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# Cube (algebra)

In arithmetic and algebra, the cube of a number is its third power: the result of the number multiplied by itself twice: It is also the number multiplied by its square: This is also the volume formula for a geometric cube with sides of length, giving rise to the name. 

70 relations: Algebra, Arithmetic, Arithmetic progression, Aryabhata, Aryabhatiya, Cabtaxi number, Chinese mathematics, Codomain, Complex number, Cube, Cube root, Cubic function, Cyclic group, Derivative, Digital root, Diophantus, Doubling the cube, Eisenstein integer, Euler's sum of powers conjecture, Even and odd functions, Exponentiation, Expression (mathematics), Factorization of polynomials, Field (mathematics), Fifth power (algebra), Finite field, First Babylonian dynasty, Fourth power, Graph of a function, Greek mathematics, Group isomorphism, Hero of Alexandria, History of mathematics, If and only if, Imaginary number, Imaginary unit, India, Inequality (mathematics), Integer, Inverse function, Liu Hui, Modular arithmetic, Monkey saddle, Monotonic function, Multiplicative group, Ordered ring, Oxford University Press, Parity (mathematics), Pell's equation, Perfect number, ... Expand index (20 more) »

## Algebra

Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.

## Arithmetic

Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.

## Arithmetic progression

In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

## Aryabhata

Aryabhata (IAST) or Aryabhata I (476–550 CE) was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy.

## Aryabhatiya

Aryabhatiya (IAST) or Aryabhatiyam, a Sanskrit astronomical treatise, is the magnum opus and only known surviving work of the 5th century Indian mathematician Aryabhata.

## Cabtaxi number

In mathematics, the n-th cabtaxi number, typically denoted Cabtaxi(n), is defined as the smallest positive integer that can be written as the sum of two positive or negative or 0 cubes in n ways.

## Chinese mathematics

Mathematics in China emerged independently by the 11th century BC.

## Codomain

In mathematics, the codomain or target set of a function is the set into which all of the output of the function is constrained to fall.

## Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

## Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

## Cube root

In mathematics, a cube root of a number x is a number y such that y3.

## Cubic function

In algebra, a cubic function is a function of the form in which is nonzero.

## Cyclic group

In algebra, a cyclic group or monogenous group is a group that is generated by a single element.

## Derivative

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

## Digital root

The digital root (also repeated digital sum) of a non-negative integer is the (single digit) value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit sum.

## Diophantus

Diophantus of Alexandria (Διόφαντος ὁ Ἀλεξανδρεύς; born probably sometime between AD 201 and 215; died around 84 years old, probably sometime between AD 285 and 299) was an Alexandrian Hellenistic mathematician, who was the author of a series of books called Arithmetica, many of which are now lost.

## Doubling the cube

Doubling the cube, also known as the Delian problem, is an ancient geometric problem.

## Eisenstein integer

In mathematics, Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are complex numbers of the form where and are integers and is a primitive (hence non-real) cube root of unity.

## Euler's sum of powers conjecture

Euler's conjecture is a disproved conjecture in mathematics related to Fermat's last theorem.

## Even and odd functions

In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses.

## Exponentiation

Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.

## Expression (mathematics)

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

## Factorization of polynomials

In mathematics and computer algebra, factorization of polynomials or polynomial factorization is the process of expressing a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.

## Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

## Fifth power (algebra)

In arithmetic and algebra, the fifth power of a number n is the result of multiplying five instances of n together.

## Finite field

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.

## First Babylonian dynasty

The chronology of the first dynasty of Babylonia (also First Babylonian Empire) is debated as there is a Babylonian King List A and a Babylonian King List B. In this chronology, the regnal years of List A are used due to their wide usage.

## Fourth power

In arithmetic and algebra, the fourth power of a number n is the result of multiplying four instances of n together.

## Graph of a function

In mathematics, the graph of a function f is, formally, the set of all ordered pairs, and, in practice, the graphical representation of this set.

## Greek mathematics

Greek mathematics refers to mathematics texts and advances written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean.

## Group isomorphism

In abstract algebra, a group isomorphism is a function between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the given group operations.

## Hero of Alexandria

Hero of Alexandria (ἭρωνGenitive: Ἥρωνος., Heron ho Alexandreus; also known as Heron of Alexandria; c. 10 AD – c. 70 AD) was a mathematician and engineer who was active in his native city of Alexandria, Roman Egypt.

## History of mathematics

The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.

## If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

## Imaginary number

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit,j is usually used in Engineering contexts where i has other meanings (such as electrical current) which is defined by its property.

## Imaginary unit

The imaginary unit or unit imaginary number is a solution to the quadratic equation.

## India

India (IAST), also called the Republic of India (IAST), is a country in South Asia.

## Inequality (mathematics)

In mathematics, an inequality is a relation that holds between two values when they are different (see also: equality).

## Integer

An integer (from the Latin ''integer'' meaning "whole")Integer&#x2009;'s first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

## Inverse function

In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.

## Liu Hui

Liu Hui was a Chinese mathematician who lived in the state of Cao Wei during the Three Kingdoms period (220–280) of China.

## Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

In mathematics, the monkey saddle is the surface defined by the equation It belongs to the class of saddle surfaces and its name derives from the observation that a saddle for a monkey requires three depressions: two for the legs, and one for the tail.

## Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

## Multiplicative group

In mathematics and group theory, the term multiplicative group refers to one of the following concepts.

## Ordered ring

In abstract algebra, an ordered ring is a (usually commutative) ring R with a total order ≤ such that for all a, b, and c in R.

## Oxford University Press

Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.

## Parity (mathematics)

In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd.

## Pell's equation

Pell's equation (also called the Pell–Fermat equation) is any Diophantine equation of the form where n is a given positive nonsquare integer and integer solutions are sought for x and y. In Cartesian coordinates, the equation has the form of a hyperbola; solutions occur wherever the curve passes through a point whose x and y coordinates are both integers, such as the trivial solution with x.

## Perfect number

In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum).

## Perfect power

In mathematics, a perfect power is a positive integer that can be expressed as an integer power of another positive integer.

## Plato's number

Plato’s number is a number enigmatically referred to by Plato in his dialogue the Republic (8.546b).

## Point reflection

In geometry, a point reflection or inversion in a point (or inversion through a point, or central inversion) is a type of isometry of Euclidean space.

## Power of two

In mathematics, a power of two is a number of the form where is an integer, i.e. the result of exponentiation with number two as the base and integer as the exponent.

## Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

## Real line

In mathematics, the real line, or real number line is the line whose points are the real numbers.

## Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

## Rotational symmetry

Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn.

## Rubik's Cube

Rubik's Cube is a 3-D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik.

## Similarity (geometry)

Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other.

## Solid geometry

In mathematics, solid geometry is the traditional name for the geometry of three-dimensional Euclidean space.

## Square (algebra)

In mathematics, a square is the result of multiplying a number by itself.

## Square number

In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself.

## Subscript and superscript

A subscript or superscript is a character (number, letter or symbol) that is (respectively) set slightly below or above the normal line of type.

## Surjective function

In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).

## Taxicab number

In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), also called the nth Hardy–Ramanujan number, is defined as the smallest number that can be expressed as a sum of two positive cube numbers in n distinct ways.

## The Nine Chapters on the Mathematical Art

The Nine Chapters on the Mathematical Art is a Chinese mathematics book, composed by several generations of scholars from the 10th&ndash;2nd century BCE, its latest stage being from the 2nd century CE.

## Triangular number

A triangular number or triangle number counts objects arranged in an equilateral triangle, as in the diagram on the right.

## Volume

Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.

## 3

3 (three) is a number, numeral, and glyph.

## References

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