- #1
- 1,518
- 1
i find it is imposible..in fact there is more matter in the end that in the principle...
Originally posted by eljose79
i find it is imposible..in fact there is more matter in the end that in the principle...
The Banach-Tarsky paradox is a mathematical paradox that states that it is possible to take a solid sphere, divide it into a finite number of pieces, and then rearrange those pieces to form two identical copies of the original sphere. This means that, theoretically, it is possible to duplicate an object without adding or removing any material.
The Banach-Tarsky paradox is possible due to the fact that the pieces used to form the two identical spheres are non-measurable, meaning they do not have a defined volume. This allows for the pieces to be rearranged in such a way that they appear to have doubled in number, resulting in two identical spheres.
The paradox was first discovered in 1924 by two Polish mathematicians, Stefan Banach and Alfred Tarski. They published their findings in a paper titled "Sur la décomposition des ensembles de points en parties respectivement congruentes", which translates to "On the decomposition of sets of points into congruent parts".
The Banach-Tarsky paradox is purely a theoretical concept and does not have any practical applications. However, it has sparked important discussions and debates within the fields of mathematics and philosophy, particularly in relation to the concept of infinity and the nature of physical reality.
While the concept of the Banach-Tarsky paradox may seem counterintuitive and illogical, it is not considered a true paradox in the strictest sense. This is because it does not create a logical contradiction, but rather challenges our understanding of space, volume, and infinity. Additionally, the paradox does not violate any established mathematical principles or axioms.