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A mathematical constant is a key number whose value is fixed by an unambiguous ... Negative one: −1 −1 300 to 200 BCE Cube root of 2 1.25992 10498 ...
y = x 3 for values of 1 ≤ x ≤ 25. In 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 or any other mathematical expression is denoted by a superscript 3, for example 2 3 = 8 or (x + 1) 3. The cube is also the number multiplied by its square:
For n equal to 2 this is called the principal square root and the n is omitted. The nth root can also be represented using exponentiation as x 1/n. For even values of n, positive numbers also have a negative nth root, while negative numbers do not have a real nth root. For odd values of n, every negative number x has a real negative nth root.
When p = ±3, the above values of t 0 are sometimes called the Chebyshev cube root. [29] 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. The value involving hyperbolic sines is similarly denoted S 1/3 (q), when p = 3.
The principal cube root is its principal value, that is a unique cube root that has been chosen once for all. The principal cube root is the cube root with the largest real part. In the case of negative real numbers, the largest real part is shared by the two nonreal cube roots, and the principal cube root is the one with positive imaginary part.
A Cabtaxi number is the smallest positive number that can be expressed as a sum of two integer cubes in n ways, allowing the cubes to be negative or zero as well as positive. The smallest cabtaxi number after Cabtaxi(1) = 0, is Cabtaxi(2) = 91, [5] expressed as: + or
The imaginary unit or unit imaginary number (i) is a mathematical constant that is a solution to the quadratic equation x 2 + 1 = 0. Although there is no real number with this property, i can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of i in a complex ...
[2] The complex cubic field obtained by adjoining to Q a root of x 3 + x 2 − 1 is not pure. It has the smallest discriminant (in absolute value) of all cubic fields, namely −23. [3] 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 ...