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  2. Cube root - Wikipedia

    en.wikipedia.org/wiki/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 ...

  3. Root of unity - Wikipedia

    en.wikipedia.org/wiki/Root_of_unity

    Roots of unity can be defined in any field. If the 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 to a finite field, and, conversely, every nonzero element of a finite field is a root of unity.

  4. Straightedge and compass construction - Wikipedia

    en.wikipedia.org/wiki/Straightedge_and_compass...

    Doubling the cube is the construction, using only a straightedge and compass, of the edge of a cube that has twice the volume of a cube with a given edge. This is impossible because the cube root of 2, though algebraic, cannot be computed from integers by addition, subtraction, multiplication, division, and taking square roots.

  5. Abel–Ruffini theorem - Wikipedia

    en.wikipedia.org/wiki/Abel–Ruffini_theorem

    Abel–Ruffini theorem. In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients. Here, general means that the coefficients of the equation are viewed and manipulated as indeterminates .

  6. Rock cycle - Wikipedia

    en.wikipedia.org/wiki/Rock_cycle

    The rock cycle explains how the three rock types are related to each other, and how processes change from one type to another over time. This cyclical aspect makes rock change a geologic cycle and, on planets containing life, a biogeochemical cycle . Structures of Igneous Rock. Legend: A = magma chamber (batholith); B = dyke /dike; C ...

  7. Talk:Cube root - Wikipedia

    en.wikipedia.org/wiki/Talk:Cube_root

    The new text would read: "In mathematics, a cube root of a number, denoted or x 1/3, is a number a such that a 3 = x. All real numbers have exactly one real cube root and 2 complex roots, and all nonzero complex numbers have 3 distinct complex cube roots." DRE 18:01, 20 February 2007 (UTC) Reply . Sounds good.

  8. Cubic field - Wikipedia

    en.wikipedia.org/wiki/Cubic_field

    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 ...

  9. Pandrosion - Wikipedia

    en.wikipedia.org/wiki/Pandrosion

    Pandrosion is credited with developing a method for calculating numerically accurate but approximate solutions to the problem of doubling the cube, or more generally of calculating cube roots. It is a "recursive geometric" solution, but three-dimensional rather than working within the plane.

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