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  2. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    A unit fraction is a common fraction with a numerator of 1 (e.g., ⁠ 1 / 7 ⁠). Unit fractions can also be expressed using negative exponents, as in 2 −1, which represents 1/2, and 2 −2, 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 ⁠.

  3. Egyptian fraction - Wikipedia

    en.wikipedia.org/wiki/Egyptian_fraction

    For instance, Fibonacci represents the fraction8 / 11 ⁠ by splitting the numerator into a sum of two numbers, each of which divides one plus the denominator: ⁠ 8 / 11 ⁠ = ⁠ 6 / 11 ⁠ + ⁠ 2 / 11 ⁠. Fibonacci applies the algebraic identity above to each these two parts, producing the expansion ⁠ 8 / 11 ⁠ = ⁠ 1 / 2 ...

  4. Continued fraction (generalized) - Wikipedia

    en.wikipedia.org/wiki/Continued_fraction...

    Note: this continued fraction's rate of convergence μ tends to 3 − √ 8 ≈ 0.1715729, hence ⁠ 1 / μ ⁠ tends to 3 + √ 8 ≈ 5.828427, whose common logarithm is 0.7655... ≈ ⁠ 13 / 17 ⁠ > ⁠ 3 / 4 ⁠. The same ⁠ 1 / μ ⁠ = 3 + √ 8 (the silver ratio squared) also is observed in the unfolded general continued fractions of ...

  5. Unit fraction - Wikipedia

    en.wikipedia.org/wiki/Unit_fraction

    Slices of approximately 1/8 of a pizza. A unit fraction is a positive fraction with one as its numerator, 1/ n. It is the multiplicative inverse (reciprocal) ...

  6. 1/2 + 1/4 + 1/8 + 1/16 + ⋯ - ⋯ - Wikipedia

    en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/...

    1/2 + 1/4 + 1/8 + 1/16 + ⋯. First six summands drawn as portions of a square. The geometric series on the real line. In mathematics, the infinite series ⁠ 1 2 ⁠ + ⁠ 1 4 ⁠ + ⁠ 1 8 ⁠ + ⁠ 1 16 ⁠ + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1. In summation notation ...

  7. Number Forms - Wikipedia

    en.wikipedia.org/wiki/Number_Forms

    Number Forms is a Unicode block containing Unicode compatibility characters that have specific meaning as numbers, but are constructed from other characters. They consist primarily of vulgar fractions and Roman numerals. In addition to the characters in the Number Forms block, three fractions (¼, ½, and ¾) were inherited from ISO-8859-1 ...

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  9. Mediant (mathematics) - Wikipedia

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

    However, if the fraction 1/1 is replaced by the fraction 2/2, which is an equivalent fraction denoting the same rational number 1, the mediant of the fractions 2/2 and 1/2 is 3/4. For a stronger connection to rational numbers the fractions may be required to be reduced to lowest terms, thereby selecting unique representatives from the ...

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