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For complex numbers, the principal

**cube root**is usually defined as the**cube root**that has the greatest real part, or, equivalently, the**cube root**whose argument has the least absolute value. It is related to the principal value of the natural logarithm by the formula If we write x as where r is a non-negative real number and θ lies in the range ,The

**cube root**law is an observation in political science that the number of members of a unicameral legislature, or the lower house of a bicameral legislature, is about the**cube root**of the population being represented. [1] The rule was devised by Rein Taagepera in his 1972 paper "The size of national assemblies". [2]The solutions of this equation are called

**roots**of the cubic function defined by the left-hand side of the equation. If all of the coefficients a, b, c, and d of the cubic equation are real numbers, then it has at least one real**root**(this is true for all odd-degree polynomial functions ).In algebraic terms, doubling a unit

**cube**requires the construction of a line segment of length x, where x3 = 2; in other words, x = , the**cube root**of two. This is because a**cube**of side length 1 has a volume of 13 = 1, and a**cube**of twice that volume (a volume of 2) has a side length of the**cube root**of 2.If f has three real

**roots**, then K is called a totally real cubic field and it is an example of a totally real field. If, on the other hand, f has a non-real**root**, then K is called a complex cubic field . A cubic field K is called a cyclic cubic field if it contains all three**roots**of its generating polynomial f.The

**cube**function is the function x ↦ x3 (often denoted y = x3) that maps a number to its**cube**. It is an odd function, as (−n)3 = − (n3). The volume of a geometric**cube**is the**cube**of its side length, giving rise to the name. The inverse operation that consists of finding a number whose**cube**is n is called extracting the**cube root**of n.Doubling the

**cube**is the construction, using only a straightedge 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**.

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