Doubling the cube cube involve neusis, the cissoid of Diocles, the conchoid of Nicomedes, or the Philo line. Archytas solved the problem in the 4th century BC 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. There is a simple neusis construction using a marked ruler for a length which is the cube root of 2 times another length. Then AG is the
Principal root of unity Principal root of unity In mathematics, a principal "n"-th root of unity (where "n" is a positive integer) of a ring is an element formula_1 satisfying the equations In an integral domain, every primitive "n"-th root of unity is also a principal formula_3-th root of unity. In any ring, if formula_3 is a power of formula_5, then any formula_6-th root of formula_7 is a principal formula_3-th root of unity. A non-example is formula_9 in the ring of integers modulo formula_10; while formula_11 and thus formula_9 is a cube root of unity, formula_13 meaning that it is not a "principal" cube