{"id":5235,"date":"2024-09-11T11:22:45","date_gmt":"2024-09-11T11:22:45","guid":{"rendered":"https:\/\/www.techopedia.com\/pl\/?post_type=definition&#038;p=5235"},"modified":"2024-09-13T12:11:20","modified_gmt":"2024-09-13T12:11:20","slug":"ciag-fibonacciego","status":"publish","type":"definition","link":"https:\/\/www.techopedia.com\/pl\/slowniczek\/ciag-fibonacciego","title":{"rendered":"Ci\u0105g Fibonacciego"},"content":{"rendered":"<h2><span id=\"czym_jest_ciag_fibonacciego\">Czym jest ci\u0105g Fibonacciego?<\/span><\/h2>\n<p>Ci\u0105g Fibonacciego to sekwencja liczb naturalnych, w kt\u00f3rej ka\u017cda liczba (pocz\u0105wszy od trzeciej) jest sum\u0105 dw\u00f3ch poprzednich. Ci\u0105g zaczyna si\u0119 od liczb 0 i 1, a wi\u0119c jego pierwsze elementy to:<\/p>\n<p>0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, &#8230;<\/p>\n<p>Nazwa ci\u0105gu pochodzi od nazwiska w\u0142oskiego matematyka. Ci\u0105g Fibonacciego jest wykorzystywany w matematyce, naukach \u015bcis\u0142ych, informatyce, ale znajdziemy go te\u017c w sztuce i w przyrodzie.<\/p>\n<h2><span id=\"techopedia_wyjasnia_pojecie_ciagu_fibonacciego\">Techopedia wyja\u015bnia poj\u0119cie ci\u0105gu Fibonacciego<\/span><\/h2>\n<p>Ci\u0105g Fibonacciego jest prostym, ale kompletnym ci\u0105giem, tzn. wszystkie dodatnie liczby ca\u0142kowite w ci\u0105gu mo\u017cna obliczy\u0107 jako sum\u0119 liczb Fibonacciego, przy czym ka\u017cda liczba ca\u0142kowita mo\u017ce by\u0107 u\u017cyta najwy\u017cej raz. Podobnie jak wszystkie sekwencje, ci\u0105g Fibonacciego mo\u017ce by\u0107 r\u00f3wnie\u017c obliczony za pomoc\u0105 sko\u0144czonej liczby operacji. Innymi s\u0142owy, ci\u0105g Fibonacciego ma rozwi\u0105zanie w postaci zamkni\u0119tej. Og\u00f3lna zasada uzyskiwania n-tej liczby w ci\u0105gu polega na dodaniu poprzedniego (n-1) i (n-2) wyrazu, tj. xn = xn-1 + xn-2.<\/p>\n<p>Ci\u0105g Fibonacciego ma wiele zastosowa\u0144. W\u015br\u00f3d nich warto wymieni\u0107 algorytmy komputerowe, analiza techniczna czy algorytmy programowania rekurencyjnego. Innym zastosowaniem ci\u0105gu Fibonacciego s\u0105 grafy zwane kostkami Fibonacciego, kt\u00f3re s\u0105 tworzone w celu \u0142\u0105czenia system\u00f3w rozproszonych i r\u00f3wnoleg\u0142ych. Niekt\u00f3re generatory liczb pseudolosowych r\u00f3wnie\u017c wykorzystuj\u0105 liczby Fibonacciego. Natura r\u00f3wnie\u017c wykorzystuje ci\u0105g Fibonacciego, na przyk\u0142ad w przypadku rozga\u0142\u0119zie\u0144 w drzewach.<\/p>\n<h3>Ciekawe w\u0142a\u015bciwo\u015bci ci\u0105gu Fibonacciego<\/h3>\n<p>Ci\u0105g Fibonacciego ma <a href=\"http:\/\/www.ftj.agh.edu.pl\/~lenda\/cicer\/fibo.htm\" target=\"_blank\">szereg ciekawych w\u0142a\u015bciwo\u015bci<\/a>:<\/p>\n<ul>\n<li>Poza wyrazami jednocyfrowymi ci\u0105gu Fibonacciego, zawsze 4 lub 5 kolejnych wyraz\u00f3w ci\u0105gu ma t\u0119 sam\u0105 liczb\u0119 cyfr w uk\u0142adzie dziesi\u0119tnym.<\/li>\n<li>Jedynymi kwadratami liczb ca\u0142kowitych w ci\u0105gu Fibonacciego s\u0105 1 i 144.<\/li>\n<li>Co trzeci wyraz ci\u0105gu Fibonacciego jest podzielny przez 2, co czwarty &#8211; przez 3.<\/li>\n<li>Ka\u017cda liczba ca\u0142kowita r\u00f3\u017cna od zera ma wielokrotno\u015b\u0107 b\u0119d\u0105c\u0105 liczb\u0105 Fibonacciego.<\/li>\n<\/ul>\n<h2><span id=\"zniesienia_fibonacciego\">Zniesienia Fibonacciego<\/span><\/h2>\n<p>Wy\u017cej wspomniano, \u017ce jednym z zastosowa\u0144 ci\u0105gu Fibonacciego jest analiza techniczna. <a href=\"https:\/\/web.archive.org\/web\/20140417061053\/http:\/\/szkolenia-gielda-finanse.pl\/gielda-blog\/zniesienia-fibonacciego\/\" target=\"_blank\">Zniesienia Fibonacciego<\/a> (ang. <strong>Fibonacci retracement<\/strong>) to jedno z narz\u0119dzi takiej analizy, u\u017cywane na rynkach finansowych. Pomaga ono pomaga inwestorom przewidzie\u0107 potencjalne poziomy wsparcia i oporu cenowego na wykresie cenowym. Opiera si\u0119 na proporcjach wynikaj\u0105cych z ci\u0105gu Fibonacciego i tzw. &#8220;z\u0142otej proporcji&#8221;.<\/p>\n<h3>G\u0142\u00f3wne poziomy zniesienia Fibonacciego:<\/h3>\n<p>Najcz\u0119\u015bciej u\u017cywane poziomy zniesienia Fibonacciego to:<\/p>\n<ul>\n<li><strong>23,6%<\/strong><\/li>\n<li><strong>38,2%<\/strong><\/li>\n<li><strong>50%<\/strong><\/li>\n<li><strong>61,8%<\/strong><\/li>\n<li><strong>78,6%<\/strong><\/li>\n<\/ul>\n<h3>Jak dzia\u0142aj\u0105 zniesienia Fibonacciego?<\/h3>\n<p>Inwestorzy rysuj\u0105 poziome linie na wykresie w celu identyfikacji mo\u017cliwych punkt\u00f3w zwrotu cen. Zaczynaj\u0105 od wyznaczenia punktu szczytowego (lokalnego maksimum) i punktu do\u0142kowego (lokalnego minimum) dla danego ruchu cenowego. Nast\u0119pnie na tej podstawie wyznaczane s\u0105 wspomniane poziomy zniesie\u0144.<\/p>\n<h3>Zastosowanie<\/h3>\n<p>Zniesienia Fibonacciego s\u0105 wykorzystywane, aby:<\/p>\n<ol>\n<li><strong>Identyfikowa\u0107 poziomy wsparcia i oporu<\/strong> \u2013 miejsca, w kt\u00f3rych cena mo\u017ce odbi\u0107 si\u0119 lub zatrzyma\u0107.<\/li>\n<li><strong>Okre\u015bla\u0107 potencjalne punkty zwrotne<\/strong> \u2013 poziomy, na kt\u00f3rych cena mo\u017ce si\u0119 odwr\u00f3ci\u0107 i zmieni\u0107 kierunek (np. po korekcie trendu).<\/li>\n<li><strong>Planowa\u0107 wej\u015bcia i wyj\u015bcia z pozycji<\/strong> \u2013 pomagaj\u0105 inwestorom zidentyfikowa\u0107 najlepsze momenty na kupno lub sprzeda\u017c.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Czym jest ci\u0105g Fibonacciego? Ci\u0105g Fibonacciego to sekwencja liczb naturalnych, w kt\u00f3rej ka\u017cda liczba (pocz\u0105wszy od trzeciej) jest sum\u0105 dw\u00f3ch poprzednich. Ci\u0105g zaczyna si\u0119 od liczb 0 i 1, a wi\u0119c jego pierwsze elementy to: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, &#8230; Nazwa ci\u0105gu pochodzi od nazwiska w\u0142oskiego [&hellip;]<\/p>\n","protected":false},"author":7813,"featured_media":5395,"comment_status":"open","ping_status":"closed","template":"","format":"standard","meta":{"_acf_changed":false,"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"definitioncat":[71],"class_list":["post-5235","definition","type-definition","status-publish","format-standard","has-post-thumbnail","hentry","definitioncat-inwestycje"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v24.2 (Yoast SEO v24.5) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Czym jest ci\u0105g Fibonacciego i zniesienia Fibonacciego?<\/title>\n<meta name=\"description\" content=\"Dowiedz si\u0119, czym jest ci\u0105g Fibonacciego i odkryj jego zastosowania. 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