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Equivalently, a powerful number is the product of a square and a cube, that is, a number m of the form m = a 2 b 3, where a and b are positive integers. Powerful numbers are also known as squareful, square-full, or 2-full. Paul Erdős and George Szekeres studied such numbers and Solomon W. Golomb named such numbers powerful.
The sixth powers of integers can be characterized as the numbers that are simultaneously squares and cubes. [1] In this way, they are analogous to two other classes of figurate numbers: the square triangular numbers, which are simultaneously square and triangular, and the solutions to the cannonball problem, which are simultaneously square and square-pyramidal.
Yoshida Mitsuyoshi (吉田 光由, 1598 – January 8, 1672), also known as Yoshida Kōyū, was a Japanese mathematician in the Edo period. [1] His popular and widely disseminated published work made him the most well known writer about mathematics in his lifetime. [2] He was a student of Kambei Mori (also known as Mōri Shigeyoshi).
The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 2 3 = 8 or (x + 1) 3. The cube is also the number multiplied by its square: n 3 = n × n 2 = n × n × n. The cube function is the function x ↦ x 3 (often denoted y = x 3) that maps a number to its cube. It is an odd function, as
The cannonball problem, asking whether there are any square pyramidal numbers that are also square numbers other than 1 and 4900, is said to have developed out of this exchange. Édouard Lucas found the 4900-ball pyramid with a square number of balls, and in making the cannonball problem more widely known, suggested that it was the only ...
A square whose side length is a triangular number can be partitioned into squares and half-squares whose areas add to cubes. From Gulley (2010).The n th coloured region shows n squares of dimension n by n (the rectangle is 1 evenly divided square), hence the area of the n th region is n times n × n.
A cube is a special case of rectangular cuboid in which the edges are equal in length. [1] Like other cuboids, every face of a cube has four vertices, each of which connects with three congruent lines. These edges form square faces, making the dihedral angle of a cube between every two adjacent squares being the interior angle of a square, 90 ...
The Super Square One is a 4-layer version of the Square-1. Just like the Square-1, it can adopt non-cubic shapes as it is twisted. As of 2009, it is sold by Uwe Mèffert in his puzzle shop, Meffert's. It consists of 4 layers of 8 pieces, each surrounding a circular column which can be rotated along a perpendicular axis.