Squaring the Circle – Ruler and Straight Edge Approximations
Given a circle, we want to
construct a square having the same area as the circle. Suppose the radius of the given circle is
one. Then the area of the circle is p. The
area of the desired square, then, is also p. Therefore, each side of the square that we want to construct will
have a length of Öp. In
order to construct such a square, we need to be able to construct a segment of
length p. We cannot construct a segment having a length equal to exactly p (see the discussion
of the proof), but we can construct some pretty good approximations. Here are two examples of approximations:
These approximations are from the following web
page: http://www.uwgb.edu/dutchs/PSEUDOSC/SquareCirc.htm
.
