Friday, 20 February 2009

From Meccania to Atlantis Part 8 – Drenched to the Bone

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Squaring the circle

To square a circle is a common metaphor describing a futile attempt to solve the unsolvable. But a glance at the root of this metaphor may prove instructive.

Since ancient times, geometricians have tried to construct a square with the same area as a given circle by using only a finite number of steps with a compass and straightedge. Without going into the details, outside this author’s competence anyway, the challenge was invalidated as per the Lindemann–Weierstrass theorem, which proved that pi (π) is a transcendental rather than algebraic irrational number.

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