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Feb20-12, 03:01 AM
P: 4,575
Squaring the Square -> Cubing the Rectangular Prism

Quote Quote by TheFerruccio View Post
I mean, given a rectangular prism of dimensions [tex]x_1, x_2, x_3[/tex], where [tex]x_1 \ge x_2 \ge x_3[/tex] can it be perfectly and finitely filled with unique cubes of edge length [tex]x_n[/tex], where [tex]x_{n+1} < x_{n}[/tex] and [tex]x_n < x_3 \forall n > 3[/tex]
Are there any other restrictions? Do the values have to be integer or rational numbers of edge size or can they be real numbers of any kind?