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René Descartes Portrait after Frans Hals[note 1] Born 31 March 1596 (1596-03-31) La Haye en Touraine, Touraine, Kingdom of France Died 11 February 1650 (1650-02-12)(aged 53) Stockholm, Swedish Empire Nationality French Education Collège Royal Henry-Le-Grand(1607–1614) University of Poitiers(LL.B., 1616) University of Franeker(no degree)

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

Equivalently, it is the number of points in a body-centered cubic pattern within a cube that has n + 1 points along each of its edges. The first few centered cube numbers are 1, 9, 35, 91, 189, 341, 559, 855, 1241, 1729, 2331, 3059, 3925, 4941, 6119, 7471, 9009, ... (sequence A005898 in the OEIS ). Contents 1 Formulas 2 Properties 3 See also

Not to be confused with Cubic function. Polynomial equation of degree 3 Graph of a cubic function with 3 realroots(where the curve crosses the horizontal axis at y= 0). The case shown has two critical points. Here the function is f(x) = (x3+ 3x2− 6x− 8)/4. In algebra, a cubic equationin one variable is an equationof the form

Doubling the cube is the construction, using only a straight-edge and compass, of the edge of a cube that has twice the volume of a cube with a given edge. This is impossible because the cube root of 2, though algebraic, cannot be computed from integers by addition, subtraction, multiplication, division, and taking square roots.

In number theory, Kaprekar's routine is an iterative algorithm that, with each iteration, takes a natural number in a given number base, creates two new numbers by sorting the digits of its number by descending and ascending order, and subtracts the second from the first to yield the natural number for the next iteration.