{"id":56687,"date":"2015-03-03T22:57:21","date_gmt":"2015-03-03T20:57:21","guid":{"rendered":"http:\/\/www.sorubak.com\/blog\/?p=56687"},"modified":"2015-03-03T22:57:21","modified_gmt":"2015-03-03T20:57:21","slug":"fibonacci-sayisi-nedir","status":"publish","type":"post","link":"https:\/\/www.sorubak.com\/blog\/fibonacci-sayisi-nedir.html","title":{"rendered":"Fibonacci say\u0131s\u0131 nedir?"},"content":{"rendered":"<p><b>Fibonacci dizisi<\/b>, her say\u0131n\u0131n kendinden \u00f6ncekiyle toplanmas\u0131 sonucu olu\u015fan bir say\u0131 dizisidir. Bu \u015fekilde devam eden bu dizide say\u0131lar birbirleriyle oranland\u0131\u011f\u0131nda alt\u0131n oran ortaya \u00e7\u0131kar, yani bir say\u0131 kendisinden \u00f6nceki say\u0131ya b\u00f6l\u00fcnd\u00fc\u011f\u00fcnde <a title=\"Alt\u0131n oran\" href=\"http:\/\/tr.wikipedia.org\/wiki\/Alt%C4%B1n_oran\" target=\"_blank\" rel=\"nofollow\">alt\u0131n orana<\/a> gittik\u00e7e yakla\u015fan bir dizi elde edilir. Bu durumda genel olarak n&#8217;inci <a class=\"mw-redirect\" title=\"Fibonacci\" href=\"http:\/\/tr.wikipedia.org\/wiki\/Fibonacci\" target=\"_blank\" rel=\"nofollow\">Fibonacci<\/a> say\u0131s\u0131 F(n) \u015fu \u015fekilde ifade edilir:<\/p>\n<dl>\n<dd><img decoding=\"async\" class=\"mwe-math-fallback-image-inline tex\" style=\"border: none; vertical-align: middle; display: inline-block;\" src=\"http:\/\/upload.wikimedia.org\/math\/8\/9\/1\/891f2490410ef44b449e3fc1e10aaf18.png\" alt=\" \n  F_n = F(n)=\n  \\begin{cases}\n    0             &amp; \\mbox{ } n = 0; \\\\\n    1             &amp; \\mbox{ } n = 1; \\\\\n    F(n-1)+F(n-2) &amp; \\mbox{ } n &gt; 1. \\\\\n   \\end{cases}=\\frac{\\left(\\frac{1+\\sqrt{5}}{2}\\right)^n-\\left(\\frac{1-\\sqrt{5}}{2}\\right)^n}{\\sqrt{5}}=\\frac{\\varphi^n-\\left(\\varphi-\\sqrt{5}\\right)^n}{\\sqrt{5}}\n\" \/><\/dd>\n<\/dl>\n<p>Bu da bir Fibonacci dizisidir:4, 4, 8, 12, 20, 32, 52, \u2026 \u00c7\u00fcnk\u00fc Fibonacci dizisi herhangi iki say\u0131dan ba\u015flayabilir.<\/p>\n<p>Fibonacci say\u0131 dizisindeki say\u0131lar\u0131n birbirleriyle oran\u0131 olan ve <a title=\"Alt\u0131n oran\" href=\"http:\/\/tr.wikipedia.org\/wiki\/Alt%C4%B1n_oran\" target=\"_blank\" rel=\"nofollow\">alt\u0131n oran<\/a> denilen 1,618 say\u0131s\u0131 ise do\u011fada, sanatta ve hayat\u0131n her alan\u0131nda g\u00f6r\u00fclen ve estetik ile ba\u011fda\u015ft\u0131r\u0131lan bir say\u0131d\u0131r.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Fibonacci dizisi, her say\u0131n\u0131n kendinden \u00f6ncekiyle toplanmas\u0131 sonucu olu\u015fan bir say\u0131 dizisidir. Bu \u015fekilde devam eden bu dizide say\u0131lar birbirleriyle oranland\u0131\u011f\u0131nda alt\u0131n oran ortaya \u00e7\u0131kar, yani bir say\u0131 kendisinden \u00f6nceki say\u0131ya b\u00f6l\u00fcnd\u00fc\u011f\u00fcnde alt\u0131n orana gittik\u00e7e yakla\u015fan bir dizi elde edilir. Bu durumda genel olarak n&#8217;inci Fibonacci say\u0131s\u0131 F(n) \u015fu \u015fekilde ifade edilir: Bu da bir &#8230; <a title=\"Fibonacci say\u0131s\u0131 nedir?\" class=\"read-more\" href=\"https:\/\/www.sorubak.com\/blog\/fibonacci-sayisi-nedir.html\" aria-label=\"More on Fibonacci say\u0131s\u0131 nedir?\">Devam\u0131n\u0131 oku&#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[],"class_list":["post-56687","post","type-post","status-publish","format-standard","hentry","category-mt"],"_links":{"self":[{"href":"https:\/\/www.sorubak.com\/blog\/wp-json\/wp\/v2\/posts\/56687","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sorubak.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sorubak.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sorubak.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sorubak.com\/blog\/wp-json\/wp\/v2\/comments?post=56687"}],"version-history":[{"count":0,"href":"https:\/\/www.sorubak.com\/blog\/wp-json\/wp\/v2\/posts\/56687\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.sorubak.com\/blog\/wp-json\/wp\/v2\/media?parent=56687"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sorubak.com\/blog\/wp-json\/wp\/v2\/categories?post=56687"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sorubak.com\/blog\/wp-json\/wp\/v2\/tags?post=56687"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}