I understand that a square with area $\pi$ cannot be constructed using straightedge and compass. But such a square surely exists (and can be constructed through other means), right? If I'm right, I'm confused by the Wikipedia article (http://en.wikipedia.org/wiki/Squaring_the_circle)'s statement that seems to say squaring the circle is equivalent to asking whether the square with area $\pi$ exists. Can someone help me resolve this contradiction?
And if someone can point me to a good book covering these matters, it would be greatly appreciated.
It's equivalent to asking whether the square with area $\pi$ exists in the set of all squares that can be constructed using a straightedge and compass.