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I must be missing something silly. What is the purpose of the original rectangle?

This describes how to find the side length of the square, who's area is smaller than the rectangle.

I was wondering that too, the best I could come up with is that the unused part of the rectangle represents the remainder we haven't "pulled down" yet, so in the first iteration, 0.17

I don't think its important to the calculation though

I believe it's just a visual aid that can help you understand how each digit is converging on the true square root. If you're not one for visual analogies, then it probably just feels like a distraction.

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