Pi (broj): razlika između inačica

Izbrisani sadržaj Dodani sadržaj
m uklonjena promjena suradnika 89.164.183.137 (razgovor), vraćeno na posljednju inačicu suradnika HmxBot
Oznaka: brzo uklanjanje
Redak 169:
koje donose 14 znamenki po izračunu.<ref name="rad"/> Braća Chudnovsky rabila su ovu formulu prilikom nekoliko rekordnih izračuna π krajem 1980-ih, uključujući prvi izračun preko milijardu znamenaka ikad (sa 1.011,196.691 znamenaka) u 1989. godini. Dotična formula i dalje je izbor za računanje u programima za računanje broja na osobnim računalima, za razliku od [[superračunala]] koja se rabe za obaranje suvremenih rekorda.
<!--
Whereas series typically increase the accuracy with a fixed amount for each added term, there exist iterative algorithms that ''multiply'' the number of correct digits at each step, with the downside that each step generally requires an expensive calculation. A breakthrough was made in 1975, when [[Richard Brent (scientist)|Richard Brent]] andi [[Eugene Salamin]] independently discovered the [[Gauss-Legendre algorithm|Brent-Salamin algorithm]], which uses only arithmetic to double the number of correct digits at each step.<ref name="brent">{{Citation | last=Brent | first=Richard | author-link=Richard Brent (scientist) | year=1975 | title=Multiple-precision zero-finding methods and the complexity of elementary function evaluation | periodical=Analytic Computational Complexity | publication-place=New York | publisher=Academic Press | editor-last=Traub | editor-first=J F | pages=151–176 | url=http://wwwmaths.anu.edu.au/~brent/pub/pub028.html | accessdate=2007-09-08}}</ref> The algorithm consists of setting
 
:<math>a_0 = 1 \quad \quad \quad b_0 = \frac{1}{\sqrt 2} \quad \quad \quad t_0 = \frac{1}{4} \quad \quad \quad p_0 = 1\!</math>