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> Geometry question
Raijinili
post Oct 17 2007, 02:51 AM
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Divide a cube into a finite number of pieces which can then be put together into two smaller cubes.


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Irysa
post Oct 17 2007, 12:21 PM
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Not cuboids? :(


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ChefMKT
post Oct 17 2007, 01:36 PM
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So basically...you're trying to find values for a b and c such that a³ + b³ = c³ ?
i.e. a³ + b³ - c³ = 0

So that implies c is greater than a and b, but because of the nature of cubes, two smaller cubes can never add up to a larger one. That is, unless I'm reading the question wrongly or that I didn't mess around enough in Excel.

This post has been edited by ChefMKT: Oct 17 2007, 02:10 PM


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H. Tsukiyono
post Oct 18 2007, 12:21 AM
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10 pieces. Cut out two triangular prisms that combine to make a smaller cube, and cut the remaining mass into eight cubes to create another cube.

Or we could say 29 pieces instead and cut the remainder down into twenty-seven cubes, but regardless it's about the same idea. I haven't actually tested it, I just visualized it. ._.;;

... Or just melt the damn thing down and recast it into two smaller cube-molds.
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Raijinili
post Oct 18 2007, 01:17 AM
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Need pictures of the first one.

Cheft: The sizes don't have to be integers.


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