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The cube of a number n is denoted n 3, using a superscript 3, [a] for example 2 3 = 8. The cube operation can also be defined for any other mathematical expression, for example (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
Semi-log plot of solutions of + + = for integer , , and , and .Green bands denote values of proven not to have a solution.. In the mathematics of sums of powers, it is an open problem to characterize the numbers that can be expressed as a sum of three cubes of integers, allowing both positive and negative cubes in the sum.
Lagrange's method can be applied directly to the general cubic equation ax 3 + bx 2 + cx + d = 0, but the computation is simpler with the depressed cubic equation, t 3 + pt + q = 0. Lagrange's main idea was to work with the discrete Fourier transform of the roots instead of with the roots themselves.
cubic the degree of a polynomial is 3 also cube or cubed for denoting the third power of a unit: cubic metre or metre cubed; albatross in golf denotes three strokes less than par. Sometimes called double eagle; hat-trick or hat trick: achievement of three feats in sport or other contexts [4] antepenultimate third from the end
The cubic inch (symbol in 3) is a unit of volume in the Imperial units and United States customary units systems. It is the volume of a cube with each of its three dimensions (length, width, and height) being one inch long which is equivalent to 1 ⁄ 231 of a US gallon.
Similarly, the expression b 3 = b · b · b is called "the cube of b" or "b cubed", because the volume of a cube with side-length b is b 3. When an exponent is a positive integer, that exponent indicates how many copies of the base are multiplied together. For example, 3 5 = 3 · 3 · 3 · 3 · 3 = 243.
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For example, in the quaternions, a real number has infinitely many cube roots. Plot of y = 3 √ x. The plot is symmetric with respect to origin, as it is an odd function. At x = 0 this graph has a vertical tangent. A unit cube (side = 1) and a cube with twice the volume (side = 3 √ 2 = 1.2599... OEIS: A002580).