64 (number) 64 (number) 64 (sixty-four) is the natural number following 63 and preceding 65. Sixty-four is the square of 8, the cube of 4, and the sixth power of 2. It is the smallest number with exactly seven divisors. It is the lowest positive power of two that is adjacent to neither a Mersenne prime nor a Fermat prime. 64 is the sum of Euler's totient function for the first fourteen integers. It is also a dodecagonal number and a centered triangular number. 64 is also the first whole number that is both a perfect square and a perfect cube. Since
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