Banach-Tarski Paradox
First stated in 1924, this theorem demonstrates that it is possible to dissect a Ball into six pieces which can bereassembled by rigid motions to form two balls of the same size as the original. The number of pieces was subsequentlyreduced to five. However, the pieces are extremely complicated. A generalization of this theorem is that any two bodiesin 
which do not extend to infinity and each containing a ball of arbitrary size can be dissected into each other(they are Equidecomposable).
References
Stromberg, K. ``The Banach-Tarski Paradox.'' Amer. Math. Monthly 86, 3, 1979. Wagon, S. The Banach-Tarski Paradox. New York: Cambridge University Press, 1993.
- Diophantine Equation--6th Powers
- Diophantine Equation--7th Powers
- Diophantine Equation--8th Powers
- Diophantine Equation--9th Powers
- Diophantine Equation--Cubic
- Diophantine Equation--Linear
- Diophantine Equation nth Powers
- Diophantine Equation--Quadratic
- Diophantine Equation--Quartic
- Diophantine Quadruple
- Diophantine Set
- Diophantus Property
- Diophantus' Riddle
- Dipyramid
- Dirac Delta Function
- Dirac Matrices
- Dirac's Theorem
- Directed Angle
- Directed Graph
- Directional Derivative
- Direction Cosine
- Directly Similar
- Director Curve
- Direct Product (Group)
- Direct Product (Matrix)