{"id":57537,"date":"2023-11-23T23:09:23","date_gmt":"2023-11-23T21:09:23","guid":{"rendered":"https:\/\/omathimatikos.gr\/?p=57537"},"modified":"2023-11-23T23:09:23","modified_gmt":"2023-11-23T21:09:23","slug":"23-%ce%bd%ce%bf%ce%b5%ce%bc%ce%b2%cf%81%ce%af%ce%bf%cf%85-h%ce%bc%ce%ad%cf%81%ce%b1-fibonacci","status":"publish","type":"post","link":"https:\/\/omathimatikos.gr\/?p=57537","title":{"rendered":"23 \u039d\u03bf\u03b5\u03bc\u03b2\u03c1\u03af\u03bf\u03c5: H\u03bc\u03ad\u03c1\u03b1 Fibonacci"},"content":{"rendered":"<p><!--more--><\/p>\n<header class=\"entry-header\">\n<div class=\"entry-meta\"><\/div>\n<\/header>\n<div class=\"article__summary\">\u039f\u03b9 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03c4\u03b7\u03c2 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1\u03c2 Fibonacci \u03ba\u03b1\u03b9 \u03bf \u03c7\u03c1\u03c5\u03c3\u03cc\u03c2 \u03bb\u03cc\u03b3\u03bf\u03c2 \u03c6<\/div>\n<div class=\"article__body\">\n<p><strong><em>\u03a4\u03bf\u03c5 \u0391\u03b8\u03b1\u03bd\u03ac\u03c3\u03b9\u03bf\u03c5 \u039a\u03bf\u03c0\u03ac\u03b4\u03b7<\/em><\/strong><\/p>\n<\/div>\n<div class=\"entry-content\">\n<blockquote class=\"wp-block-quote\"><p>H 23 \u039d\u03bf\u03b5\u03bc\u03b2\u03c1\u03af\u03bf\u03c5 \u03ad\u03c7\u03b5\u03b9 \u03ba\u03b1\u03b8\u03b9\u03b5\u03c1\u03c9\u03b8\u03b5\u03af \u03c9\u03c2 \u03b7 \u03b7\u03bc\u03ad\u03c1\u03b1 \u03c4\u03c9\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd Fibonacci.<\/p><\/blockquote>\n<p><strong>\u03a0\u03bf\u03b9\u03bf\u03c2 \u03ae\u03c4\u03b1\u03bd \u03cc\u03bc\u03c9\u03c2 \u03bf Fibonacci<\/strong><\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-2054\" src=\"https:\/\/i0.wp.com\/www.ma8imatikos.gr\/wp-content\/uploads\/2019\/11\/images-7.jpg?resize=192%2C262&#038;ssl=1\" alt=\"\" width=\"192\" height=\"262\" data-recalc-dims=\"1\" \/><\/figure>\n<\/div>\n<p>\u039f\u00a0<strong>Fibonacci<\/strong>\u00a0\u03ae\u03c4\u03b1\u03bd \u03c0\u03bf\u03bb\u03cd \u03b3\u03bd\u03c9\u03c3\u03c4\u03cc\u03c2 \u03c3\u03c4\u03b7\u03bd \u03b5\u03c0\u03bf\u03c7\u03ae \u03c4\u03bf\u03c5 \u03ba\u03b1\u03b9 \u03b1\u03bd\u03b1\u03b3\u03bd\u03c9\u03c1\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c3\u03ae\u03bc\u03b5\u03c1\u03b1 \u03c9\u03c2 \u03bf \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2 \u03c4\u03bf\u03c5 \u039c\u03b5\u03c3\u03b1\u03af\u03c9\u03bd\u03b1. \u0393\u03b5\u03bd\u03bd\u03ae\u03b8\u03b7\u03ba\u03b5 \u03c3\u03c4\u03b7\u03bd \u03a0\u03af\u03b6\u03b1 \u03c4\u03b7 \u03b4\u03b5\u03ba\u03b1\u03b5\u03c4\u03af\u03b1 \u03c4\u03bf\u03c5 1170 \u03ba\u03b1\u03b9 \u03c0\u03ad\u03b8\u03b1\u03bd\u03b5 \u03b1\u03c5\u03c4\u03ae \u03c4\u03bf\u03c5 1240. \u03a4\u03bf \u03cc\u03bd\u03bf\u03bc\u03ac \u03c4\u03bf\u03c5 \u03ad\u03c7\u03b5\u03b9 \u03b4\u03bf\u03b8\u03b5\u03af \u03c3\u03b5 \u03b4\u03cd\u03bf \u03b4\u03c1\u03cc\u03bc\u03bf\u03c5\u03c2, \u03c3\u03c4\u03b7\u03bd \u03a0\u03af\u03b6\u03b1 \u03ba\u03b1\u03b9 \u03c3\u03c4\u03b7 \u03a6\u03bb\u03c9\u03c1\u03b5\u03bd\u03c4\u03af\u03b1. \u03a4\u03bf \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u03c4\u03bf\u03c5 \u03cc\u03bd\u03bf\u03bc\u03b1 \u03ae\u03c4\u03b1\u03bd Leonardo Pisano, \u03cc\u03bc\u03c9\u03c2 \u03bf \u03af\u03b4\u03b9\u03bf\u03c2 \u03b1\u03c0\u03bf\u03ba\u03b1\u03bb\u03bf\u03cd\u03c3\u03b5 \u03c4\u03bf\u03bd \u03b5\u03b1\u03c5\u03c4\u03cc \u03c4\u03bf\u03c5 Fibonacci, \u03c3\u03cd\u03bd\u03c4\u03bc\u03b7\u03c3\u03b7 \u03c4\u03bf\u03c5 Filius Bonacci (\u03c5\u03b9\u03cc\u03c2 \u03c4\u03bf\u03c5 Bonacci), \u03b1\u03c0\u03cc \u03c4\u03bf \u03cc\u03bd\u03bf\u03bc\u03b1 \u03c4\u03bf\u03c5 \u03c0\u03b1\u03c4\u03ad\u03c1\u03b1 \u03c4\u03bf\u03c5.<\/p>\n<p>\u03a3\u03c4\u03bf\u03bd \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u03ba\u03bb\u03ac\u03b4\u03bf \u03b5\u03af\u03bd\u03b1\u03b9 \u03b3\u03bd\u03c9\u03c3\u03c4\u03cc\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03b7 \u03c3\u03c5\u03bc\u03b2\u03bf\u03bb\u03ae \u03c4\u03bf\u03c5 \u03c3\u03c4\u03bf\u03bd\u00a0<em>\u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03b9\u03ba\u03cc<\/em>\u00a0\u03ba\u03b1\u03b9\u00a0<em>\u03bf\u03bb\u03bf\u03ba\u03bb\u03b7\u03c1\u03c9\u03c4\u03b9\u03ba\u03cc \u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc<\/em>\u00a0\u03ba\u03b1\u03b9 \u03b3\u03b9\u03b1 \u03c4\u03bf\u03c5\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2 \u03c4\u03bf\u03c5 \u03c0\u03bf\u03c5, \u03cc\u03c0\u03c9\u03c2 \u03b8\u03b1 \u03b4\u03bf\u03cd\u03bc\u03b5, \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03af\u03b1 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1 \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd \u03b3\u03b9\u03b1 \u03c4\u03bf\u03c5\u03c2 \u03bf\u03c0\u03bf\u03af\u03bf\u03c5\u03c2 \u03b7 \u03c6\u03cd\u03c3\u03b7 \u03c0\u03b1\u03c1\u03bf\u03c5\u03c3\u03b9\u03ac\u03b6\u03b5\u03b9 \u03b9\u03b4\u03b9\u03b1\u03af\u03c4\u03b5\u03c1\u03b7 \u03c0\u03c1\u03bf\u03c4\u03af\u03bc\u03b7\u03c3\u03b7, \u03b3\u03b5\u03b3\u03bf\u03bd\u03cc\u03c2 \u03c0\u03bf\u03c5 \u03b1\u03ba\u03cc\u03bc\u03b1 \u03ba\u03b1\u03b9 \u03c3\u03ae\u03bc\u03b5\u03c1\u03b1 \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03bb\u03ae\u03c1\u03c9\u03c2 \u03ba\u03b1\u03c4\u03b1\u03bd\u03bf\u03b7\u03c4\u03cc.<\/p>\n<p><strong>\u03a4\u03bf \u03c0\u03c1\u03cc\u03b2\u03bb\u03b7\u03bc\u03b1 \u03bc\u03b5 \u03c4\u03b1 \u03ba\u03bf\u03c5\u03bd\u03ad\u03bb\u03b9\u03b1<\/strong><\/p>\n<p>\u03a4\u03bf \u03c0\u03c1\u03cc\u03b2\u03bb\u03b7\u03bc\u03b1 \u03c0\u03bf\u03c5 \u03bc\u03b5\u03bb\u03ad\u03c4\u03b7\u03c3\u03b5 \u03ba\u03b1\u03b9 \u03c4\u03bf\u03bd \u03bf\u03b4\u03ae\u03b3\u03b7\u03c3\u03b5 \u03bc\u03ac\u03bb\u03bb\u03bf\u03bd \u03c4\u03c5\u03c7\u03b1\u03af\u03b1 \u00a0\u03c3\u03c4\u03bf\u03bd \u03bf\u03c1\u03b9\u03c3\u03bc\u03cc \u03c4\u03b7\u03c2 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1\u03c2 \u03c4\u03bf\u03c5, \u03b1\u03c6\u03bf\u03c1\u03bf\u03cd\u03c3\u03b5 \u03c4\u03b7\u03bd \u03b1\u03bd\u03b1\u03c0\u03b1\u03c1\u03b1\u03b3\u03c9\u03b3\u03ae \u03ba\u03bf\u03c5\u03bd\u03b5\u03bb\u03b9\u03ce\u03bd. \u03a4\u03bf \u03ad\u03b8\u03b5\u03c3\u03b5 \u03c3\u03c4\u03bf \u03b9\u03c3\u03c4\u03bf\u03c1\u03b9\u03ba\u03cc \u03b2\u03b9\u03b2\u03bb\u03af\u03bf \u03c4\u03bf\u03c5 Liber Abaci(\u03b2\u03b9\u03b2\u03bb\u03af\u03bf \u03c4\u03c9\u03bd \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03ce\u03bd) \u03c0\u03bf\u03c5 \u03b4\u03b7\u03bc\u03bf\u03c3\u03b9\u03b5\u03cd\u03b8\u03b7\u03ba\u03b5 \u03b3\u03b9\u03b1 \u03c0\u03c1\u03ce\u03c4\u03b7 \u03c6\u03bf\u03c1\u03ac \u03c4\u03bf 1202.<\/p>\n<p>\u03a4\u03bf \u03c0\u03c1\u03cc\u03b2\u03bb\u03b7\u03bc\u03b1 \u03ad\u03c7\u03b5\u03b9 \u03c9\u03c2 \u03b5\u03be\u03ae\u03c2:<\/p>\n<p>\u03a3\u03b5 \u03ad\u03bd\u03b1 \u03c3\u03c0\u03af\u03c4\u03b9 \u03c3\u03c4\u03bf \u03c7\u03c9\u03c1\u03b9\u03cc \u03b3\u03b5\u03bd\u03bd\u03b9\u03ad\u03c4\u03b1\u03b9 \u03ad\u03bd\u03b1 \u03b6\u03b5\u03c5\u03b3\u03ac\u03c1\u03b9 \u03ba\u03bf\u03c5\u03bd\u03ad\u03bb\u03b9\u03b1. \u03a4\u03b1 \u03ba\u03bf\u03c5\u03bd\u03ad\u03bb\u03b9\u03b1 \u03b1\u03c5\u03c4\u03ac \u03c7\u03c1\u03b5\u03b9\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 2 \u03bc\u03ae\u03bd\u03b5\u03c2 \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03bc\u03b5\u03b3\u03b1\u03bb\u03ce\u03c3\u03bf\u03c5\u03bd \u03ba\u03b1\u03b9 \u03bd\u03b1 \u03b1\u03c1\u03c7\u03af\u03c3\u03bf\u03c5\u03bd \u03bd\u03b1 \u03b3\u03b5\u03bd\u03bd\u03bf\u03cd\u03bd. \u0388\u03c4\u03c3\u03b9 \u03bc\u03b5\u03c4\u03ac \u03b1\u03c0\u03cc \u03b4\u03cd\u03bf \u03bc\u03ae\u03bd\u03b5\u03c2 \u03c4\u03bf \u03b6\u03b5\u03c5\u03b3\u03ac\u03c1\u03b9 \u03b1\u03c5\u03c4\u03cc \u03b3\u03b5\u03bd\u03bd\u03ac \u03ad\u03bd\u03b1 \u03bd\u03ad\u03bf \u03b6\u03b5\u03c5\u03b3\u03ac\u03c1\u03b9 \u03c3\u03c4\u03b7\u03bd \u03b1\u03c1\u03c7\u03ae \u03ba\u03ac\u03b8\u03b5 \u03bc\u03ae\u03bd\u03b1. \u03a4\u03b1 \u03bd\u03ad\u03b1 \u03b6\u03b5\u03c5\u03b3\u03ac\u03c1\u03b9\u03b1 \u03bc\u03b5\u03b3\u03b1\u03bb\u03ce\u03bd\u03bf\u03c5\u03bd \u03ba\u03b1\u03b9 \u03b1\u03bd\u03b1\u03c0\u03b1\u03c1\u03ac\u03b3\u03bf\u03bd\u03c4\u03b1\u03b9 \u03ba\u03b9 \u03b1\u03c5\u03c4\u03ac \u03bc\u03b5 \u03c4\u03bf\u03bd \u03af\u03b4\u03b9\u03bf \u03c4\u03c1\u03cc\u03c0\u03bf. \u03a0\u03cc\u03c3\u03b1 \u03b6\u03b5\u03c5\u03b3\u03ac\u03c1\u03b9\u03b1 \u03ba\u03bf\u03c5\u03bd\u03ad\u03bb\u03b9\u03b1 \u03b8\u03b1 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 \u03bc\u03b5\u03c4\u03ac \u03b1\u03c0\u03cc 3 \u03bc\u03ae\u03bd\u03b5\u03c2, 4 \u03bc\u03ae\u03bd\u03b5\u03c2, 6 \u03bc\u03ae\u03bd\u03b5\u03c2, \u03bc\u03b5\u03c4\u03ac \u03b1\u03c0\u03cc \u03ad\u03bd\u03b1 \u03c7\u03c1\u03cc\u03bd\u03bf;<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-2069\" src=\"https:\/\/i0.wp.com\/www.ma8imatikos.gr\/wp-content\/uploads\/2019\/11\/fibrab.gif?resize=375%2C315&#038;ssl=1\" alt=\"\" width=\"375\" height=\"315\" data-recalc-dims=\"1\" \/><\/figure>\n<\/div>\n<p><strong>\u0391\u03c0\u03ac\u03bd\u03c4\u03b7\u03c3\u03b7:<\/strong><\/p>\n<p>\u03a3\u03c4\u03b7\u03bd \u03b1\u03c1\u03c7\u03ae \u03c4\u03bf\u03c5 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c5 \u03bc\u03ae\u03bd\u03b1 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 1 \u03b6\u03b5\u03c5\u03b3\u03ac\u03c1\u03b9 \u03ba\u03bf\u03c5\u03bd\u03ad\u03bb\u03b9\u03b1<br \/>\n\u03a3\u03c4\u03b7\u03bd \u03b1\u03c1\u03c7\u03ae \u03c4\u03bf\u03c5 \u03b4\u03b5\u03cd\u03c4\u03b5\u03c1\u03bf\u03c5 \u03bc\u03ae\u03bd\u03b1 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 \u03c0\u03ac\u03bb\u03b9 \u03ad\u03bd\u03b1 \u03b6\u03b5\u03c5\u03b3\u03ac\u03c1\u03b9<br \/>\n\u03a3\u03c4\u03b7\u03bd \u03b1\u03c1\u03c7\u03ae \u03c4\u03bf\u03c5 \u03c4\u03c1\u03af\u03c4\u03bf\u03c5 \u03bc\u03ae\u03bd\u03b1 \u03c4\u03bf \u03b6\u03b5\u03c5\u03b3\u03ac\u03c1\u03b9 \u03b3\u03b5\u03bd\u03bd\u03ac \u03ba\u03b1\u03b9 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 2 \u03b6\u03b5\u03c5\u03b3\u03ac\u03c1\u03b9\u03b1<br \/>\n\u03a3\u03c4\u03b7\u03bd \u03b1\u03c1\u03c7\u03ae \u03c4\u03bf\u03c5 \u03c4\u03ad\u03c4\u03b1\u03c1\u03c4\u03bf\u03c5 \u03bc\u03ae\u03bd\u03b1 \u03c4\u03bf \u03c0\u03c1\u03ce\u03c4\u03bf \u03b6\u03b5\u03c5\u03b3\u03ac\u03c1\u03b9 \u03b3\u03b5\u03bd\u03bd\u03ac \u03c0\u03ac\u03bb\u03b9 , \u03b1\u03bb\u03bb\u03ac \u03c4\u03bf \u03b4\u03b5\u03cd\u03c4\u03b5\u03c1\u03bf \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03c3\u03b5 \u03b8\u03ad\u03c3\u03b7 \u03b1\u03ba\u03cc\u03bc\u03b7, \u00a0\u03b4\u03b7\u03bb\u03b1\u03b4\u03ae 3 \u03b6\u03b5\u03c5\u03b3\u03ac\u03c1\u03b9\u03b1.<br \/>\n\u03a3\u03c4\u03b7\u03bd \u03b1\u03c1\u03c7\u03ae \u03c4\u03bf\u03c5 \u03c0\u03ad\u03bc\u03c0\u03c4\u03bf\u03c5 \u03bc\u03ae\u03bd\u03b1 \u03b3\u03b5\u03bd\u03bd\u03ac \u03c0\u03ac\u03bb\u03b9 \u03c4\u03bf \u03b1\u03c1\u03c7\u03b9\u03ba\u03cc \u03b6\u03b5\u03c5\u03b3\u03ac\u03c1\u03b9 , \u03b3\u03b5\u03bd\u03bd\u03ac \u03ba\u03b1\u03b9 \u03c4\u03bf \u03b4\u03b5\u03cd\u03c4\u03b5\u03c1\u03bf , \u03b4\u03b5 \u03b3\u03b5\u03bd\u03bd\u03ac \u03c4\u03bf \u03c4\u03c1\u03af\u03c4\u03bf. \u03a3\u03cd\u03bd\u03bf\u03bb\u03bf 5 \u03b6\u03b5\u03c5\u03b3\u03ac\u03c1\u03b9\u03b1<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-2071\" src=\"https:\/\/i0.wp.com\/www.ma8imatikos.gr\/wp-content\/uploads\/2019\/11\/rabbits.png?resize=519%2C245&#038;ssl=1\" sizes=\"(max-width: 519px) 100vw, 519px\" srcset=\"https:\/\/i0.wp.com\/www.ma8imatikos.gr\/wp-content\/uploads\/2019\/11\/rabbits.png?resize=519%2C245&#038;ssl=1 576w, https:\/\/www.ma8imatikos.gr\/wp-content\/uploads\/2019\/11\/rabbits-300x142.png 300w\" alt=\"\" width=\"519\" height=\"245\" data-recalc-dims=\"1\" \/><\/figure>\n<\/div>\n<p>\u0388\u03c4\u03c3\u03b9, \u03c4\u03bf \u03c0\u03bb\u03ae\u03b8\u03bf\u03c2 \u03c4\u03c9\u03bd \u03b6\u03b5\u03c5\u03b3\u03b1\u03c1\u03b9\u03ce\u03bd \u03c4\u03c9\u03bd \u03ba\u03bf\u03c5\u03bd\u03b5\u03bb\u03b9\u03ce\u03bd \u03c3\u03c4\u03b7\u03bd \u03b1\u03c1\u03c7\u03ae \u03ba\u03ac\u03b8\u03b5 \u03bc\u03ae\u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 1, 1, 2, 3, 5, 8, 13, 21, 34, .. \u03a0\u03b1\u03c1\u03b1\u03c4\u03b7\u03c1\u03ae\u03c3\u03c4\u03b5 \u03cc\u03c4\u03b9 \u03ba\u03ac\u03b8\u03b5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03c3\u03c4\u03b7\u03bd \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03ac\u03b8\u03c1\u03bf\u03b9\u03c3\u03bc\u03b1 \u03c4\u03c9\u03bd \u03b4\u03cd\u03bf \u03c0\u03c1\u03bf\u03b7\u03b3\u03bf\u03cd\u03bc\u03b5\u03bd\u03c9\u03bd. \u0391\u03c5\u03c4\u03cc \u03b5\u03af\u03bd\u03b1\u03b9 \u03bb\u03bf\u03b3\u03b9\u03ba\u03cc \u03bd\u03b1 \u03c3\u03c5\u03bc\u03b2\u03b1\u03af\u03bd\u03b5\u03b9 \u03bc\u03b9\u03b1 \u03ba\u03b1\u03b9 \u03c3\u03c4\u03b7\u03bd \u03b1\u03c1\u03c7\u03ae \u03ba\u03ac\u03b8\u03b5 \u03bc\u03ae\u03bd\u03b1 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b1 \u03b6\u03b5\u03c5\u03b3\u03ac\u03c1\u03b9\u03b1 \u03c0\u03bf\u03c5 \u03b5\u03af\u03c7\u03b1\u03bc\u03b5 \u03c4\u03bf\u03bd \u03c0\u03c1\u03bf\u03b7\u03b3\u03bf\u03cd\u03bc\u03b5\u03bd\u03bf \u03bc\u03ae\u03bd\u03b1 \u03ba\u03b1\u03b9 \u03b5\u03c0\u03b9\u03c0\u03bb\u03ad\u03bf\u03bd \u03c4\u03cc\u03c3\u03b1 \u03bd\u03b5\u03bf\u03b3\u03ad\u03bd\u03bd\u03b7\u03c4\u03b1 \u03b6\u03b5\u03c5\u03b3\u03ac\u03c1\u03b9\u03b1 \u03cc\u03c3\u03b1 \u03ba\u03b1\u03b9 \u03b5\u03bd\u03ae\u03bb\u03b9\u03ba\u03b1 \u03b6\u03b5\u03c5\u03b3\u03ac\u03c1\u03b9\u03b1 \u03b3\u03bf\u03bd\u03ad\u03c9\u03bd \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5.<\/p>\n<p>\u0386\u03c1\u03b1 \u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af Fibonacci \u03b5\u03af\u03bd\u03b1\u03b9: 1,1,2,3,5,8,13,21,34,55,89,\u2026.. \u00a0\u03bc\u03b5 \u03c4\u03bf\u03bd \u03ba\u03ac\u03b8\u03b5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03bd\u03b1 \u03c0\u03c1\u03bf\u03ba\u03cd\u03c0\u03c4\u03b5\u03b9 \u03b1\u03c0\u03cc \u03c4\u03bf \u03ac\u03b8\u03c1\u03bf\u03b9\u03c3\u03bc\u03b1 \u03c4\u03c9\u03bd \u03b4\u03cd\u03bf \u03c0\u03c1\u03bf\u03b7\u03b3\u03bf\u03cd\u03bc\u03b5\u03bd\u03c9\u03bd \u03c4\u03bf\u03c5.<\/p>\n<p>1+1=2 , 1+2=3 , 3+5=8 , 5+8=13 ,\u2026..<\/p>\n<p><strong>\u039f\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af Fibonacci \u03ba\u03b1\u03b9 \u03bf \u03c7\u03c1\u03c5\u03c3\u03cc\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03c6<\/strong><\/p>\n<p>\u0397 \u03b4\u03b5\u03cd\u03c4\u03b5\u03c1\u03b7 \u03ba\u03b1\u03b9 \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03cc\u03c4\u03b5\u03c1\u03b7 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c4\u03c9\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd \u03b1\u03c5\u03c4\u03ce\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03b5\u03be\u03ae\u03c2: \u0391\u03bd \u03b4\u03b9\u03b1\u03b9\u03c1\u03ad\u03c3\u03bf\u03c5\u03bc\u03b5 \u03ba\u03ac\u03b8\u03b5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03bc\u03b5 \u03c4\u03bf\u03bd \u03b5\u03c0\u03cc\u03bc\u03b5\u03bd\u03cc \u03c4\u03bf\u03c5 , \u03c4\u03cc\u03c4\u03b5 \u03bf\u03b9 \u03bb\u03cc\u03b3\u03bf\u03b9 \u03c0\u03bf\u03c5 \u03b8\u03b1 \u03b2\u03c1\u03bf\u03cd\u03bc\u03b5 \u03c4\u03b5\u03af\u03bd\u03bf\u03c5\u03bd \u03bd\u03b1 \u03c0\u03c1\u03bf\u03c3\u03b5\u03b3\u03b3\u03af\u03c3\u03bf\u03c5\u03bd \u03c4\u03bf\u03bd \u03ac\u03c1\u03c1\u03b7\u03c4\u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc 0,618\u2026 , \u03c4\u03bf \u03b3\u03bd\u03c9\u03c3\u03c4\u03cc \u03c7\u03c1\u03c5\u03c3\u03cc \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03c0\u03bf\u03c5 \u03b4\u03b9\u03b5\u03b8\u03bd\u03ce\u03c2 \u03c3\u03c5\u03bc\u03b2\u03bf\u03bb\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03c4\u03bf \u03b5\u03bb\u03bb\u03b7\u03bd\u03b9\u03ba\u03cc \u03b3\u03c1\u03ac\u03bc\u03bc\u03b1 \u03c6.<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-2052\" src=\"https:\/\/i0.wp.com\/www.ma8imatikos.gr\/wp-content\/uploads\/2019\/11\/23-11-1024x512.png?resize=510%2C255&#038;ssl=1\" sizes=\"(max-width: 510px) 100vw, 510px\" srcset=\"https:\/\/www.ma8imatikos.gr\/wp-content\/uploads\/2019\/11\/23-11.png 1024w, https:\/\/www.ma8imatikos.gr\/wp-content\/uploads\/2019\/11\/23-11-300x150.png 300w, https:\/\/www.ma8imatikos.gr\/wp-content\/uploads\/2019\/11\/23-11-768x384.png 768w\" alt=\"\" width=\"510\" height=\"255\" data-recalc-dims=\"1\" \/><\/figure>\n<\/div>\n<p><strong>\u0394\u03b5\u03af\u03c4\u03b5 \u03bc\u03b5\u03c1\u03b9\u03ba\u03ac \u03c0\u03b1\u03c1\u03b1\u03b4\u03b5\u03af\u03b3\u03bc\u03b1\u03c4\u03b1:<\/strong><\/p>\n<p>8:13=0,615..<br \/>\n13:21=0,619.<br \/>\n21:34=0,6176..<br \/>\n34:55=0,61818.. \u03ba\u03b1\u03b9 \u03cc\u03c3\u03bf \u03c3\u03c5\u03bd\u03b5\u03c7\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03c4\u03cc\u03c3\u03bf \u03c0\u03b9\u03bf \u03ba\u03bf\u03bd\u03c4\u03ac \u03c3\u03c4\u03bf\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03c6 \u03b2\u03c1\u03b9\u03c3\u03ba\u03cc\u03bc\u03b1\u03c3\u03c4\u03b5.<\/p>\n<p>\u039f \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03c6 \u03b4\u03b5\u03bd \u03ae\u03c4\u03b1\u03bd \u03ac\u03b3\u03bd\u03c9\u03c3\u03c4\u03bf\u03c2 \u03c3\u03c4\u03bf\u03c5\u03c2 \u03b1\u03c1\u03c7\u03b1\u03af\u03bf\u03c5\u03c2 \u0388\u03bb\u03bb\u03b7\u03bd\u03b5\u03c2. \u039f \u03a0\u03c5\u03b8\u03b1\u03b3\u03cc\u03c1\u03b1\u03c2 \u03ae\u03c4\u03b1\u03bd \u03b1\u03c0\u03cc \u03c4\u03bf\u03c5\u03c2 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c5\u03c2 \u03c0\u03bf\u03c5 \u03c0\u03b1\u03c1\u03b1\u03c4\u03ae\u03c1\u03b7\u03c3\u03b5 \u03cc\u03c4\u03b9 \u03c4\u03b1 \u03c6\u03c5\u03c4\u03ac \u03ba\u03b1\u03b9 \u03c4\u03b1 \u03b6\u03ce\u03b1 \u03b4\u03b5\u03bd \u03bc\u03b5\u03b3\u03b1\u03bb\u03ce\u03bd\u03bf\u03c5\u03bd \u03c4\u03c5\u03c7\u03b1\u03af\u03b1 , \u03b1\u03bb\u03bb\u03ac \u03bc\u03b5 \u03b1\u03ba\u03c1\u03b9\u03b2\u03b5\u03af\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03ba\u03b1\u03bd\u03cc\u03bd\u03b5\u03c2.<\/p>\n<p>\u03a4\u03b1 \u03c3\u03c7\u03ad\u03b4\u03b9\u03b1 \u03c4\u03c9\u03bd \u03bb\u03bf\u03c5\u03bb\u03bf\u03c5\u03b4\u03b9\u03ce\u03bd , \u03b7 \u03b1\u03bd\u03ac\u03c0\u03c4\u03c5\u03be\u03b7 \u03c4\u03c9\u03bd \u03c6\u03cd\u03bb\u03bb\u03c9\u03bd \u03b3\u03cd\u03c1\u03c9 \u03b1\u03c0\u03cc \u03c4\u03bf \u03bc\u03af\u03c3\u03c7\u03bf , \u03b7 \u03b1\u03bd\u03ac\u03c0\u03c4\u03c5\u03be\u03b7 \u03c4\u03c9\u03bd \u03b2\u03b5\u03bb\u03cc\u03bd\u03c9\u03bd \u03c3\u03c4\u03b1 \u03ad\u03bb\u03b1\u03c4\u03b1 \u03ba.\u03b1. \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03bf\u03cd\u03bd \u03c4\u03b9\u03c2 \u03c0\u03c1\u03bf\u03b7\u03b3\u03bf\u03cd\u03bc\u03b5\u03bd\u03b5\u03c2 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b5\u03c2. \u03a7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03ae\u03b8\u03b7\u03ba\u03b5 \u03c3\u03c4\u03b7\u03bd \u03b1\u03c1\u03c7\u03b9\u03c4\u03b5\u03ba\u03c4\u03bf\u03bd\u03b9\u03ba\u03ae (\u03a0\u03b1\u03c1\u03b8\u03b5\u03bd\u03ce\u03bd\u03b1\u03c2) , \u03c3\u03c4\u03b7 \u03b6\u03c9\u03b3\u03c1\u03b1\u03c6\u03b9\u03ba\u03ae (\u039c\u03cc\u03bd\u03b1 \u039b\u03af\u03b6\u03b1) \u03bc\u03b5 \u03c4\u03b1 \u03b3\u03bd\u03c9\u03c3\u03c4\u03ac \u03c4\u03ad\u03bb\u03b5\u03b9\u03b1 \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03ad\u03c3\u03bc\u03b1\u03c4\u03b1. \u03a4\u03bf\u03c5\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2 Fibonacci \u03c4\u03bf\u03c5\u03c2 \u03c3\u03c5\u03bd\u03b1\u03bd\u03c4\u03ac\u03bc\u03b5 \u03b5\u03c0\u03af\u03c3\u03b7\u03c2 \u03c3\u03c4\u03bf \u03b1\u03bd\u03b8\u03c1\u03ce\u03c0\u03b9\u03bd\u03bf \u03c7\u03ad\u03c1\u03b9 (\u03ba\u03ac\u03b8\u03b5 \u03ac\u03bd\u03b8\u03c1\u03c9\u03c0\u03bf\u03c2 \u03ad\u03c7\u03b5\u03b9 2 \u03c7\u03ad\u03c1\u03b9\u03b1, \u03ba\u03ac\u03b8\u03b5 \u03ad\u03bd\u03b1 \u03b1\u03c0\u03cc \u03c4\u03b1 \u03bf\u03c0\u03bf\u03af\u03b1 \u03ad\u03c7\u03b5\u03b9 5 \u03b4\u03ac\u03c7\u03c4\u03c5\u03bb\u03b1, \u03ba\u03ac\u03b8\u03b5 \u03b4\u03ac\u03ba\u03c4\u03c5\u03bb\u03bf \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03b5\u03af\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc 3 \u03c4\u03bc\u03ae\u03bc\u03b1\u03c4\u03b1 \u03c0\u03bf\u03c5 \u03c7\u03c9\u03c1\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc 2 \u03b1\u03c1\u03b8\u03c1\u03ce\u03c3\u03b5\u03b9\u03c2) , \u03c3\u03c4\u03bf \u03b1\u03bd\u03b8\u03c1\u03ce\u03c0\u03b9\u03bd\u03bf \u03c0\u03c1\u03cc\u03c3\u03c9\u03c0\u03bf , \u03c3\u03c4\u03b7 \u03b4\u03bf\u03bc\u03ae \u03c4\u03bf\u03c5 D.N.A. \u03ba\u03b1\u03b9 \u03af\u03c3\u03c9\u03c2 \u03c3\u03c7\u03b5\u03b4\u03cc\u03bd \u03c0\u03b1\u03bd\u03c4\u03bf\u03cd \u03c3\u03c4\u03b7 \u03c6\u03cd\u03c3\u03b7).<\/p>\n<figure class=\"wp-block-gallery aligncenter columns-3 is-cropped wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex\">\n<ul class=\"blocks-gallery-grid\">\n<li class=\"blocks-gallery-item\">\n<figure><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-2055\" src=\"https:\/\/i0.wp.com\/www.ma8imatikos.gr\/wp-content\/uploads\/2019\/11\/images-8.jpg?resize=259%2C194&#038;ssl=1\" alt=\"\" width=\"259\" height=\"194\" data-id=\"2055\" data-recalc-dims=\"1\" \/><\/figure>\n<\/li>\n<li class=\"blocks-gallery-item\">\n<figure><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-2056\" src=\"https:\/\/i0.wp.com\/www.ma8imatikos.gr\/wp-content\/uploads\/2019\/11\/images-9.jpg?resize=189%2C267&#038;ssl=1\" alt=\"\" width=\"189\" height=\"267\" data-id=\"2056\" data-link=\"https:\/\/www.ma8imatikos.gr\/?attachment_id=2056\" data-recalc-dims=\"1\" \/><\/figure>\n<\/li>\n<li class=\"blocks-gallery-item\">\n<figure><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-2057\" src=\"https:\/\/i0.wp.com\/www.ma8imatikos.gr\/wp-content\/uploads\/2019\/11\/b31b0737663ba086865b42a87c6c26ff-221x300.png?resize=221%2C300&#038;ssl=1\" alt=\"\" width=\"221\" height=\"300\" data-id=\"2057\" data-link=\"https:\/\/www.ma8imatikos.gr\/?attachment_id=2057\" data-recalc-dims=\"1\" \/><\/figure>\n<\/li>\n<\/ul>\n<\/figure>\n<p>\u0394\u03b5\u03af\u03c4\u03b5 \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03b1 \u03b5\u03b4\u03ce:\u00a0<a href=\"https:\/\/www.ma8imatikos.gr\/%ce%bf-%cf%87%cf%81%cf%85%cf%83%cf%8c%cf%82-%ce%b1%cf%81%ce%b9%ce%b8%ce%bc%cf%8c%cf%82-%cf%86-%cf%80%cf%89%cf%82-%ce%b7-%ce%b1%cf%81%ce%bc%ce%bf%ce%bd%ce%af%ce%b1-%cf%84%ce%ad%cf%87%ce%bd\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"https:\/\/www.ma8imatikos.gr\/%ce%bf-%cf%87%cf%81%cf%85%cf%83%cf%8c%cf%82-%ce%b1%cf%81%ce%b9%ce%b8%ce%bc%cf%8c%cf%82-%cf%86-%cf%80%cf%89%cf%82-%ce%b7-%ce%b1%cf%81%ce%bc%ce%bf%ce%bd%ce%af%ce%b1-%cf%84%ce%ad%cf%87%ce%bd\/ (\u03b1\u03bd\u03bf\u03af\u03b3\u03b5\u03b9 \u03c3\u03b5 \u03bd\u03ad\u03b1 \u03ba\u03b1\u03c1\u03c4\u03ad\u03bb\u03b1)\">\/<\/a><a href=\"https:\/\/www.ma8imatikos.gr\/%ce%bf-%cf%87%cf%81%cf%85%cf%83%cf%8c%cf%82-%ce%b1%cf%81%ce%b9%ce%b8%ce%bc%cf%8c%cf%82-%cf%86-%cf%80%cf%89%cf%82-%ce%b7-%ce%b1%cf%81%ce%bc%ce%bf%ce%bd%ce%af%ce%b1-%cf%84%ce%ad%cf%87%ce%bd\/\">\u039f \u00ab\u03c7\u03c1\u03c5\u03c3\u03cc\u03c2\u00bb \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03a6: \u03a0\u03c9\u03c2 \u03b7 \u03b1\u03c1\u03bc\u03bf\u03bd\u03af\u03b1 \u03c4\u03ad\u03c7\u03bd\u03b7\u03c2 \u03ba\u03b1\u03b9 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd \u03c3\u03c5\u03bd\u03b4\u03ad\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03ad\u03bd\u03b1 \u03b1\u03c0\u03bb\u03cc \u03ba\u03bb\u03ac\u03c3\u03bc\u03b1<\/a><\/p>\n<p>H 23\/11 \u03ad\u03c7\u03b5\u03b9 \u03ba\u03b1\u03b8\u03b9\u03b5\u03c1\u03c9\u03b8\u03b5\u03af \u03c9\u03c2 \u03b7\u03bc\u03ad\u03c1\u03b1 \u03c4\u03c9\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd Fibonacci, \u03bf\u03c0\u03cc\u03c4\u03b5 Happy Fibonacci Day!<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-2053\" src=\"https:\/\/i0.wp.com\/www.ma8imatikos.gr\/wp-content\/uploads\/2019\/11\/75392640_2261439803962342_3535532145088921600_n.jpg?resize=270%2C422&#038;ssl=1\" sizes=\"(max-width: 270px) 100vw, 270px\" srcset=\"https:\/\/i0.wp.com\/www.ma8imatikos.gr\/wp-content\/uploads\/2019\/11\/75392640_2261439803962342_3535532145088921600_n.jpg?resize=270%2C422&#038;ssl=1 365w, https:\/\/www.ma8imatikos.gr\/wp-content\/uploads\/2019\/11\/75392640_2261439803962342_3535532145088921600_n-192x300.jpg 192w\" alt=\"\" width=\"270\" height=\"422\" data-recalc-dims=\"1\" \/><\/figure>\n<p>&nbsp;<\/p>\n<\/div>\n<p>\u03a0\u03b7\u03b3\u03ae:\u00a0<a href=\"https:\/\/www.alfavita.gr\/kosmos\/304950_23-noembrioy-i-imera-ton-arithmon-fibonacci\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (\u03b1\u03bd\u03bf\u03af\u03b3\u03b5\u03b9 \u03c3\u03b5 \u03bd\u03ad\u03b1 \u03ba\u03b1\u03c1\u03c4\u03ad\u03bb\u03b1)\">https:\/\/www.alfavita.gr\/kosmos\/304950_23-noembrioy-i-imera-ton-arithmon-fibonacci<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":57538,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false,"jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[33],"tags":[],"jetpack_publicize_connections":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.5 - 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