{"id":2933,"date":"2017-02-14T06:00:30","date_gmt":"2017-02-14T04:00:30","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2933"},"modified":"2021-04-25T16:25:00","modified_gmt":"2021-04-25T14:25:00","slug":"calculo-de-pi-usando-la-formula-de-vieta-2017","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/calculo-de-pi-usando-la-formula-de-vieta-2017\/","title":{"rendered":"C\u00e1lculo de pi usando la f\u00f3rmula de Vieta"},"content":{"rendered":"<p>La <a href=\"http:\/\/bit.ly\/2kpf5cu\">f\u00f3rmula de Vieta<\/a> para el c\u00e1lculo de pi es la siguiente<br \/>\n<a href=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2017\/02\/Calculo_de_pi_usando_la_formula_de_Vieta.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2017\/02\/Calculo_de_pi_usando_la_formula_de_Vieta.png?resize=895%2C114\" alt=\"Calculo_de_pi_usando_la_formula_de_Vieta\" width=\"895\" height=\"114\" class=\"aligncenter size-full wp-image-2937\" srcset=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2017\/02\/Calculo_de_pi_usando_la_formula_de_Vieta.png?w=895&amp;ssl=1 895w, https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2017\/02\/Calculo_de_pi_usando_la_formula_de_Vieta.png?resize=300%2C38&amp;ssl=1 300w, https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2017\/02\/Calculo_de_pi_usando_la_formula_de_Vieta.png?resize=100%2C12&amp;ssl=1 100w, https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2017\/02\/Calculo_de_pi_usando_la_formula_de_Vieta.png?resize=150%2C19&amp;ssl=1 150w\" sizes=\"(max-width: 895px) 100vw, 895px\" data-recalc-dims=\"1\" \/><\/a><\/p>\n<p>Definir las funciones<\/p>\n<pre lang=\"text\">\n   aproximacionPi :: Int -> Double\n   errorPi :: Double -> Int\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li>(aproximacionPi n) es la aproximaci\u00f3n de pi usando n factores de la f\u00f3rmula de Vieta. Por ejemplo, <\/li>\n<\/ul>\n<pre lang=\"text\">\n     aproximacionPi  5  ==  3.140331156954753\n     aproximacionPi 10  ==  3.1415914215112\n     aproximacionPi 15  ==  3.141592652386592\n     aproximacionPi 20  ==  3.1415926535886207\n     aproximacionPi 25  ==  3.141592653589795\n<\/pre>\n<ul>\n<li>(errorPi x) es el menor n\u00famero de factores de la f\u00f3rmula de Vieta necesarios para obtener pi con un error menor que x. Por ejemplo, <\/li>\n<\/ul>\n<pre lang=\"text\">\n     errorPi 0.1        ==  2\n     errorPi 0.01       ==  4\n     errorPi 0.001      ==  6\n     errorPi 0.0001     ==  7\n     errorPi 1e-4       ==  7\n     errorPi 1e-14      ==  24\n     pi                 ==  3.141592653589793\n     aproximacionPi 24  ==  3.1415926535897913\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\n-- 1\u00aa definici\u00f3n de aproximacionPi\naproximacionPi :: Int -> Double\naproximacionPi n = product [2 \/ aux x | x <- [0..n]]\n  where\n    aux 0 = 1\n    aux 1 = sqrt 2\n    aux n = sqrt (2 + aux (n-1))\n\n-- 2\u00aa definici\u00f3n de aproximacionPi\naproximacionPi2 :: Int -> Double\naproximacionPi2 n = product [2\/x | x <- 1 : xs] \n  where xs = take n $ iterate (\\x -> sqrt (2+x)) (sqrt 2)\n\n-- 3\u00aa definici\u00f3n de aproximaxionPi\naproximacionPi3 :: Int -> Double\naproximacionPi3 n =  product (2 : take n (map (2\/) xs))\n  where xs = sqrt 2 : [sqrt (2 + x) | x <- xs]\n\n-- 1\u00aa definici\u00f3n de errorPi\nerrorPi :: Double -> Int\nerrorPi x = head [n | n <- [1..]\n                    , abs (pi - aproximacionPi n) < x]\n\n-- 2\u00aa definici\u00f3n de errorPi\nerrorPi2 :: Double -> Int\nerrorPi2 x = until aceptable (+1) 1\n  where aceptable n = abs (pi - aproximacionPi n) < x\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>La f\u00f3rmula de Vieta para el c\u00e1lculo de pi es la siguiente Definir las funciones aproximacionPi :: Int -> Double errorPi :: Double -> Int tales que (aproximacionPi n) es la aproximaci\u00f3n de pi usando n factores de la f\u00f3rmula de Vieta. Por ejemplo, aproximacionPi 5 == 3.140331156954753 aproximacionPi 10 == 3.1415914215112 aproximacionPi 15 ==&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[4],"tags":[130,8,71,50,10,11,366,157,6,236,47,367],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2933"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/comments?post=2933"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2933\/revisions"}],"predecessor-version":[{"id":2990,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2933\/revisions\/2990"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2933"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2933"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2933"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}