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  2. Leibniz formula for π - Wikipedia

    en.wikipedia.org/wiki/Leibniz_formula_for_π

    In mathematics, the Leibniz formula for π, named after Gottfried Wilhelm Leibniz, states that = + + = = +,. an alternating series.. It is sometimes called the Madhava–Leibniz series as it was first discovered by the Indian mathematician Madhava of Sangamagrama or his followers in the 14th–15th century (see Madhava series), [1] and was later independently rediscovered by James Gregory in ...

  3. Approximations of π - Wikipedia

    en.wikipedia.org/wiki/Approximations_of_π

    The latter fraction is the best possible rational approximation of π using fewer than five decimal digits in the numerator and denominator. Zu Chongzhi's results surpass the accuracy reached in Hellenistic mathematics, and would remain without improvement for close to a millennium.

  4. Pi - Wikipedia

    en.wikipedia.org/wiki/Pi

    Fractions: Approximate fractions include (in order of increasing accuracy) ⁠ 22 / 7 ⁠, ⁠ 333 / 106 ⁠, ⁠ 355 / 113 ⁠, ⁠ 52163 / 16604 ⁠, ⁠ 103993 / 33102 ⁠, ⁠ 104348 / 33215 ⁠, and ⁠ 245850922 / 78256779 ⁠. [34]

  5. Continued fraction - Wikipedia

    en.wikipedia.org/wiki/Continued_fraction

    A continued fraction is an expression of the form. where the an (n > 0) are the partial numerators, the bn are the partial denominators, and the leading term b0 is called the integer part of the continued fraction. The successive convergents of the continued fraction are formed by applying the fundamental recurrence formulas:

  6. Product (mathematics) - Wikipedia

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

    Product of two numbers. Originally, a product was and is still the result of the multiplication of two or more numbers. For example, 15 is the product of 3 and 5. The fundamental theorem of arithmetic states that every composite number is a product of prime numbers, that is unique up to the order of the factors.

  7. Product rule - Wikipedia

    en.wikipedia.org/wiki/Product_rule

    Calculus. In calculus, the product rule (or Leibniz rule[1] or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions. For two functions, it may be stated in Lagrange's notation as or in Leibniz's notation as.

  8. Lowest common denominator - Wikipedia

    en.wikipedia.org/wiki/Lowest_common_denominator

    Description. The lowest common denominator of a set of fractions is the lowest number that is a multiple of all the denominators: their lowest common multiple. The product of the denominators is always a common denominator, as in: but it is not always the lowest common denominator, as in: Here, 36 is the least common multiple of 12 and 18.

  9. Harmonic series (mathematics) - Wikipedia

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

    Calculus. In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions: The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it ...

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