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construct a square that perfectly circumscribes (surrounds) a given square

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What? The same square will do it - perfectly!

It is, in fact, the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge. As pi (π) is a transcendental, rather than an algebraic irrational number, it cannot be done.

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Q: What were people trying to do when they tried to square the circle?
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