An oversimplified account of the mind - numbingly paradoxicalBanach - Tarski theoremstates that a solid sphere can be cut into non - overlapping pieces ( geometricians would say that such a ball has been “ moulder ” ) , and reassembled in a new arrangement , such that the end result is two identical copies of the original sphere — preservation of mass be damned .
disordered ? BoingBoing ’s Maggie Koerth - Bakergives a good summation :
Imagine a egg . Now imagine cut that orb up into a finite turn of pieces . Six , maybe . Or five . The Banach - Tarski paradox pop the question that you could take those pieces and , without stretch or expanding them in any way , practice them to shape two balls selfsame to the first . fundamentally , you ’ve just created mass out of nothing . That is , to put it gently , not supposed to be able to bump . Thus , the part about the paradox .
Still confounded ? Me too . But do n’t allow that cease you from appreciate the TV up top . In it , extremity of the University of Copenhagen mathematics department overwork the Banach - Tarski paradox , decomposing and reassemble a people of oranges to the ( slightly modified ) tune of Duck Sauce ’s “ Barbara Streisand . ” On a related to note , this picture will make you recognize how much more you wish you partied with mathematician .
[ Spotted onBoingBoing ]
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