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duplication of the cube


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One of the problems that Greek geometers attempted (like squaring the circle and trisection of an angle) was to find a construction, with ruler and pair of compasses, to obtain the side of a cube whose volume was twice the volume of a given cube. This is equivalent to finding a geometrical construction to obtain a length of from a given unit length. Now constructions of the kind envisaged can only give lengths belonging to a class of numbers obtained, essentially, by addition, subtraction, multiplication, division and the taking of square roots. Since does not belong to this class of numbers, the duplication of the cube is impossible.

Subjects: Mathematics.


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