radius (with the chord of 90° as diagonal). Together, they describe the circle shown in the figure, whose diameter is ten and circumference is 32; the chord of 90° is taken to be 7. Both values 7 and 32 are within a few percent of the true lengths for a diameter-10 circle (which does not justify Goodwin's presentation of them as exact). The circumference should be nearer to 31.4159, and the diagonal "7" should be the square root of 50 () or nearer to 7.071. Area of the circle Goodwin's main goal was not to measure lengths in the circle but to find a square with the same area as the circle. He knew that Archimedes' formula for the area of a circle, which calls for multiplying the diameter by one-fourth of the circumference, is not considered a solution to the ancient problem of squaring the circle. This is because the problem is to construct the area using a compass and straightedge only. Archimedes did not give a method for constructing a straight line with the same length as the circumference. Goodwin was unaware of this central requirement; he believed that the problem with the Archimedean formula was that it gave wrong numerical results; a solution to the ancient problem should replace it with a "correct" formula. So, in the bill that he proposed, without argument, his method: This appears needlessly convoluted, as an "equilateral rectangle" is, by definition, a square. In simple terms, the assertion is that the area of a circle is the same as that of a square with the same perimeter. This claim results in other mathematical contradictions to which Goodwin attempts to respond. For example, right after the above quotation, the bill goes on to say: In the model circle above, the Archimedean area (accepting Goodwin's values for the circumference and diameter) would be 80. In contrast, Goodwin's proposed rule leads to an area of 64. Now, 80 exceeds 64 by one-fifth of 80. Goodwin appears to confuse with , an approximation that works only for fractions much smaller than . The area found by Goodwin's rule is times the true area of the circle, which, in many accounts of the Pi Bill, is interpreted as a claim that . However, there is no internal evidence in the bill that Goodwin intended to make such a claim. On the contrary, he repeatedly denies that the