This intuitive justification likewise indicates that one should be able to do the Banach-Tarski thing with a 2-dimensional disc rather than a 3-dimensional ball. Unfortunately, that isn’t true. (Though it is if you allow area-preserving affine transformations as well as isometries.)
This intuitive justification likewise indicates that one should be able to do the Banach-Tarski thing with a 2-dimensional disc rather than a 3-dimensional ball. Unfortunately, that isn’t true. (Though it is if you allow area-preserving affine transformations as well as isometries.)