{"id":1099,"date":"2016-12-01T10:18:46","date_gmt":"2016-12-01T10:18:46","guid":{"rendered":"http:\/\/ragipsahin.com\/?p=1099"},"modified":"2016-10-22T10:15:42","modified_gmt":"2016-10-22T10:15:42","slug":"fibonacci-sayi-dizisiserisi-nedir-ve-nerede-kullanilir","status":"publish","type":"post","link":"https:\/\/www.ragipsahin.com.tr\/?p=1099","title":{"rendered":"Fibonacci Say\u0131 Dizisi\/Serisi Nedir ve Nerede Kullan\u0131l\u0131r ?"},"content":{"rendered":"<p><span style=\"color: #000000;\">Fibonacci serisi say\u0131lar\u0131:0, 1,1,2,3,5,8,13,21,34,55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, \u2026 vb. \u015feklinde devam eder. Her say\u0131 kendisinden \u00f6nce gelen iki say\u0131n\u0131n toplam\u0131d\u0131r.<\/span><\/p>\n<a href=\"http:\/\/www.ragipsahin.com.tr\/ozel-sayi-oruntuleri-16-soru-ve-cozumleri-video\/\" target=\"_blank\" class=\"shortc-button medium red \"><strong>Konuyla \u0130lgili Soru \u00c7\u00f6z\u00fcmleri \u0130\u00e7in TIKLAYINIZ<\/strong><\/a>\n<p><span style=\"color: #000000;\"><strong>Fibonacci Kimdir?<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">FibonacciAd\u0131 orta \u00e7a\u011f\u0131n en b\u00fcy\u00fck matematik\u00e7ileri aras\u0131nda ge\u00e7en Fibonacci\u2019nin hayat\u0131 ile ilgili pek fazla bilgi bulunmamaktad\u0131r. \u0130talya\u2019n\u0131n Pisa \u015fehrinde 1170\u2019li y\u0131llarda do\u011fdu\u011fu san\u0131lmakta, babas\u0131n\u0131n i\u015fi nedeniyle Kuzey Afrika\u2019ya ve Cezayir\u2019e gittti\u011fi ve burada Arap hocalardan matematik dersleri ald\u0131\u011f\u0131 bilinmektedir. Hint-Arap say\u0131lar\u0131n\u0131 (1, 2, 3\u2026) \u00f6\u011frenerek, bunlar\u0131 Avrupa\u2019ya tan\u0131tm\u0131\u015ft\u0131r. Bu bak\u0131mdan Fibonacci, matemati\u011fi Araplardan al\u0131p Avrupa\u2019ya tan\u0131tan ki\u015fi olarak an\u0131l\u0131r.<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>Tav\u015fan Problemi<\/strong><\/span><br \/>\n<span style=\"color: #000000;\"> \u201cD\u00f6rt yan\u0131 duvarlarla \u00e7evrili bir yere bir \u00e7ift tav\u015fan konmu\u015ftur. Her \u00e7ift tav\u015fan\u0131n bir ay i\u00e7inde yeni bir \u00e7ift tav\u015fan yavrulad\u0131\u011f\u0131, her yeni \u00e7iftin de erginle\u015fmesi i\u00e7in bir ay gerekti\u011fi ve tav\u015fanlar\u0131n \u00f6lmedi\u011fi varsay\u0131l\u0131rsa, 100 ay sonunda d\u00f6rt duvar\u0131n aras\u0131nda ka\u00e7 \u00e7ift tav\u015fan olur?\u201d Bu \u015fekilde d\u00fc\u015f\u00fcn\u00fcld\u00fc\u011f\u00fc takdirde tav\u015fan \u00e7iftleri aylara g\u00f6re \u015fu s\u0131ralamay\u0131 ortaya koymaktad\u0131r: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,\u2026 G\u00f6r\u00fcld\u00fc\u011f\u00fc gibi ilk iki say\u0131 hari\u00e7, her say\u0131 kendisinden \u00f6nce gelen iki say\u0131n\u0131n toplam\u0131na e\u015fittir. Bu say\u0131lar\u0131n aras\u0131ndaki oran ise bize alt\u0131n oran\u0131 vermektedir.<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>Fibonacci Dizisinin G\u00f6r\u00fcld\u00fc\u011f\u00fc ve Kullan\u0131ld\u0131\u011f\u0131 Yerler<\/strong><\/span><br \/>\n<span style=\"color: #000000;\"> 1) Ay\u00e7i\u00e7e\u011fi: Ay\u00e7i\u00e7e\u011fi\u2019nin merkezinden d\u0131\u015far\u0131ya do\u011fru sa\u011fdan sola ve soldan sa\u011fa do\u011fru taneler say\u0131ld\u0131\u011f\u0131nda \u00e7\u0131kan say\u0131lar Fibonacci Dizisinin ard\u0131\u015f\u0131k terimleridir.<\/span><\/p>\n<p><span style=\"color: #000000;\">2) Papatya \u00c7i\u00e7e\u011fi: Papatya \u00c7i\u00e7e\u011finde de ay\u00e7i\u00e7e\u011finde oldu\u011fu gibi bir Fibonacci Dizisi mevcuttur.<\/span><\/p>\n<p><span style=\"color: #000000;\">3) Fibonacci Dizisinin Fark Dizisi: Fibonacci Dizisindeki ard\u0131\u015f\u0131k terimlerin fark\u0131yla olu\u015fan dizi de Fibonacci Dizisidir.<\/span><\/p>\n<p><span style=\"color: #000000;\">4) \u00d6mer Hayyam veya Pascal veya Binom \u00dc\u00e7geni: \u00d6mer Hayyam \u00fc\u00e7genindeki t\u00fcm katsay\u0131lar veya terimler yaz\u0131l\u0131p \u00e7apraz toplamlar\u0131 al\u0131nd\u0131\u011f\u0131nda Fibonacci Dizisi ortaya \u00e7\u0131kar.<\/span><\/p>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/i0.wp.com\/www.ragipsahin.com.tr\/wp-content\/uploads\/2011\/10\/fibonacci1.jpg\"><span style=\"color: #000000;\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" class=\"alignright\" title=\"fibonacci\" src=\"https:\/\/i0.wp.com\/www.ragipsahin.com.tr\/wp-content\/uploads\/2011\/10\/fibonacci1.jpg?resize=200%2C200\" alt=\"\" width=\"200\" height=\"200\" \/><\/span><\/a>5) Tav\u015fan: Zaten sorumuz tav\u015fanla alakal\u0131\u2026<\/span><\/p>\n<p><span style=\"color: #000000;\">6) \u00c7am Kozala\u011f\u0131: \u00c7am kozala\u011f\u0131ndaki taneler kozala\u011f\u0131n alt\u0131ndaki sabit bir noktadan kozala\u011f\u0131n tepesindeki ba\u015fka bir sabit noktaya do\u011fru spiraller (e\u011friler) olu\u015fturarak \u00e7\u0131karlar. \u0130\u015fte bu taneler soldan sa\u011fa ve sa\u011fdan sola say\u0131ld\u0131\u011f\u0131nda \u00e7\u0131kan say\u0131lar, Fibonacci Dizisi\u2019nin ard\u0131\u015f\u0131k terimleridir.<\/span><\/p>\n<p><span style=\"color: #000000;\">7) T\u00fct\u00fcn Bitkisi: T\u00fct\u00fcn Bitkisinin yapraklar\u0131n\u0131n dizili\u015finde bir Fibonacci Dizisi s\u00f6z konusudur; yani yapraklar\u0131n diziliminde bu dizi mevcuttur. Bundan dolay\u0131 t\u00fct\u00fcn bitkisi G\u00fcne\u015f\u2019ten en iyi \u015fekilde g\u00fcne\u015f \u0131\u015f\u0131\u011f\u0131 ve havadan en iyi \u015fekilde Karbondioksit alarak Fotosentez\u2019i m\u00fckemmel bir \u015fekilde ger\u00e7ekle\u015ftirir.<\/span><\/p>\n<p><span style=\"color: #000000;\">8 ) E\u011frelti Otu: T\u00fct\u00fcn Bitkisindeki ayn\u0131 \u00f6zellik E\u011frelti Otu\u2019nda da vard\u0131r.<\/span><\/p>\n<p><span style=\"color: #000000;\">9) M\u0130MAR S\u0130NAN: Mimar Sinan\u2019\u0131n da bir \u00e7ok eserinde Fibonacci Dizisi g\u00f6r\u00fclmektedir. Mesela S\u00fcleymaniye ve Selimiye Camileri\u2019nin minarelerinde bu dizi mevcuttur.<\/span><\/p>\n<h3 style=\"text-align: center;\"><span style=\"color: #ff0000;\"><a href=\"http:\/\/ragipsahin.com.tr\/pisali-leonardo-fibonacci\/\" target=\"_blank\"><span style=\"color: #ff0000;\"><strong>F\u0130BONACC\u0130&#8217;N\u0130N HAYATI HAKKINDA<\/strong><\/span><\/a><\/span><\/h3>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Fibonacci serisi say\u0131lar\u0131:0, 1,1,2,3,5,8,13,21,34,55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, \u2026 vb. \u015feklinde devam eder. Her say\u0131 kendisinden \u00f6nce gelen iki say\u0131n\u0131n toplam\u0131d\u0131r. Fibonacci Kimdir? FibonacciAd\u0131 orta \u00e7a\u011f\u0131n en b\u00fcy\u00fck matematik\u00e7ileri aras\u0131nda ge\u00e7en Fibonacci\u2019nin hayat\u0131 ile ilgili pek fazla bilgi bulunmamaktad\u0131r. \u0130talya\u2019n\u0131n Pisa \u015fehrinde 1170\u2019li y\u0131llarda do\u011fdu\u011fu san\u0131lmakta, babas\u0131n\u0131n i\u015fi &hellip;<\/p>\n","protected":false},"author":1,"featured_media":2511,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":true,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[1],"tags":[438],"class_list":["post-1099","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-genel","tag-fibonacci-sayi-dizisi"],"aioseo_notices":[],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/www.ragipsahin.com.tr\/wp-content\/uploads\/2011\/10\/fibonacci1.jpg?fit=200%2C200&ssl=1","jetpack_shortlink":"https:\/\/wp.me\/p2YBEC-hJ","jetpack_sharing_enabled":true,"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=\/wp\/v2\/posts\/1099","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1099"}],"version-history":[{"count":1,"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=\/wp\/v2\/posts\/1099\/revisions"}],"predecessor-version":[{"id":22874,"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=\/wp\/v2\/posts\/1099\/revisions\/22874"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=\/wp\/v2\/media\/2511"}],"wp:attachment":[{"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1099"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1099"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1099"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}