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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 ...

  3. Approximations of π - Wikipedia

    en.wikipedia.org/wiki/Approximations_of_π

    The cells (±3, ±4) and (±4, ±3) are labeled. The 12 cells (0, ±5), (±5, 0), (±3, ±4), (±4, ±3) are exactly on the circle, and 69 cells are completely inside, so the approximate area is 81, and π is calculated to be approximately 3.24 because 81⁄52 = 3.24. Results for some values of r are shown in the table below: r.

  4. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    Unit fractions can also be expressed using negative exponents, as in 2 −1, which represents 1/2, and 22, which represents 1/(2 2) or 1/4. A dyadic fraction is a common fraction in which the denominator is a power of two , e.g. ⁠ 1 / 8 ⁠ = ⁠ 1 / 2 3 ⁠ .

  5. Pi - Wikipedia

    en.wikipedia.org/wiki/Pi

    The volume of a sphere with radius r is ⁠ 4 / 3 ⁠ πr 3. The surface area of a sphere with radius r is 4πr 2. Some of the formulae above are special cases of the volume of the n-dimensional ball and the surface area of its boundary, the (n−1)-dimensional sphere, given below. Apart from circles, there are other curves of constant width.

  6. Particular values of the Riemann zeta function - Wikipedia

    en.wikipedia.org/wiki/Particular_values_of_the...

    It is known that ζ(3) is irrational (Apéry's theorem) and that infinitely many of the numbers ζ(2n + 1) : n ∈ , are irrational. [1] There are also results on the irrationality of values of the Riemann zeta function at the elements of certain subsets of the positive odd integers; for example, at least one of ζ (5), ζ (7), ζ (9), or ζ ...

  7. Odds - Wikipedia

    en.wikipedia.org/wiki/Odds

    For example, given that there is a pattern of odds of 5/4, 7/4, 9/4 and so on, odds which are mathematically 3/2 are more easily compared if expressed in the equivalent form 6/4. Fractional odds are also known as British odds, UK odds, [9] or, in that country, traditional odds. They are typically represented with a "/" but can also be ...

  8. Partial fraction decomposition - Wikipedia

    en.wikipedia.org/wiki/Partial_fraction_decomposition

    Partial fraction decomposition. In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions ...

  9. Duodecimal - Wikipedia

    en.wikipedia.org/wiki/Duodecimal

    Numeral systems. The duodecimal system, also known as base twelve or dozenal, is a positional numeral system using twelve as its base. In duodecimal, the number twelve is denoted "10", meaning 1 twelve and 0 units; in the decimal system, this number is instead written as "12" meaning 1 ten and 2 units, and the string "10" means ten.

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