Thingiverse
Cube Dissection Puzzle/ Model for 3^3 + 4^3 +5^3 = 6^3 by lgbu
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Last crawled date: 3 years ago
Cube Dissection/Puzzle/ Model for 3^3 + 4^3 +5^3 = 6^3
This is a classic 8-piece dissection of a 6 x 6 x 6 cube that is used to show the
3^3 + 4^3 +5^3 = 6^3. This design highlights the unit cubes for young children to count the number of unit cubes in a specific pieces. The counting itself is a worthwhile exercise for K-5 children, I think.
The 3^3 cube is one of the piece; so it is obvious.
The 4^3 cube is almost there. One only needs to put in the 2x1x1 piece.
The 5^3 cube is a bit challenging but is definitely feasible with elementarychildren. I have listed the 5^3 cube as a separate thing to avoid unnecessary confusion. Please refer to https://www.thingiverse.com/thing:3012566
To assemble all the 8 pieces into a 6^3 cube, please follow the figures. Of course, there are other ways to put them together.
Reference
Cundy, H. M. & Rollett, A. P. (1961). Mathematical models. London: Oxford University Press. (p. 203). The authors gave credit to a solution in Eureka, the magazine of the Cambridge Archimedeans.
This is a classic 8-piece dissection of a 6 x 6 x 6 cube that is used to show the
3^3 + 4^3 +5^3 = 6^3. This design highlights the unit cubes for young children to count the number of unit cubes in a specific pieces. The counting itself is a worthwhile exercise for K-5 children, I think.
The 3^3 cube is one of the piece; so it is obvious.
The 4^3 cube is almost there. One only needs to put in the 2x1x1 piece.
The 5^3 cube is a bit challenging but is definitely feasible with elementarychildren. I have listed the 5^3 cube as a separate thing to avoid unnecessary confusion. Please refer to https://www.thingiverse.com/thing:3012566
To assemble all the 8 pieces into a 6^3 cube, please follow the figures. Of course, there are other ways to put them together.
Reference
Cundy, H. M. & Rollett, A. P. (1961). Mathematical models. London: Oxford University Press. (p. 203). The authors gave credit to a solution in Eureka, the magazine of the Cambridge Archimedeans.
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