Ana Sayfa
Matematikçiler
Makaleler
Matematik Seçkileri
Fraktallar
Paradokslar
=> Zeno's Paradoxes
=> Allais Paradox
=> Arnauld's Paradox
=> Banach-Tarski Paradox
=> Barber Paradox
=> Berry Paradox
=> Bottle Imp Paradox
=> Buchowski Paradox
=> Cantor's Paradox
=> Catalogue Paradox
=> Coin Paradox
=> Complex Number Paradox
=> Crocodile's Dilemma
=> Destructive Dilemma
=> Diagonal Paradox
=> Dilemma
=> Elevator Paradox
=> Epimenides Paradox
=> Eubulides Paradox
=> Grelling's Paradox
=> Hempel's Paradox
=> Liar's Paradox
=> Line Point Picking
=> Missing Dollar Paradox
=> Newcomb's Paradox
=> Parrondo's Paradox
=> Potato Paradox
=> Richard's Paradox
=> Russell's Antinomy
=> Skolem Paradox
=> Smarandache Paradox
=> Socrates' Paradox
=> Sorites Paradox
=> Strange Loop
=> Thompson Lamp Paradox
=> Unexpected Hanging Paradox
=> Fallacy
=> Plaindrome
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Banach-Tarski Paradox

First stated in 1924, the Banach-Tarski paradox states that it is possible to decompose a ball into six pieces which can be reassembled by rigid motions to form two balls of the same size as the original. The number of pieces was subsequently reduced to five by Robinson (1947), although the pieces are extremely complicated. (Five pieces are minimal, although four pieces are sufficient as long as the single point at the center is neglected.) A generalization of this theorem is that any two bodies in R^3 that do not extend to infinity and each containing a ball of arbitrary size can be dissected into each other (i.e., they are equidecomposable
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