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The Mathematician's Pyramid!




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Make several cubes out of wood, folded paper, or foam for this one! Randomly, number the sides from 1 to 20. Lay out the base of a pyramid using any 4 cubes. Now, try building your pyramid systematically: you can pile a cube on top only if it is the sum or difference of the cubes upon which it sits. The pyramid below is an example.



Watch how the Mathematician's Pyramid above was built by passing your mouse slowly over each equation from left to right; see the pyramid grow! (The equations are based on the orange faces of the cubes.)

A
4-cube base
B
6-2=4
C
10-2=8
D
10+8=18
E
18-8=10
F
4+8=12
G
12-10=2

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