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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 maps a number to its cube. It is an odd function, as (−n) 3 = −(n 3).
The set is defined in the complex plane as the complex numbers for which the function () = + does not diverge to infinity when iterated starting at =, i.e., for which the sequence (), (()), etc., remains bounded in absolute value. This set was first defined and drawn by Robert W. Brooks and Peter Matelski in 1978, as part of a study of Kleinian ...
In computational geometry, the smallest enclosing box problem is that of finding the oriented minimum bounding box enclosing a set of points. It is a type of bounding volume. "Smallest" may refer to volume, area, perimeter, etc. of the box. It is sufficient to find the smallest enclosing box for the convex hull of the objects in question. It is ...
One often reserves the term cubical complex, or cube complex, for such cubed complexes where no two faces of a same cube are identified, i.e. where the boundary of each cube is embedded, and the intersection of two cubes is a face in each cube. [2] A cube complex is said to be finite-dimensional if the dimension of the cubical cells is bounded ...
An example of this is R 3 = R × R × R, with R again the set of real numbers, [1] and more generally R n. The n-ary Cartesian power of a set X is isomorphic to the space of functions from an n-element set to X. As a special case, the 0-ary Cartesian power of X may be taken to be a singleton set, corresponding to the empty function with codomain X.
A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i 2 = −1.
The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1 and is therefore a constructible number. In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length | | can be constructed with compass and straightedge in a finite number of steps.
The set of prime powers which are not prime (i.e., all numbers of the form p n with n ≥ 2 and p prime) is small although the primes are large. This property is frequently used in analytic number theory. More generally, the set of perfect powers is small; even the set of powerful numbers is small. The set of numbers whose expansions in a given ...