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  2. Doubling the cube - Wikipedia

    en.wikipedia.org/wiki/Doubling_the_cube

    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 ...

  3. Quartic function - Wikipedia

    en.wikipedia.org/wiki/Quartic_function

    In algebra, a quartic function is a function of the form. α. where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial . A quartic equation, or equation of the fourth degree, is an equation that equates a quartic polynomial to zero, of the form. where a ≠ 0. [1]

  4. Golden ratio - Wikipedia

    en.wikipedia.org/wiki/Golden_ratio

    The golden ratio is also an algebraic number and even an algebraic integer. It has minimal polynomial. This quadratic polynomial has two roots, and. The golden ratio is also closely related to the polynomial. which has roots and As the root of a quadratic polynomial, the golden ratio is a constructible number.

  5. Polynomial root-finding algorithms - Wikipedia

    en.wikipedia.org/wiki/Polynomial_root-finding...

    For finding all the roots, arguably the most reliable method is the Francis QR algorithm computing the eigenvalues of the Companion matrix corresponding to the polynomial, implemented as the standard method [1] in MATLAB. The oldest method of finding all roots is to start by finding a single root. When a root r has been found, it can be removed ...

  6. Halley's method - Wikipedia

    en.wikipedia.org/wiki/Halley's_method

    Halley's method. In numerical analysis, Halley's method is a root-finding algorithm used for functions of one real variable with a continuous second derivative. Edmond Halley was an English mathematician and astronomer who introduced the method now called by his name. The algorithm is second in the class of Householder's methods, after Newton's ...

  7. Quadratic residue - Wikipedia

    en.wikipedia.org/wiki/Quadratic_residue

    The quadratic excess E ( p) is the number of quadratic residues on the range (0, p /2) minus the number in the range ( p /2, p) (sequence A178153 in the OEIS ). For p congruent to 1 mod 4, the excess is zero, since −1 is a quadratic residue and the residues are symmetric under r ↔ p − r.

  8. Root system - Wikipedia

    en.wikipedia.org/wiki/Root_system

    e. In mathematics, a root system is a configuration of vectors in a Euclidean space satisfying certain geometrical properties. The concept is fundamental in the theory of Lie groups and Lie algebras, especially the classification and representation theory of semisimple Lie algebras.

  9. Baudhayana sutras - Wikipedia

    en.wikipedia.org/wiki/Baudhayana_sutras

    Baudhayana 's Śrauta sūtras related to performing Vedic sacrifices have followers in some Smārta brāhmaṇas ( Iyers) and some Iyengars of Tamil Nadu, Yajurvedis or Namboothiris of Kerala, Gurukkal Brahmins (Aadi Saivas) and Kongu Vellalars. The followers of this sūtra follow a different method and do 24 Tila-tarpaṇa, as Lord Krishna had ...

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