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  2. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    The entire fraction may be expressed as a single composition, in which case it is hyphenated, or as a number of fractions with a numerator of one, in which case they are not. (For example, "two-fifths" is the fraction2 / 5 ⁠ and "two fifths" is the same fraction understood as 2 instances of ⁠ 1 / 5 ⁠.) Fractions should always be ...

  3. 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 ...

  4. List of mathematical constants - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_constants

    A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]

  5. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    The roots of the quadratic function y = ⁠ 1 / 2x 2 − 3x + ⁠ 5 / 2 ⁠ are the places where the graph intersects the x-axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.

  6. Continued fraction - Wikipedia

    en.wikipedia.org/wiki/Continued_fraction

    where c 1 = ⁠ 1 / a 1 ⁠, c 2 = ⁠ a 1 / a 2 ⁠, c 3 = ⁠ a 2 / a 1 a 3 ⁠, and in general c n+1 = ⁠ 1 / a n+1 c n ⁠. Second, if none of the partial denominators b i are zero we can use a similar procedure to choose another sequence { d i } to make each partial denominator a 1:

  7. Farey sequence - Wikipedia

    en.wikipedia.org/wiki/Farey_sequence

    Thus the first term to appear between ⁠ 1 / 3 ⁠ and ⁠ 2 / 5 ⁠ is ⁠ 3 / 8 ⁠, which appears in F 8. The total number of Farey neighbour pairs in F n is 2| F n | − 3. The Stern–Brocot tree is a data structure showing how the sequence is built up from 0 (= ⁠ 0 / 1 ⁠) and 1 (= ⁠ 1 / 1 ⁠), by taking successive mediants.

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  9. Equation - Wikipedia

    en.wikipedia.org/wiki/Equation

    When R is chosen to have the value of 2 (R = 2), this equation would be recognized in Cartesian coordinates as the equation for the circle of radius of 2 around the origin. Hence, the equation with R unspecified is the general equation for the circle. Usually, the unknowns are denoted by letters at the end of the alphabet, x, y, z, w ...

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