One of the best ways to motivate little kids to learn math (n = 2 admittedly) is to present it as secrets for cheating.
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Hell yeah, he's a local Aussie. I'm going to try interview him for my podcast.
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Glad to be of service! :-)
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Actually, the best way of looking at this material is also the most ancient. The Babylonian approach (c. 1600 BC) was never improved on.
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The Babylonians asked how to find two numbers if you know their sum and their product. Their product they saw as the area of a rectangle.
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And their sum is half the perimeter of that same rectangle. But this is geometrically rather unnatural. The Babylonians found a better way.
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They took two copies of the rectangle, rotated one by 90 degrees, and juxtaposed them to make a shape whose base is the sum of the sides.
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But this shape is unappealingly asymmetrical. So they made a second copy of it, rotated it by 180 degrees, and assembled both into a square.
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Or rather, into a square with a square hole at its center. The whole now consisting of four copies of the original rectangle.
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The area of this new almost-square is 4 times the product of the two unknown numbers. Its side length is their sum.
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The crucial final point is that the side length of the missing square at its center is the difference between the two unknown numbers.
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