This goes against our [[Geometry|geometric]] [[intuition]]. However, it is mathematically possible and it turns out that in this case our intuition is not correct. == Other websites == * [https://www.youtube.com/watch?v=s86-Z-CbaHA The Banach-Tarski Paradox] {{math-stub}} {{DEFAULTSORT:Banach-Tarski paradox}} [[Category:Mathematical paradoxes]]