{"id":5030,"date":"2022-10-11T07:00:32","date_gmt":"2022-10-11T05:00:32","guid":{"rendered":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/?p=5030"},"modified":"2024-09-25T16:55:41","modified_gmt":"2024-09-25T14:55:41","slug":"sucesion-de-fibonacci-y-ternas-pitagoricas","status":"publish","type":"post","link":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/sucesion-de-fibonacci-y-ternas-pitagoricas\/","title":{"rendered":"Sucesi\u00f3n de Fibonacci y ternas pitag\u00f3ricas"},"content":{"rendered":"

Los primeros t\u00e9rminos de la sucesi\u00f3n de Fibonacci<\/strong><\/a> son:<\/span><\/p>\n

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, …<\/span><\/p>\n

Si a<\/strong>, b<\/strong>, c<\/strong> y d<\/strong> son cuatro t\u00e9rminos consecutivos de la la sucesi\u00f3n de Fibonacci, los n\u00fameros:<\/span><\/p>\n

\"\"<\/p>\n

forman una terna pitag\u00f3rica<\/strong><\/a>.<\/span><\/p>\n

 <\/span><\/p>\n

     Demostraci\u00f3n:<\/span><\/p>\n

Cada t\u00e9rmino de la sucesi\u00f3n de Fibonacci se obtiene sumando los dos anteriores:<\/span><\/p>\n

\"\"<\/p>\n

La terna pitag\u00f3rica est\u00e1 formada por los n\u00fameros:<\/span><\/p>\n

\"\"<\/p>\n

Se comprueba que estos n\u00fameros forman una terna pitag\u00f3rica:<\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

 <\/p>\n

Veamos algunos ejemplos:<\/span><\/p>\n\n\n\n\n\n\n
 <\/span><\/td>\n <\/span><\/td>\n<\/tr>\n
N\u00fameros<\/span><\/td>\nComprobaci\u00f3n<\/span><\/td>\n<\/tr>\n
1, 1, 2, 3<\/span><\/td>\n32 <\/sup>+ 42 <\/sup>= 52<\/sup><\/span><\/td>\n<\/tr>\n
1\u00b73=3<\/strong>    ,   2\u00b7(1\u00b72) = 4<\/strong>   ,   12<\/sup>+22<\/sup>=5<\/strong><\/span><\/td>\n9 + 16 = 25<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n\n\n\n\n\n
N\u00fameros<\/span><\/td>\nComprobaci\u00f3n<\/span><\/td>\n<\/tr>\n
1, 2, 3, 5<\/span><\/td>\n52 <\/sup>+ 122 <\/sup>= 132<\/sup><\/span><\/td>\n<\/tr>\n
1\u00b75=5<\/strong>    ,   2\u00b7(2\u00b73) = 12<\/strong>   ,   22<\/sup>+32<\/sup>=13<\/strong><\/span><\/td>\n25 + 144 = 169<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n\n\n\n\n\n
N\u00fameros<\/span><\/td>\nComprobaci\u00f3n<\/span><\/td>\n<\/tr>\n
2, 3, 5, 8<\/span><\/td>\n162 <\/sup>+ 302 <\/sup>= 342<\/sup><\/span><\/td>\n<\/tr>\n
2\u00b78=16<\/strong>    ,   2\u00b7(3\u00b75) = 30<\/strong>   ,   32<\/sup>+52<\/sup>=34<\/strong><\/span><\/td>\n256 + 900 = 1156<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n\n\n\n\n\n
N\u00fameros<\/span><\/td>\nComprobaci\u00f3n<\/span><\/td>\n<\/tr>\n
3, 5, 8, 13<\/span><\/td>\n392 <\/sup>+ 802 <\/sup>= 892<\/sup><\/span><\/td>\n<\/tr>\n
3\u00b713=39<\/strong>    ,   2\u00b7(5\u00b78) = 80<\/strong>   ,   52<\/sup>+82<\/sup>=89<\/strong><\/span><\/td>\n1521 + 6400 = 7921<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

. . .<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Los primeros t\u00e9rminos de la sucesi\u00f3n de Fibonacci son: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, … Si a, b, c...<\/p>\n","protected":false},"author":7927,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[2075204,2075216],"tags":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/5030"}],"collection":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/users\/7927"}],"replies":[{"embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/comments?post=5030"}],"version-history":[{"count":16,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/5030\/revisions"}],"predecessor-version":[{"id":5054,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/5030\/revisions\/5054"}],"wp:attachment":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/media?parent=5030"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/categories?post=5030"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/tags?post=5030"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}