Sobre o paradoxo de Banach-Tarski

Stefan Banach
(1892, Krakow, Austria-Hungary (now Poland), 1945, Lvov, Ukraine)

• Banach-Tarski Paradox
  Banach-Tarski Paradox or Banach-Hausdorff-Tarski Paradox
  

  The Banach-Tarski Paradox

  The Banach-Tarski Paradox. Yes, it is true. It is possible to take a cannonball apart into finitely many pieces, and put those pieces together to form a solid sphere the size of the sun.
  

  CUTTING A SPHERE INTO PIECES OF LARGER VOLUME

  Is it possible to cut a sphere into a finite number of pieces and reassemble into a solid of twice the volume?
  

  Banach-Tarski paradox

  
  

  Cutting a sphere into pieces of larger volume

  Is it possible to cut a sphere into a finite number of pieces and reassemble into a solid of twice the volume?
  

  Cutting a sphere into pieces of larger volume

  Banach-Tarski paradox (postscript)
  

  The Banach-Tarski Paradox

  The Banach-Tarski Paradox. Wagon, Stan. Asserting that a solid ball may be taken apart into many pieces that can be rearranged to form a ball twice as large as the original, the Banach-Tarski paradox is examined in relationship to measure and group theory, geometry and logic.
  

  The Ultimate Homepage Index: "Banach-Tarski paradox"

  The ULTIMATE place to find out about Banach-Tarski paradox! Everything you could possibly want is right here!
  

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  Última alteração: 22 de Novembro de 1997