Solutions
Menaechmus' original solution involves the intersection of two conic curves. Other more complicated methods of doubling the cube involve the cissoid of Diocles, the conchoid of Nicomedes, or the Philo line. Archytas solved the problem in the fourth century B.C. using geometric construction in three dimensions, determining a certain point as the intersection of three surfaces of revolution.
False claims of doubling the cube with compass and straightedge abound in mathematical crank literature (pseudomathematics).
Origami may also be used to construct the cube root of two by folding paper.
Read more about this topic: Doubling The Cube
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