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  2. Apophysis (software) - Wikipedia

    en.wikipedia.org/wiki/Apophysis_(software)

    Apophysis is an open source fractal flame editor and renderer for Microsoft Windows and Macintosh. [1]Apophysis has many features for creating and editing fractal flames, including an editor that allows one to directly edit the transforms by manipulating triangles, a mutations window, which applies random edits to the triangles, an adjust window, which allows the adjustment of coloring and ...

  3. 1 + 2 + 3 + 4 - 3 + 4 + ... - Wikipedia

    en.wikipedia.org/wiki/-1/12

    where f (2k−1) is the (2k − 1)th derivative of f and B 2k is the (2k)th Bernoulli number: B 2 = ⁠ 1 / 6 ⁠, B 4 = ⁠− + 1 / 30 ⁠, and so on. Setting f ( x ) = x , the first derivative of f is 1, and every other term vanishes, so [ 15 ]

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

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

    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.

  5. Greedy algorithm for Egyptian fractions - Wikipedia

    en.wikipedia.org/wiki/Greedy_algorithm_for...

    The simplest fraction3 / y ⁠ with a three-term expansion is ⁠ 3 / 7 ⁠. A fraction4 / y ⁠ requires four terms in its greedy expansion if and only if y ≡ 1 or 17 (mod 24), for then the numerator −y mod x of the remaining fraction is 3 and the denominator is 1 (mod 6). The simplest fraction4 / y ⁠ with a four-term ...

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    mail.aol.com

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  7. Ancient Greek units of measurement - Wikipedia

    en.wikipedia.org/wiki/Ancient_Greek_units_of...

    Some Greek measures of length were named after parts of the body, such as the δάκτυλος (daktylos, plural: δάκτυλοι daktyloi) or finger (having the size of a thumb), and the πούς (pous, plural: πόδες podes) or foot (having the size of a shoe).

  8. Solving quadratic equations with continued fractions - Wikipedia

    en.wikipedia.org/wiki/Solving_quadratic...

    By applying the fundamental recurrence formulas we may easily compute the successive convergents of this continued fraction to be 1, 3/2, 7/5, 17/12, 41/29, 99/70, 239/169, ..., where each successive convergent is formed by taking the numerator plus the denominator of the preceding term as the denominator in the next term, then adding in the ...

  9. Apophasis - Wikipedia

    en.wikipedia.org/wiki/Apophasis

    Apophasis (/ ə ˈ p ɒ f ə s ɪ s /; from Ancient Greek ἀπόφασις (apóphasis), from ἀπόφημι (apóphemi) 'to say no') [1] [2] is a rhetorical device wherein the speaker or writer brings up a subject by either denying it, or denying that it should be brought up. [3] Accordingly, it can be seen as a rhetorical relative of irony ...