{"id":6164,"date":"2021-03-15T06:00:55","date_gmt":"2021-03-15T04:00:55","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=6164"},"modified":"2021-03-22T11:09:35","modified_gmt":"2021-03-22T09:09:35","slug":"calculo-de-pi-mediante-la-formula-de-euler","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/calculo-de-pi-mediante-la-formula-de-euler\/","title":{"rendered":"C\u00e1lculo de pi mediante la f\u00f3rmula de Euler"},"content":{"rendered":"<p>El pasado 6 de marzo se public\u00f3 en Twitter un <a href=\"https:\/\/bit.ly\/30mmlNT\">mensaje<\/a> con una f\u00f3rmula de Euler para el c\u00e1lculo de pi<br \/>\n<a href=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2021\/03\/Calculo_de_pi_mediante_la_formula_de_Euler.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2021\/03\/Calculo_de_pi_mediante_la_formula_de_Euler.png?resize=300%2C71\" alt=\"\" width=\"300\" height=\"71\" class=\"aligncenter size-medium wp-image-6165\" srcset=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2021\/03\/Calculo_de_pi_mediante_la_formula_de_Euler.png?resize=300%2C71&amp;ssl=1 300w, https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2021\/03\/Calculo_de_pi_mediante_la_formula_de_Euler.png?w=567&amp;ssl=1 567w\" sizes=\"(max-width: 300px) 100vw, 300px\" data-recalc-dims=\"1\" \/><\/a><\/p>\n<p>Definir las funciones<\/p>\n<pre lang=\"text\">\n   aproximacionPi :: Int -> Double\n   grafica        :: [Int] -> IO ()\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li>(aproximacionPi n) es la n-\u00e9sima aproximaci\u00f3n de pi con la f\u00f3rmula de Euler. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     aproximacionPi 1        ==  2.449489742783178\n     aproximacionPi 10       ==  3.04936163598207\n     aproximacionPi 100      ==  3.1320765318091053\n     aproximacionPi 1000     ==  3.1406380562059946\n     aproximacionPi 10000    ==  3.1414971639472147\n     aproximacionPi 100000   ==  3.141583104326456\n     aproximacionPi 1000000  ==  3.1415916986605086\n     pi                      ==  3.141592653589793\n<\/pre>\n<ul>\n<li>(grafica xs) dibuja la gr\u00e1fica de las k-\u00e9simas aproximaciones de pi para k en xs. Por ejemplo, (grafica [1..100]) dibuja<br \/>\n<a href=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2021\/03\/Calculo_de_pi_mediante_la_formula_de_Euler_1.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2021\/03\/Calculo_de_pi_mediante_la_formula_de_Euler_1.png?resize=300%2C225\" alt=\"\" width=\"300\" height=\"225\" class=\"aligncenter size-medium wp-image-6166\" srcset=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2021\/03\/Calculo_de_pi_mediante_la_formula_de_Euler_1.png?resize=300%2C225&amp;ssl=1 300w, https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2021\/03\/Calculo_de_pi_mediante_la_formula_de_Euler_1.png?w=640&amp;ssl=1 640w\" sizes=\"(max-width: 300px) 100vw, 300px\" data-recalc-dims=\"1\" \/><\/a><\/li>\n<\/ul>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Graphics.Gnuplot.Simple (Attribute (Key, PNG), plotList)\n\naproximacionPi :: Int -> Double\naproximacionPi n =\n  sqrt (6 * sum [1\/k^2 | k <- [1.0..fromIntegral n]])\n\ngrafica :: [Int] -> IO ()\ngrafica xs =\n  plotList [ Key Nothing\n           -- , PNG \"Calculo_de_pi_mediante_la_formula_de_Euler_1.png\"\n           ]\n           [(k,aproximacionPi k) | k <- xs]\n<\/pre>\n<h4>Nuevas soluciones<\/h4>\n<ul>\n<li>En los comentarios se pueden escribir nuevas soluciones.\n<li>El c\u00f3digo se debe escribir entre una l\u00ednea con &#60;pre lang=&quot;haskell&quot;&#62; y otra con &#60;\/pre&#62;\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>El pasado 6 de marzo se public\u00f3 en Twitter un mensaje con una f\u00f3rmula de Euler para el c\u00e1lculo de pi Definir las funciones aproximacionPi :: Int -> Double grafica :: [Int] -> IO () tales que (aproximacionPi n) es la n-\u00e9sima aproximaci\u00f3n de pi con la f\u00f3rmula de Euler. Por ejemplo, aproximacionPi 1 ==&#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":[5],"tags":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6164"}],"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=6164"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6164\/revisions"}],"predecessor-version":[{"id":6216,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6164\/revisions\/6216"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=6164"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=6164"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=6164"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}