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  2. Continued fraction - Wikipedia

    en.wikipedia.org/wiki/Continued_fraction

    which can be simplified, by folding each pair of fractions into one fraction, to ... which can be simplified by noting that ⁠ 5 / 10 ⁠ = ⁠ 3 / 6 ...

  3. Simplification - Wikipedia

    en.wikipedia.org/wiki/Simplification

    Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include:

  4. List of integer sequences - Wikipedia

    en.wikipedia.org/wiki/List_of_integer_sequences

    1, 1, 2, 2, 4, 2, 6, 4, 6, 4, ... φ(n) is the number of positive integers not greater than n that are coprime with n. A000010: Lucas numbers L(n) 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, ... L(n) = L(n − 1) + L(n − 2) for n ≥ 2, with L(0) = 2 and L(1) = 1. A000032: Prime numbers p n: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ... The prime numbers p ...

  5. Number Forms - Wikipedia

    en.wikipedia.org/wiki/Number_Forms

    35: 0.6 Vulgar Fraction Three Fifths 2157 8535 ⅘ 45: 0.8 Vulgar Fraction Four Fifths 2158 8536 ⅙ 1 ⁄ 6: 0.166... Vulgar Fraction One Sixth 2159 8537 ⅚ 56: 0.833... Vulgar Fraction Five Sixths 215A 8538 ⅛ 1 ⁄ 8: 0.125 Vulgar Fraction One Eighth 215B 8539 ⅜ 3 ⁄ 8: 0.375 Vulgar Fraction Three Eighths 215C 8540 ⅝ 5 ...

  6. SBB Ae 4/6 - Wikipedia

    en.wikipedia.org/wiki/SBB-CFF-FFS_Ae_4/6

    SBB Ae 4/6, with Winterthur drive. Both these and the Ae 8/14 had used regenerative braking, useful for descending the Gotthard's steep gradients without overheating and also returning electrical power to the network. The Ae 4/6 had a simplified and lighter system, where one traction motor could serve as the exciter for

  7. Mental calculation - Wikipedia

    en.wikipedia.org/wiki/Mental_calculation

    For example: 24 x 11 = 264 because 2 + 4 = 6 and the 6 is placed in between the 2 and the 4. Second example: 87 x 11 = 957 because 8 + 7 = 15 so the 5 goes in between the 8 and the 7 and the 1 is carried to the 8.

  8. Rule of twelfths - Wikipedia

    en.wikipedia.org/wiki/Rule_of_twelfths

    Then in the second period by 2/12, in the third by 3/12, in the fourth by 3/12, fifth by 2/12 and at the end of the sixth period reaches its maximum with an increase of 1/12. The steps are 1:2:3:3:2:1 giving a total change of 12/12. Over the next six intervals the quantity reduces in a similar manner by 1, 2, 3, 3, 2, 1 twelfths.

  9. 1/4 + 1/16 + 1/64 + 1/256 + ⋯ - ⋯ - Wikipedia

    en.wikipedia.org/wiki/1/4_%2B_1/16_%2B_1/64_%2B...

    Archimedes' figure with a = ⁠ 3 / 4 ⁠ In mathematics , the infinite series ⁠ 1 / 4 ⁠ + ⁠ 1 / 16 ⁠ + ⁠ 1 / 64 ⁠ + ⁠ 1 / 256 ⁠ + ⋯ is an example of one of the first infinite series to be summed in the history of mathematics ; it was used by Archimedes circa 250–200 BC. [ 1 ]