103.13 Squaring the circle by using proportion

摘要

The task of constructing a square equal in area to a given circle is called squaring the circle. This was one of the three unsolvable problems of antiquity. The geometrical construction of this square must be realised by using only a straight-edge and compass. The construction should be completed in a finite number of steps. It was proved to be an impossible problem as a consequence of the fact that the number is transcendental. A German mathematician von Lindemann in 1882 [1] has shown that the mathematical constant is not an algebraic number.