| This problem, "quadrature of the circle," was one of three famous problems that goes back at least to the time of Anaxagoras, about 150 years before Euclid. It is equivalent to constructing a line segment of length pi (relative to a unit length). This problem was solved by ancient Greek geometers but not by means of the Euclidean tools of straightedge and compass; higher curves were required. In fact, by the time of Pappus it was believed that the circle could not be squared using only straightedge, compass, and even the conic sections (parabola, hyperbola, and ellipse). But the ancient Greeks had no mathematical proof that it could not be squared. That the circle could not be squared with Euclidean tools was not shown until 1882 when Lindemann proved that pi is a transcendental number. |
| To pose a contradictory situation and then claim some proof of anything is foolish. To me this whole sequence is equivalent to saying God cannot multiply two even numbers together and get an odd result, therefore He is not all powerful. |
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