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Add up the first few cubes and you always land on a perfect square: 1³ 2³ 3³ 4³ 5³ = 225 = 15². Slice each cube into flat slabs and they fold into one L-shaped layer around the last square. An even cube has half a slab too many for its arms, so one slab is cut in half. The side of the finished square is just 1 2 3 4 5. In general, 1³ 2³ ⋯ n³ = (n(n 1)/2)². It's Nicomachus's theorem, shown with a classic proof without words. #math #maths #proof #geometry #numbertheory
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