3 ms·
Mathematically, it’s quite different. The Banach-Tarski paradox (https://en.wikipedia.org/wiki/Banach–Tarski_paradox https://en.wikipedia.org/wiki/Banach–Tarski
by Someone 5y ago
Mathematically, it’s quite different. The Banach-Tarski paradox (https://en.wikipedia.org/wiki/Banach–Tarski_paradox https://en.wikipedia.org/wiki/Banach–Tarski_paradox) changes the _volume_ of the objects. That’s requires some of the prices to be immeasurable.
It also is about a 3D sphere, and the strong form (cutting a sphere in finitely many parts and reassembling those into two equal-sized spheres) doesn’t work in 2D or 1D (in contrast, in 3D, five pieces suffice. I don’t know whether that is a tight bound)
- thaumasiotes 5y ago> The Banach-Tarski paradox (https://en.wikipedia.org/wiki/Banach–Tarski_paradox https://en.wikipedia.org/wiki/Banach–Tarski_paradox) changes the _volume_ of the objects. That’s requires some of the prices to be immeasurable. It changes the volume by a discretionary amount; you can create two spheres of the same size as the original sphere, or 500 spheres of the same size as the original sphere, or you can create one sphere of double the radius [= four times the size] of the original sphere. I see no reason to believe that you couldn't also make one cube of equal volume to the original sphere?
- OscarCunningham 5y agoIt is a tight bound. http://matwbn.icm.edu.pl/ksiazki/fm/fm34/fm34125.pdf http://matwbn.icm.edu.pl/ksiazki/fm/fm34/fm34125.pdf https://www.irregularwebcomic.net/2339.html https://www.irregularwebcomic.net/2339.html