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  2. Farey sequence - Wikipedia

    en.wikipedia.org/wiki/Farey_sequence

    In mathematics, the Farey sequence of order n is the sequence of completely reduced fractions, either between 0 and 1, or without this restriction, [ a] which when in lowest terms have denominators less than or equal to n, arranged in order of increasing size. With the restricted definition, each Farey sequence starts with the value 0, denoted ...

  3. Approximations of π - Wikipedia

    en.wikipedia.org/wiki/Approximations_of_π

    Starting at 0, add 1 for each cell whose distance to the origin (0,0) is less than or equal to r. When finished, divide the sum, representing the area of a circle of radius r, by r2 to find the approximation of π. For example, if r is 5, then the cells considered are: (−5,5) (−4,5)

  4. Fibonacci sequence - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_sequence

    Fibonacci sequence. In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes ...

  5. Egyptian fraction - Wikipedia

    en.wikipedia.org/wiki/Egyptian_fraction

    The Rhind Mathematical Papyrus. An Egyptian fraction is a finite sum of distinct unit fractions, such as That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other. The value of an expression of this type is a positive rational number ; for ...

  6. Repeating decimal - Wikipedia

    en.wikipedia.org/wiki/Repeating_decimal

    Every terminating decimal representation can be written as a decimal fraction, a fraction whose denominator is a power of 10 (e.g. 1.585 = ⁠ 1585 / 1000 ⁠); it may also be written as a ratio of the form ⁠ k / 2 n ·5 m ⁠ (e.g. 1.585 = ⁠ 317 / 2 3 ·5 2 ⁠).

  7. List of fractals by Hausdorff dimension - Wikipedia

    en.wikipedia.org/wiki/List_of_fractals_by...

    ~2.7: The surface of Broccoli: San-Hoon Kim used a direct scanning method and a cross section analysis of a broccoli to conclude that the fractal dimension of it is ~2.7. [49] Measured ~2.8: Surface of human brain: Measured with segmented three-dimensional high-resolution magnetic resonance images [50] Measured and calculated ~2.8: Cauliflower

  8. Pell number - Wikipedia

    en.wikipedia.org/wiki/Pell_number

    In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins ⁠ 1 1 ⁠, ⁠ 3 2 ⁠, ⁠ 7 5 ⁠, ⁠ 17 12 ⁠, and ⁠ 41 29 ⁠, so the sequence of Pell numbers begins ...

  9. Geometric series - Wikipedia

    en.wikipedia.org/wiki/Geometric_series

    A two dimensional geometric series diagram Nicole Oresme used to determine that the infinite series 1/2 + 2/4 + 3/8 + 4/16 + 5/32 + 6/64 + 7/128 + ... converges to 2. In addition to his elegantly simple proof of the divergence of the harmonic series, Nicole Oresme [9] proved that the series

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