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  2. Golden ratio - Wikipedia

    en.wikipedia.org/wiki/Golden_ratio

    In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if. φ. where the Greek letter phi ( or ) denotes the golden ratio.

  3. Fractional ideal - Wikipedia

    en.wikipedia.org/wiki/Fractional_ideal

    The principal fractional ideals form a subgroup. A (nonzero) fractional ideal is invertible if and only if it is projective as an R {\displaystyle R} - module . Geometrically, this means an invertible fractional ideal can be interpreted as rank 1 vector bundle over the affine scheme Spec ( R ) {\displaystyle {\text{Spec}}(R)} .

  4. Euclidean algorithm - Wikipedia

    en.wikipedia.org/wiki/Euclidean_algorithm

    The number 1 (expressed as a fraction 1/1) is placed at the root of the tree, and the location of any other number a/b can be found by computing gcd(a,b) using the original form of the Euclidean algorithm, in which each step replaces the larger of the two given numbers by its difference with the smaller number (not its remainder), stopping when ...

  5. Real number - Wikipedia

    en.wikipedia.org/wiki/Real_number

    These two representations are identical, unless x is a decimal fraction of the form . In this case, in the first decimal representation, all a n {\displaystyle a_{n}} are zero for n > h , {\displaystyle n>h,} and, in the second representation, all a n {\displaystyle a_{n}} 9.

  6. Continued fraction - Wikipedia

    en.wikipedia.org/wiki/Continued_fraction

    Continued fraction. A finite regular continued fraction, where is a non-negative integer, is an integer, and is a positive integer, for . In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this ...

  7. Lambert W function - Wikipedia

    en.wikipedia.org/wiki/Lambert_W_function

    The Lambert W function is used to solve equations in which the unknown quantity occurs both in the base and in the exponent, or both inside and outside of a logarithm. The strategy is to convert such an equation into one of the form zez = w and then to solve for z using the W function. For example, the equation.

  8. Series (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Series_(mathematics)

    In mathematics, a series is, roughly speaking, an addition of infinitely many quantities, one after the other. [1] The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures (such as in combinatorics) through generating functions.

  9. Fractional calculus - Wikipedia

    en.wikipedia.org/wiki/Fractional_calculus

    t. e. Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator. and of the integration operator [Note 1] and developing a calculus for such operators generalizing the classical one.

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