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When p = ±3, the above values of t 0 are sometimes called the Chebyshev cube root. More precisely, the values involving cosines and hyperbolic cosines define, when p = −3, the same analytic function denoted C 1/3 (q), which is the proper Chebyshev cube root.
Cube root. In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted , is 2, because 23 = 8, while the other ...
if a has a cube root in K, there exists a unique b such that a = b 3.Otherwise, it is necessary to consider an extension field of K (e.g., K(a 1/3)). Then, since b 3 · x 3 = bx 3, defining t = b · x, the following equation is needed (in Hessian form) to do the transformation: + + =.
Doubling the cube, also known as the Delian problem, is an ancient [a] [1] : 9 geometric problem. Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume is double that of the first. As with the related problems of squaring the circle and trisecting the angle, doubling the cube is now known to ...
For any given choice of cube root and its conjugate, this contains nested radicals involving complex numbers, yet it is reducible (even though not obviously so) to one of the solutions 1, 2, or –3. Infinitely nested radicals Square roots. Under certain conditions infinitely nested square roots such as
Cube Route is a fantasy novel by British-American writer Piers Anthony, the twenty-seventh book of the Xanth series. Pangrammatic window. The shortest known published pangrammatic window, a stretch of naturally occurring text that contains all the letters in the alphabet, is found on page 98 of the 2004 First Mass Market Edition.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
Adjoining a root of x 3 + x 2 − 2x − 1 to Q yields a cyclic cubic field, and hence a totally real cubic field. It has the smallest discriminant of all totally real cubic fields, namely 49. The field obtained by adjoining to Q a root of x 3 + x 2 − 3x − 1 is an example of a totally real cubic field that is not cyclic. Its discriminant is ...