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The idea would be more obvious if `a` woldn't be exactly `2b` in this example (granted, author wasn't at liberty to choose values). Being previously unaware of what is Babylonian multiplication, it took me quite some time to get what exactly is being conveyed. It is too tempting to read it as "2 x 1" in this case, which doesn't register as a very notable generic discovery. I suspect many people who would find it otherwise interesting simply passed by before understanding what he is trying to show us.


For those of us too lazy to think this through, do you care to post an explanation?


Sure, here you go.

a — height of a white tile

b — width of a white tile

a x b — S₁, area of a white tile (this is what we are trying to "find")

(a - b)² — S₀, area of a black square

(a + b)² — S, area of a whole block (4 white tiles, 1 black tile)

Now, looking at the image it is obvious, that (S - S₀) = 4S₁.




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