{"id":4856,"date":"2023-10-17T11:18:55","date_gmt":"2023-10-17T08:18:55","guid":{"rendered":"https:\/\/blog.inekle.com\/?p=4856"},"modified":"2026-08-25T20:07:45","modified_gmt":"2026-08-25T17:07:45","slug":"bir-cift-tavsandan-sonrasi-fibonacci-dizisi","status":"publish","type":"post","link":"https:\/\/blog.inekle.com\/bir-cift-tavsandan-sonrasi-fibonacci-dizisi\/","title":{"rendered":"Bir \u00c7ift Tav\u015fandan Sonras\u0131\u2013Fibonacci Dizisi"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Merhaba sevgili inekle Blog Okurlar\u0131. Bu zamana kadar matematik hakk\u0131nda \u00e7ok fazla \u015fa\u015f\u0131rd\u0131\u011f\u0131n\u0131z bir olayla kar\u015f\u0131la\u015ft\u0131n\u0131z m\u0131 bilmiyorum. Kimilerine g\u00f6re olduk\u00e7a karma\u015f\u0131k olan matematikte \u015fa\u015f\u0131rmamak zaten m\u00fcmk\u00fcn de\u011fil, fark\u0131nday\u0131m. Kimilerine g\u00f6re ise \u015fa\u015fk\u0131nl\u0131k yaratan bu olaylar bir ayd\u0131nlanmadan hatta farkl\u0131 bak\u0131\u015f a\u00e7\u0131lar\u0131 geli\u015ftirmekten ibaret. \u015eimdi gelin size o ilgin\u00e7 durumlar\u0131n birinden bahsedeyim. Bir \u00e7ift tav\u015fandan sonras\u0131ndan\u2026<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/10\/image-4.png\"><img loading=\"lazy\" decoding=\"async\" width=\"600\" height=\"300\" src=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/10\/image-4.png\" alt=\"\" class=\"wp-image-4857\" srcset=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/10\/image-4.png 600w, https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/10\/image-4-300x150.png 300w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/a><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Bir g\u00fcn \u0130talyan matematik\u00e7ilerden biri olan Leonardo Fibonacci d\u00f6rt bir yan\u0131n\u0131n duvarla \u00e7evrili oldu\u011fu bir ortamda 1 \u00e7ift tav\u015fandan y\u0131lda ka\u00e7 \u00e7ift tav\u015fan elde edebilece\u011fini ara\u015ft\u0131rmak istiyor. Detaylar\u0131na ge\u00e7meden \u00f6nce belirtmek isterim ki ben bu yaz\u0131mda olay\u0131n varsay\u0131mlar\u0131n\u0131 ve \u015fartlar\u0131n\u0131 bir kenara b\u0131rak\u0131p olay\u0131n \u00f6z\u00fcne odaklanmak istiyorum. \u015eimdi gelelim olay\u0131n kendisine, ocak ay\u0131nda 1 \u00e7ift tav\u015fan\u0131 olan Fibonacci\u2019nin 1 y\u0131l i\u00e7indeki aylara g\u00f6re tav\u015fan da\u011f\u0131l\u0131m\u0131na bakt\u0131\u011f\u0131m\u0131zda elimizdeki veriler \u015fu \u015fekilde:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/10\/image-6.png\"><img loading=\"lazy\" decoding=\"async\" width=\"400\" height=\"270\" src=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/10\/image-6.png\" alt=\"\" class=\"wp-image-4859\" srcset=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/10\/image-6.png 400w, https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/10\/image-6-300x203.png 300w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">1 Ocak: 1 \u00e7ift tav\u015fan\u0131 var.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1 \u015eubat: Hen\u00fcz yeni yavrulama olmad\u0131\u011f\u0131 i\u00e7in tav\u015fan say\u0131s\u0131 1 \u00e7iftten ibarettir.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1 Mart: \u0130lk \u00e7iftten iki ay sonra ilk yavru \u00e7ift do\u011fuyor ve 2 \u00e7ift tav\u015fan\u0131 oluyor.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1 Nisan: \u0130lk \u00e7ift yeni bir \u00e7ift daha yavruluyor ama mart ay\u0131nda do\u011fan \u00e7ift hen\u00fcz yavru vermiyor. Toplam tav\u015fan say\u0131s\u0131 3 \u00e7ift.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1 May\u0131s: Ocak ve mart do\u011fumlu \u00e7iftlerden birer \u00e7ift do\u011fuyor, nisan do\u011fumlu \u00e7ift hen\u00fcz yavru vermiyor. Toplam tav\u015fan say\u0131s\u0131 5 \u00e7ift.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1 Haziran: Ocak, mart ve nisan do\u011fumlu \u00e7iftler birer \u00e7ift yavru veriyor, may\u0131s do\u011fumlu \u00e7iftler hen\u00fcz yavru vermiyor. Toplam tav\u015fan say\u0131m\u0131z 8 \u00e7ift.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1 Temmuz: Ocak, mart, nisan ve may\u0131s do\u011fumlu \u00e7iftler birer \u00e7ift yavru veriyor, haziran do\u011fumlu \u00e7iftler hen\u00fcz yavru vermiyor. Toplam tav\u015fan say\u0131m\u0131z 13 \u00e7ift.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1 A\u011fustos: Ocak, mart, nisan, may\u0131s ve haziran do\u011fumlu \u00e7iftler birer \u00e7ift yavru veriyor, temmuz do\u011fumlu \u00e7iftler hen\u00fcz yavru vermiyor. Toplam tav\u015fan say\u0131m\u0131z 21 \u00e7ift.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1 Eyl\u00fcl: Ocak, mart, nisan, may\u0131s, haziran ve temmuz do\u011fumlu \u00e7iftler birer \u00e7ift yavru veriyor, a\u011fustos do\u011fumlu \u00e7iftler hen\u00fcz yavru vermiyor. Toplam tav\u015fan say\u0131m\u0131z 34 \u00e7ift.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1 Ekim: Ocak, mart, nisan, may\u0131s, haziran, temmuz ve a\u011fustos do\u011fumlu \u00e7iftler birer \u00e7ift yavru veriyor, eyl\u00fcl do\u011fumlu \u00e7iftler hen\u00fcz yavru vermiyor. Toplam tav\u015fan say\u0131m\u0131z 55 \u00e7ift.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1 Kas\u0131m: Ocak, mart, nisan, may\u0131s, haziran, temmuz, a\u011fustos ve eyl\u00fcl do\u011fumlu \u00e7iftler birer \u00e7ift yavru veriyor, ekim do\u011fumlu \u00e7iftler hen\u00fcz yavru vermiyor. Toplam tav\u015fan say\u0131m\u0131z 89 \u00e7ift.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1 Aral\u0131k: Ocak, mart, nisan, may\u0131s, haziran, temmuz, a\u011fustos, eyl\u00fcl ve ekim do\u011fumlu \u00e7iftler birer \u00e7ift yavru veriyor, kas\u0131m do\u011fumlu \u00e7iftler hen\u00fcz yavru vermiyor. Toplam tav\u015fan say\u0131m\u0131z 144 \u00e7ift.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;\u0130\u015fte Fibonacci y\u0131l\u0131n ilk ay\u0131 olan ocak ay\u0131ndan ba\u015flayarak elde etti\u011fi verileri bu \u015fekilde not ediyor. Elde etti\u011fi verileri analiz etti\u011fi s\u0131rada tav\u015fan say\u0131s\u0131n\u0131n her ay belirli bir mant\u0131k sisteminde ilerledi\u011fini fark ediyor. Fark etti\u011fi ili\u015fki asl\u0131nda \u00f6r\u00fcnt\u00fcdeki her say\u0131 kendisinden \u00f6nce gelen iki say\u0131n\u0131n toplam\u0131ndan olu\u015fuyor.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/10\/image-5.png\"><img loading=\"lazy\" decoding=\"async\" width=\"653\" height=\"462\" src=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/10\/image-5.png\" alt=\"\" class=\"wp-image-4858\" srcset=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/10\/image-5.png 653w, https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/10\/image-5-300x212.png 300w\" sizes=\"auto, (max-width: 653px) 100vw, 653px\" \/><\/a><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Dizinin terimlerine bakt\u0131\u011f\u0131m\u0131z zaman 1, 1, 2, 3, 5, 8, 13, 21, 34 \u015feklinde devam ediyor, \u015fimdi gelin bir de terimleri beraber inceleyelim.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2 = 1 + 1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">3 = 1 + 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">5 = 2 + 3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">8 = 3 + 5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">13 = 5 + 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">21 = 8 + 13<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">34 = 13 + 21<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Bu ili\u015fki sonsuza kadar devam etmekle kalm\u0131yor ayn\u0131 zamanda g\u00f6rsel alanda g\u00fczelli\u011fin taht\u0131 olan alt\u0131n oran\u0131 da bizlere sunuyor.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Emre Kahraman<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/10\/image-7.png\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/10\/image-7.png\" alt=\"\" class=\"wp-image-4860\"\/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">17.10.2023<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Merhaba sevgili inekle Blog Okurlar\u0131. Bu zamana kadar matematik hakk\u0131nda \u00e7ok fazla \u015fa\u015f\u0131rd\u0131\u011f\u0131n\u0131z bir olayla kar\u015f\u0131la\u015ft\u0131n\u0131z m\u0131 bilmiyorum. Kimilerine g\u00f6re olduk\u00e7a karma\u015f\u0131k\u2026<\/p>\n","protected":false},"author":1,"featured_media":4861,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_inekle_views":0,"footnotes":""},"categories":[380],"tags":[708,2391,22,2392,1054,711,163,42,2361,49,154,686,70,151,685],"class_list":["post-4856","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ogrenciler-soruyor","tag-ayt","tag-bir-ciftt-tavsandan-sonrasi","tag-canli-ders","tag-fibonacci-dizisi","tag-inekle-blog","tag-lgs","tag-lys-tavsiyeleri","tag-matematik","tag-matematik-tarihi","tag-online-dershane","tag-online-ozel-ders","tag-tyt","tag-universite-tercih","tag-universiteliden-ozel-ders","tag-yks"],"_links":{"self":[{"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/posts\/4856","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/comments?post=4856"}],"version-history":[{"count":1,"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/posts\/4856\/revisions"}],"predecessor-version":[{"id":11164,"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/posts\/4856\/revisions\/11164"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/media\/4861"}],"wp:attachment":[{"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/media?parent=4856"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/categories?post=4856"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/tags?post=4856"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}