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64 is: the first whole number (greater than one) that is both a perfect square, and a perfect cube. the lowest positive power of two that is not adjacent to either a Mersenne prime or a Fermat prime. 64 is the fourth superperfect number — a number such that σ (σ ( n )) = 2 n.
In geometry, a hypercube is an n -dimensional analogue of a square ( n = 2) and a cube ( n = 3 ). It is a closed, compact, convex figure whose 1- skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length. A unit hypercube's longest diagonal in n ...
A cube of this class was first constructed in late 2004 by Mitsutoshi Nakamura. This cube is a combination pantriagonal magic cube and diagonal magic cube. Therefore, all main and broken space diagonals sum correctly, and it contains 3 m planar simple magic squares. In addition, all 6 oblique squares are pandiagonal magic squares.
In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted , is 2, because 23 = 8, while the other cube roots of ...
Fermat's theorem on sums of two squares. In additive number theory, Fermat 's theorem on sums of two squares states that an odd prime p can be expressed as: with x and y integers, if and only if. The prime numbers for which this is true are called Pythagorean primes . For example, the primes 5, 13, 17, 29, 37 and 41 are all congruent to 1 ...
Euler brick. In mathematics, an Euler brick, named after Leonhard Euler, is a rectangular cuboid whose edges and face diagonals all have integer lengths. A primitive Euler brick is an Euler brick whose edge lengths are relatively prime. A perfect Euler brick is one whose space diagonal is also an integer, but such a brick has not yet been found.
Hendricks was also an authority on the design of inlaid magic squares and cubes (and in 1999, a magic tesseract). Following his retirement, he gave many public lectures on magic squares and cubes in schools and in-service teacher's conventions in Canada and the northern United States.
Sixth powers can be formed by multiplying a number by its fifth power, multiplying the square of a number by its fourth power, by cubing a square, or by squaring a cube.