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  2. Cube root - Wikipedia

    The cube roots of a number x are the numbers y which satisfy the equation Properties Real numbers For any real number x, there is one real number y such that y3 = x. The cube function is increasing, so does not give the same result for two different inputs, and it covers all real numbers. In other words, it is a bijection, or one-to-one.

  3. Cube root rule - Wikipedia

    The cube root rule or 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. The rule was devised by Rein Taagepera in his 1972 paper "The size of national assemblies".

  4. Cube (algebra) - Wikipedia

    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.

  5. Cubic equation - Wikipedia

    the cubic has three distinct real roots If the cubic has one real root and two non-real complex conjugate roots. This can be proved as follows. First, if r is a root of a polynomial with real coefficients, then its complex conjugate is also a root. So the non-real roots, if any, occur as pairs of complex conjugate roots.

  6. Cube - Wikipedia

    The cube is also a square parallelepiped, an equilateral cuboid and a right rhombohedron a 3-zonohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations. The cube is dual to the octahedron. It has cubical or octahedral symmetry. The cube is the only convex polyhedron whose faces are all squares

  7. Cubic field - Wikipedia

    Adjoining the real cube root of 2 to the rational numbers gives the cubic field . This is an example of a pure cubic field, and hence of a complex cubic field. In fact, of all pure cubic fields, it has the smallest discriminant (in absolute value ), namely −108. The complex cubic field obtained by adjoining to Q a root of x3 + x2 − 1 is not pure.

  8. Square–cube law - Wikipedia

    The square–cube law was first mentioned in Two New Sciences (1638). The square–cube law (or cube–square law) is a mathematical principle, applied in a variety of scientific fields, which describes the relationship between the volume and the surface area as a shape's size increases or decreases.

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