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The Exact Pi value solves partially one UNSOLVED GEOMETRICAL PROBLEM : "Doubling of the Cube "

The three unsolved geometrical problems are trisection of an arbitrary angle, duplication of the cube and squaring of circle. Here is one attempt to get the side of the cube equal to its doubled volume 2.0001… by the help of straight edge and compass only and in terms of the new Pi value (14 – root2)/4.

Here is the documental evidence