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Number raised to the third power
arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number
Cube_(algebra)
Result of multiplying five instances of a number together
1966) Eighth power Seventh power Sixth power Fourth power Cube (algebra) Square (algebra) Perfect power "Webster's 1913". Lander, L. J.; Parkin, T. R
Fifth_power_(algebra)
Topics referred to by the same term
Cube Orange County, a science museum in Santa Ana, California Cube (algebra), the third power of a number CuBe, an alloy of copper and beryllium Cubé
Cube_(disambiguation)
Natural number
light, take aim on the second and fire on the third. Mathematics portal Cube (algebra) – (3 superscript) Thrice Third Triad Trio Rule of three ɜ, U+025C ɜ
3
Natural number
main feast day is celebrated on November 27. 72 (number) – 27 reversed Cube (algebra) "Weird Al" Yankovic § Recurring themes for his frequent use of the
27_(number)
Result of multiplying four instances of a number together
having a general solution using radicals. Square (algebra) Cube (algebra) Exponentiation Fifth power (algebra) Sixth power Seventh power Eighth power Perfect
Fourth_power
Product of a number by itself
mean is the variance, and its square root is the standard deviation. Cube (algebra) Euclidean distance Exponentiation by squaring Hilbert's seventeenth
Square_(algebra)
3D combination puzzle
Rubik's Cube is a 3D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the
Rubik's_Cube
Convex polytope, the n-dimensional analogue of a square and a cube
geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3); the special case for n = 4 is known as a tesseract. It is a closed
Hypercube
Solid with six equal square faces
Jesper (2010). "The Algebra of Geometric Impossibility: Descartes and Montucla on the Impossibility of the Duplication of the Cube and the Trisection of
Cube
Number whose cube is a given number
In an algebraically closed field of characteristic three, every element has exactly one cube root. In other number systems or other algebraic structures
Cube_root
Cube with edge length one
A unit cube, more formally a cube of side 1, is a cube whose sides are 1 unit long. The volume of a 3-dimensional unit cube is 1 cubic unit, and its total
Unit_cube
Topics referred to by the same term
in Wiktionary, the free dictionary. Cubic may refer to: Cube (algebra), "cubic" measurement Cube, a three-dimensional solid object bounded by six square
Cubic
Result of multiplying six instances of a number
equation Eighth power Seventh power Fifth power (algebra) Fourth power Cube (algebra) Square (algebra) Dowden, Richard (April 30, 1825), "(untitled)",
Sixth_power
Branch of mathematics
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems
Algebra
Branch of mathematics
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations
Abstract_algebra
Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until
History_of_algebra
Cube that fits through hole in smaller cube
In geometry, Prince Rupert's cube is the largest cube that can pass through a hole cut through a unit cube without splitting it into separate pieces.
Prince_Rupert's_cube
Mathematical group
The Rubik's Cube group ( G , ⋅ ) {\displaystyle (G,\cdot )} represents the mathematical structure of the Rubik's Cube mechanical puzzle. Each element
Rubik's_Cube_group
Mathematical polynomial formula
In mathematics, the sum of two cubes is a cubed number added to another cubed number. Every sum of cubes may be factored according to the identity a 3
Sum_of_two_cubes
Result of multiplying seven instances of a number
powers 4 and 5. Eighth power Sixth power Fifth power (algebra) Fourth power Cube (algebra) Square (algebra) Womack, D. (2015), "Beyond tetration operations:
Seventh_power
Ancient geometric construction problem
solution was finally proven by Pierre Wantzel in 1837. In algebraic terms, doubling a unit cube requires the construction of a line segment of length x
Doubling_the_cube
Method of drawing geometric objects
side of a cube whose volume is twice the volume of a cube with a given side. Hippocrates and Menaechmus showed that the volume of the cube could be doubled
Straightedge and compass construction
Straightedge_and_compass_construction
Polynomial equation of degree 3
In algebra, a cubic equation in one variable is an equation of the form a x 3 + b x 2 + c x + d = 0 {\displaystyle ax^{3}+bx^{2}+cx+d=0} in which a is
Cubic_equation
Branch of mathematics
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems
Algebraic_geometry
English physicist and inventor (1802–1875)
mathematician, Wheatstone published a mathematical proof in 1854 (see Cube (algebra)). In 1840, Wheatstone brought out his magneto-electric machine for
Charles_Wheatstone
Centered figurate number that counts points in a three-dimensional pattern
A centered cube number is a centered figurate number that counts the points in a three-dimensional pattern formed by a point surrounded by concentric cubical
Centered_cube_number
theorem (algebraic surfaces) Riemann–Roch theorem for surfaces (algebraic surfaces) Sylvester pentahedral theorem (invariant theory) Theorem of the cube (algebraic
List_of_theorems
Topological group
In mathematics, a Cantor cube is a topological group of the form {0, 1}A for some index set A. Its algebraic and topological structures are the group
Cantor_cube
Set of vectors used to define coordinates
n-dimensional cube [−1, 1]n as a function of dimension, n. A point is first randomly selected in the cube. The second point is randomly chosen in the same cube. If
Basis_(linear_algebra)
Basic concepts of algebra
{b^{2}-4ac}}}{2a}}}}}} Elementary algebra, also known as high school algebra or college algebra, encompasses the basic concepts of algebra. It is often contrasted
Elementary_algebra
Natural number
faces, whose first stellation is the cube-octahedron compound. The octonions are a hypercomplex normed division algebra that are an extension of the complex
8
Four-dimensional analogue of the cube
geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. Just as the perimeter
Tesseract
Branch of mathematics
especially algebraic geometry. Al-Mahani (b. 853) conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra. Thābit
Geometry
Multi-dimensional data structure
derived from linear algebra and vector mathematics. Some languages (such as PDL) distinguish between a list of images and a data cube, while many (such
Data_cube
Triangular array of the binomial coefficients
coefficients which play a crucial role in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician
Pascal's_triangle
Geometric space with four dimensions
possible regular 4D objects, the tesseract, which is analogous to the 3D cube. The idea of making time the fourth dimension began with Jean le Rond d'Alembert's
Four-dimensional_space
Branch of mathematics
Noncommutative algebraic geometry is a branch of mathematics, and more specifically a direction in noncommutative geometry, that studies the geometric
Noncommutative algebraic geometry
Noncommutative_algebraic_geometry
Hungarian inventor (born 1944)
of his cube, made of 27 wooden blocks; it took Rubik a month to solve the problem of the cube. It proved a useful tool for teaching algebraic group theory
Ernő_Rubik
Arithmetic operation, inverse of nth power
radicand. A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred by using ordinal numbers, as in
Nth_root
non-associative division algebra. A similar construction works for any cubic alternative separable algebra over a field containing a primitive cube root of unity
Okubo_algebra
Optimal solutions for the Rubik's Cube are solutions that are the shortest in some sense. There are two common ways to measure the length of a solution
Optimal solutions for the Rubik's Cube
Optimal_solutions_for_the_Rubik's_Cube
Number with an integer power equal to 1
characteristic of the field is zero, the roots are complex numbers that are also algebraic integers. For fields with a positive characteristic, the roots belong
Root_of_unity
6-dimensional hypercube
geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces
6-cube
Application of Clifford algebra
Plane-based geometric algebra is an application of Clifford algebra to modelling planes, lines, points, and rigid transformations. Generally this is with
Plane-based_geometric_algebra
Geometric space with eight dimensions
polytopes, of which there are only three in eight dimensions: the 8-simplex, 8-cube, and 8-orthoplex. A broader family are the uniform 8-polytopes, constructed
Eight-dimensional_space
Property of a mathematical space
Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates
Dimension
Natural number
elements. 6 the answer to the two-dimensional kissing number problem. A cube has 6 faces. A tetrahedron has 6 edges. In four dimensions, there are a total
6
Finite extension of the rationals
In mathematics, an algebraic number field (or simply number field) is an extension field K {\displaystyle K} of the field of rational numbers Q {\displaystyle
Algebraic_number_field
Number constructible via compass and straightedge
In geometry and algebra, a real number r {\displaystyle r} is constructible if and only if, given a line segment of unit length, a line segment of length
Constructible_number
Field of knowledge
including number theory (the study of integers and their properties), algebra (the study of operations and the structures they form), geometry (the study
Mathematics
Niblo, Graham (2005). "From wall spaces to CAT(0) cube complexes". International Journal of Algebra and Computation. 15 (05n06): 875–885. arXiv:math/0309036
Cubical_complex
Algebraic structure with addition, multiplication, and division
rational numbers do. A field is thus a fundamental algebraic structure that is widely used in algebra, number theory, and many other areas of mathematics
Field_(mathematics)
Roots of an algebraic element's minimal polynomial
since the algebraic conjugates over R {\displaystyle \mathbb {R} } of a complex number are the number itself and its complex conjugate. The cube roots of
Conjugate element (field theory)
Conjugate_element_(field_theory)
Solution in radicals of a polynomial equation
A solution in radicals or algebraic solution is an expression of a solution of a polynomial equation that is algebraic, that is, relies only on addition
Solution_in_radicals
Geometry problem on tiling by hypercubes
S2CID 120163301. Szabó, Sándor (1993), "Cube tilings as contributions of algebra to geometry", Beiträge zur Algebra und Geometrie, 34 (1): 63–75, MR 1239279
Keller's_conjecture
Polyhedron with four faces
the cube. The cube can be dissected into six such 3-orthoschemes four different ways, with all six surrounding the same √3 cube diagonal. The cube can
Tetrahedron
Method of cryptanalysis
Michael Vielhaber's "Algebraic IV Differential Attack" (AIDA) as a precursor of the Cube attack. Dinur has stated at Eurocrypt 2009 that Cube generalises and
Cube_attack
Removal of square roots from denominators
be extended to all algebraic numbers and algebraic functions (as an application of norm forms). For example, to rationalise a cube root, two linear factors
Rationalisation_(mathematics)
Branch of algebraic geometry
mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered
Arithmetic_geometry
Branch of mathematics
manifolds. It uses the techniques of vector calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry
Differential_geometry
Four-dimensional number system
Split-quaternion – Four-dimensional associative algebra over the reals Tesseract – Four-dimensional analogue of the cube Versor – Quaternion of norm 1 (unit quaternion)
Quaternion
Algebraic object with geometric applications
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space
Tensor
Field of mathematics dealing with three-dimensional Euclidean spaces
the cube of its radius. Basic topics in solid geometry and stereometry include: incidence of planes and lines dihedral angle and solid angle the cube, cuboid
Solid_geometry
3rd-century Greek mathematician
problems that are solved through algebraic equations. Joseph-Louis Lagrange called Diophantus "the inventor of algebra"; his exposition became the standard
Diophantus
Symbolic description of a mathematical object
equality", that is, both expressions "mean the same thing." In elementary algebra, a variable in an expression is a letter that represents a number whose
Expression_(mathematics)
Positive real number which when multiplied by itself gives 5
{\displaystyle x^{2}-5=0} , making it a quadratic integer, a type of algebraic number. 5 {\displaystyle {\sqrt {5}}} is an irrational number, meaning
Square_root_of_5
Study of categorified structures
higher-dimensional algebra is the study of categorified structures. It has applications in nonabelian algebraic topology, and generalizes abstract algebra. A first
Higher-dimensional_algebra
American mathematician (1916–2001)
Information Age. Shannon was the first to describe the use of Boolean algebra—essential to all digital electronic circuits—and helped found the field
Claude_Shannon
Complex number that solves a monic polynomial with integer coefficients
In algebraic number theory, an algebraic integer is a complex number that is integral over the integers. That is, an algebraic integer is a complex root
Algebraic_integer
Branch of mathematics that studies the properties of groups
In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known
Group_theory
Unit hypercube of variable dimension whose corners have been perturbed
The Klee–Minty cube or Klee–Minty polytope (named after Victor Klee and George J. Minty) is a unit hypercube of variable dimension whose corners have been
Klee–Minty_cube
Persian mathematician and engineer (c. 953 – c. 1029)
particular for the beginnings of freeing algebra from geometry. Among historians, his most widely studied work is his algebra book al-fakhri fi al-jabr wa al-muqabala
Al-Karaji
Notable events in the history of geometry
the idea of reducing geometrical problems such as doubling the cube to problems in algebra. ca. 900 – Abu Kamil of Egypt had begun to understand what we
Timeline_of_geometry
Geometric arrangements of points, foundational to Lie theory
algebras, especially the classification and representation theory of semisimple Lie algebras. Since Lie groups (and some analogues such as algebraic groups)
Root_system
Branch of mathematics
operator-algebraic methods based on C*-algebras, von Neumann algebras, and spectral triples; algebraic approaches to noncommutative rings and graded algebras;
Noncommutative_geometry
Mathematical idealization of the trace left by a moving point
are unions of curves and isolated points), and algebraic curves (see below). Level curves and algebraic curves are sometimes called implicit curves, since
Curve
Mathematical connection between field theory and group theory
only the usual algebraic operations (addition, subtraction, multiplication, division) and application of radicals (square roots, cube roots, etc)? The
Galois_theory
Positive real number which when multiplied by itself gives 6
double cube, as illustrated above. The square roots of all lower natural numbers appear as the distances between other vertex pairs in the double cube (including
Square_root_of_6
Notable events in the history of algebra
a timeline of key developments of algebra: Mathematics portal History of algebra – Historical development of algebra Archibald, Raymond Clare (December
Timeline_of_algebra
Generalization of associativity properties
these operations. Given an operad O {\displaystyle O} , one defines an algebra over O {\displaystyle O} to be a set together with concrete operations
Operad
Mathematical expression with outer and inner radicals
In algebra, a nested radical is a radical expression (one containing a square root sign, cube root sign, etc.) that contains (nests) another radical expression
Nested_radical
Indian mathematician and astronomer (598–668)
astronomy, but it also contains key chapters on mathematics, including algebra, geometry, trigonometry and algorithmics, which are believed to contain
Brahmagupta
Array of numbers
"two-by-three matrix", a 2 × 3 matrix, or a matrix of dimension 2 × 3. In linear algebra, matrices are used as linear maps. In geometry, matrices are used for geometric
Matrix_(mathematics)
British mathematician (1938–2023)
the Rubik's Cube. His Notes on Rubik's "Magic Cube" which he began compiling in 1979 provided the first mathematical analysis of the Cube as well as providing
David_Singmaster
Concept in algebraic topology
In mathematics, particularly in algebraic topology, the n-skeleton of a topological space X presented as a simplicial complex (resp. CW complex) refers
N-skeleton
specifically the field of algebra, Sklyanin algebras are a class of noncommutative algebra named after Evgeny Sklyanin. This class of algebras was first studied
Sklyanin_algebra
Method for visually representing three-dimensional objects
same, or 120°. For example, with a cube, this is done by first looking straight towards one face. Next, the cube is rotated ±45° about the vertical axis
Isometric_projection
Shape with four equal sides and angles
The area of a square is the side length multiplied by itself, and so in algebra, multiplying a number by itself is called squaring. Equal squares can tile
Square
Variant of Rubik's Cube
Schönert "Analyzing Rubik's Cube with GAP": the permutation group of Rubik's Cube is examined with GAP computer algebra system "GAMES Magazine #29".
Pyraminx
Cantor cube Space-filling curve Topologist's sine curve Tychonoff plank Comb space Uniform norm Weak topology Strong topology Hilbert cube Lower limit
List of general topology topics
List_of_general_topology_topics
Graphs formed by a hypercube's edges and vertices
For instance, the cube graph Q 3 {\displaystyle Q_{3}} is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube. Q n {\displaystyle
Hypercube_graph
Non-tensorial representation of the spin group
spin group or of the associated Clifford algebra. After choosing a matrix realization of the Clifford algebra, spinors may be represented concretely as
Spinor
Technical treatment of Boolean algebras
mathematically rich branch of abstract algebra. Stanford Encyclopaedia of Philosophy defines Boolean algebra as 'the algebra of two-valued logic with only sentential
Boolean algebras canonically defined
Boolean_algebras_canonically_defined
Algebraic expansion of powers of a binomial
(12th century), there credited to al-Karajī. Al-Samawʾal algebraically expanded the square, cube, and fourth power of a binomial, each in terms of the previous
Binomial_theorem
Magma obeying the Latin square property
In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure that resembles a group in the sense that "division" is always possible
Quasigroup
linear equivalence, by the Italian school of algebraic geometry. The final version of the theorem of the cube was first published by Lang (1959), who credited
Theorem_of_the_cube
7-cube, Rectified 7-cube, 7-cube, Truncated 7-cube, Cantellated 7-cube, Runcinated 7-cube, Stericated 7-cube, Pentellated 7-cube, Hexicated 7-cube 7-orthoplex
List_of_mathematical_shapes
Multi-dimensional generalization of triangle
solving a problem in geometric probability. Henri Poincaré, writing about algebraic topology in 1900, called them "generalized tetrahedra". In 1902 Pieter
Simplex
In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known
List_of_group_theory_topics
CUBE ALGEBRA
CUBE ALGEBRA
Male
African
zebra.
Girl/Female
Tamil
Cute
Girl/Female
Muslim
Cure
Boy/Male
English
Ropemaker.
Girl/Female
British, English
Cute
Boy/Male
German
Bright; Shining Intellect
Girl/Female
Muslim
Cute
Surname or Lastname
French (Aubé)
French (Aubé) : from the Old French personal name Aube, a variant of Albert. This is a common surname in VT.English (of Norman origin) : nickname from Old French aube, albe ‘white’ (i.e. blond), from Latin albus. Compare Albin.
Girl/Female
Bengali, Gujarati, Hindu, Indian, Modern
Cute
Girl/Female
Hindu, Indian
Cute
Surname or Lastname
Scottish and Irish
Scottish and Irish : reduced form of McCure, an Anglicized form of Gaelic Mac Ãomhair (see McIver).English : possibly from Middle English cure ‘charge’, ‘care’, ‘concern’.
Boy/Male
Hindu, Indian
Golf; Ice Cube
Boy/Male
American, Australian, British, English, Irish
Rope-maker; A Cape
Girl/Female
British, English
Cute
Male
English
Pet form of English Reuben, RUBE means "behold, a son!"Â
Boy/Male
Arabic
Cure.
Girl/Female
Hindu
Cute
Boy/Male
British, English
Cute
Boy/Male
British, English
Cute
Girl/Female
Tamil
Rakshina | ரகà¯à®·à¯€à®¨à®¾
Cute
CUBE ALGEBRA
CUBE ALGEBRA
Boy/Male
Gujarati, Hindu, Indian, Modern
To Rise
Female
Arthurian
, the "unsympathetic" lover of Pelleas.
Girl/Female
Tamil
Sweet person, Sweet, Surgery
Male
Czechoslovakian
, usurp glory.
Girl/Female
Hindu
Wisdom, One with good morals, Good guidance, Righteous
Boy/Male
Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Marwadi, Oriya, Sanskrit, Tamil, Telugu, Traditional
Master of Religion; Lord of Religion
Boy/Male
Indian
The Planet Mars; Son of Earth
Boy/Male
English
Anne's son; son of God. Famous Bearer: actor Anson Williams.
Boy/Male
Hindu, Indian
One of the Four Vedas; Lord Vishnu
Boy/Male
Muslim
Name of abu Jafar, A jurist
CUBE ALGEBRA
CUBE ALGEBRA
CUBE ALGEBRA
CUBE ALGEBRA
CUBE ALGEBRA
v. t.
To furnish with a tube; as, to tube a well.
imp. & p. p.
of Cube
v. i.
To restore health; to effect a cure.
a.
Having the form or properties of a cube; contained, or capable of being contained, in a cube.
n.
A combination of a cube and octahedron, esp. one in which the octahedral faces meet at the middle of the cubic edges.
a.
Of the form of a cube.
v. t.
To prepare for preservation or permanent keeping; to preserve, as by drying, salting, etc.; as, to cure beef or fish; to cure hay.
v. t.
To form into a cue; to braid; to twist.
n.
The product obtained by taking a number or quantity three times as a factor; as, 4x4=16, and 16x4=64, the cube of 4.
n.
A cube.
p. pr. & vb. n.
of Cube
n.
Medical or hygienic care; remedial treatment of disease; a method of medical treatment; as, to use the water cure.
a.
Presenting a combination of a cube and an octahedron.
n.
A regular solid body, with six equal square sides.
n.
Any bivalve mollusk which secretes a shelly tube around its siphon, as the watering-shell.
n.
A priming tube, or friction primer. See under Priming, and Friction.
v. t.
To raise to the third power; to obtain the cube of.
n.
Spiritual charge; care of soul; the office of a parish priest or of a curate; hence, that which is committed to the charge of a parish priest or of a curate; a curacy; as, to resign a cure; to obtain a cure.