Mathematical
Banach-Tarski Paradox
You can decompose a ball into two identical balls
Overview
A theorem in set-theoretic geometry showing a solid ball can be split and reassembled into two identical copies of the original.
Using the axiom of choice, you can divide a sphere into a finite number of non-measurable pieces and reassemble them into two spheres identical to the original. No distortion or stretching - just cutting and rotating.