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Zu's contemporary calendarist and mathematician He Chengtian invented a fraction interpolation method called "harmonization of the divisor of the day" (Chinese: zh:调日法; pinyin: diaorifa) to increase the accuracy of approximations of π by iteratively adding the numerators and denominators of fractions.
He was the first Chinese mathematician to calculate π=3.1416 with his π algorithm. He discovered the usage of Cavalieri's principle to find an accurate formula for the volume of a cylinder, and also developed elements of the infinitesimal calculus during the 3rd century CE. fraction interpolation for pi
Fenzi and Fenmu are also the modern Chinese name for numerator and denominator, respectively. As shown on the right, 1 is the numerator remainder, 7 is the denominator divisor, formed a fraction 1 / 7 . The quotient of the division 309 / 7 is 44 + 1 / 7 . Liu Hui used a lot of calculations with fractions in Haidao Suanjing.
Examples of algorithms for this task include New Edge-Directed Interpolation (NEDI), [1] [2] Edge-Guided Image Interpolation (EGGI), [3] Iterative Curvature-Based Interpolation (ICBI), [citation needed] and Directional Cubic Convolution Interpolation (DCCI). [4] A study found that DCCI had the best scores in PSNR and SSIM on a series of test ...
Hence Mikami strongly urged that the fraction 355 / 113 be named after Zu Chongzhi as Zu's fraction. [7] In Chinese literature, this fraction is known as "Zu's ratio". Zu's ratio is a best rational approximation to π, and is the closest rational approximation to π from all fractions with denominator less than 16600. [8]
Let be a metric space with distance function .Let be a set of indices and let () be a tuple (indexed collection) of nonempty subsets (the sites) in the space .The Voronoi cell, or Voronoi region, , associated with the site is the set of all points in whose distance to is not greater than their distance to the other sites , where is any index different from .
In crystallography, a fractional coordinate system is used in order to better reflect the symmetry of the underlying lattice of a crystal pattern (or any other periodic pattern in space). In a fractional coordinate system the basis vectors of the coordinate system are chosen to be lattice vectors and the basis is then termed a crystallographic ...
In mathematics, Thiele's interpolation formula is a formula that defines a rational function from a finite set of inputs and their function values (). The problem of generating a function whose graph passes through a given set of function values is called interpolation .