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  2. Farey sequence - Wikipedia

    en.wikipedia.org/wiki/Farey_sequence

    See this by interpreting consecutive rationals r 1 = p/q and r 2 = p′/q′ as vectors (p, q) in the xy plane. The area of A ( p / q , p ′/ q ′) is given by qp ′ − q ′ p . As any added fraction in between two previous consecutive Farey sequence fractions is calculated as the mediant (⊕), then A ( r 1 , r 1 ⊕ r 2 ) = A ( r 1 ...

  3. Approximations of π - Wikipedia

    en.wikipedia.org/wiki/Approximations_of_π

    Consider all cells (x, y) in which both x and y are integers between − r and r. 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 r 2 to find the approximation of π. For example, if r is 5, then the cells ...

  4. Axiality (geometry) - Wikipedia

    en.wikipedia.org/wiki/Axiality_(geometry)

    Equivalently it is the largest fraction of the area of the shape that can be covered by a mirror reflection of the shape (with any orientation). A shape that is itself axially symmetric, such as an isosceles triangle , will have an axiality of exactly one, whereas an asymmetric shape, such as a scalene triangle , will have axiality less than one.

  5. One half - Wikipedia

    en.wikipedia.org/wiki/One_half

    u+00be ¾ vulgar fraction three quarters The "one-half" symbol has its own code point as a precomposed character in the Number Forms block of Unicode , rendering as ½ . The reduced size of this symbol may make it illegible to readers with relatively mild visual impairment ; consequently the decomposed forms 1 ⁄ 2 or ⁠ 1 / 2 ⁠ may be more ...

  6. Egyptian fraction - Wikipedia

    en.wikipedia.org/wiki/Egyptian_fraction

    An obvious necessary condition is that the starting fraction ⁠ x / y ⁠ have an odd denominator y, and it is conjectured but not known that this is also a sufficient condition. It is known [20] that every ⁠ x / y ⁠ with odd y has an expansion into distinct odd unit fractions, constructed using a different method than the greedy algorithm.

  7. Theta function - Wikipedia

    en.wikipedia.org/wiki/Theta_function

    There are several closely related functions called Jacobi theta functions, and many different and incompatible systems of notation for them. One Jacobi theta function (named after Carl Gustav Jacob Jacobi) is a function defined for two complex variables z and τ, where z can be any complex number and τ is the half-period ratio, confined to the upper half-plane, which means it has positive ...

  8. 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) of the denominator of the fraction, which must be a positive natural number.

  9. Algebraic fraction - Wikipedia

    en.wikipedia.org/wiki/Algebraic_fraction

    A rational fraction is an algebraic fraction whose numerator and denominator are both polynomials. Thus 3 x x 2 + 2 x − 3 {\displaystyle {\frac {3x}{x^{2}+2x-3}}} is a rational fraction, but not x + 2 x 2 − 3 , {\displaystyle {\frac {\sqrt {x+2}}{x^{2}-3}},} because the numerator contains a square root function.