Actually, the best way of looking at this material is also the most ancient. The Babylonian approach (c. 1600 BC) was never improved on.
And once you know the sum and the difference of two numbers, the numbers themselves are easy to determine.
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The great thing about this approach is that it generalizes. One "completes the cube" in essentially the same way, to solve cubic equations.
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Oh, and it is also very pretty. The usual picture, described in the video above, comes from dividing the Babylonians' square in quarters.
End of conversation
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