History of the Problems
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History of the problem

Problem Definition:

To construct a square which has the same area as the given circle.

This is equivalent to construct a line segment of length p or its square root.

******** circle_squaring_problem.dwg *********

Origin of the Problem :

The circle is the simplest , and hence the first curve men has created. So naturally from the earliest days

in history, men have had a keen interest in the area and circumference of this curve.

Rule of the Game ( Platonian Rule ) :

Tools allowed
the compasses and unmarked straight-edge
Permitted use of these 2 tools
1. The drawing of a straight line of indefinite length through two given points.

2. The construction of a circle with center at a given point and passing through a second given point.

Summary of Early Attempts:

Proof of impossibility:

In 1880 Ferndinand von Lindemann (1852 - 1939) proved that p is transcendental, that it is not the root of any polynomial equation

with rational coefficients. Thus he proved that it is not possible to square the circle with ruler and compass.

Comments on the References:

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Last Updated Nov 22, 2006

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