{"id":23097,"date":"2020-02-27T13:20:00","date_gmt":"2020-02-27T11:20:00","guid":{"rendered":"http:\/\/omathimatikos.gr\/?p=23097"},"modified":"2020-02-27T13:24:02","modified_gmt":"2020-02-27T11:24:02","slug":"%ce%ac%cf%81%ce%b8%ce%bf%cf%85%cf%81-%ce%bc%cf%80%ce%ad%ce%bd%cf%84%ce%b6%ce%b1%ce%bc%ce%b9%ce%bd-%ce%b7-%ce%bc%ce%b1%ce%b3%ce%b5%ce%af%ce%b1-%cf%84%ce%b7%cf%82-%ce%b1%ce%ba%ce%bf%ce%bb%ce%bf%cf%85","status":"publish","type":"post","link":"https:\/\/omathimatikos.gr\/?p=23097","title":{"rendered":"\u0386\u03c1\u03b8\u03bf\u03c5\u03c1 \u039c\u03c0\u03ad\u03bd\u03c4\u03b6\u03b1\u03bc\u03b9\u03bd: \u0397 \u03bc\u03b1\u03b3\u03b5\u03af\u03b1 \u03c4\u03b7\u03c2 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1\u03c2 \u03a6\u03b9\u03bc\u03c0\u03bf\u03bd\u03ac\u03c4\u03c3\u03b9 (\u03b2\u03af\u03bd\u03c4\u03b5\u03bf)"},"content":{"rendered":"<p><!--more--><\/p>\n<blockquote>\n<h3><b>\u039f\u03b9 \u03c5\u03c0\u03ad\u03c1\u03bf\u03c7\u03bf\u03b9 \u03ba\u03b1\u03b9 \u03bc\u03c5\u03c3\u03c4\u03ae\u03c1\u03b9\u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af Fibonacci<\/b><\/h3>\n<\/blockquote>\n<div>\u0397 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1 \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd \u03c3\u03c4\u03b7\u03bd \u03bf\u03c0\u03bf\u03af\u03b1 \u03bf \u03ba\u03ac\u03b8\u03b5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03af\u03c3\u03bf\u03c2 \u03bc\u03b5 \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 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b3\u03bd\u03c9\u03c3\u03c4\u03ae \u03ce\u03c2&nbsp;<b>\u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1&nbsp;<\/b><b>Fibonacci<\/b>: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181,&#8230; (\u03ba\u03ac\u03b8\u03b5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03af\u03c3\u03bf\u03c2 \u03bc\u03b5 \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).<\/div>\n<div>\u0395\u03c0\u03b9\u03c0\u03bb\u03ad\u03bf\u03bd, \u03bf \u03bb\u03cc\u03b3\u03bf\u03c2 \u03b4\u03cd\u03bf \u03b4\u03b9\u03b1\u03b4\u03bf\u03c7\u03b9\u03ba\u03ce\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd \u03c4\u03b7\u03c2 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1\u03c2 \u03c4\u03b5\u03af\u03bd\u03b5\u03b9 \u03c0\u03c1\u03bf\u03c2 \u03c4\u03b7\u03bd \u03b1\u03c0\u03bf\u03ba\u03b1\u03bb\u03bf\u03cd\u03bc\u03b5\u03bd\u03b7&nbsp;<b>\u03a7\u03c1\u03c5\u03c3\u03ae \u03a4\u03bf\u03bc\u03ae,&nbsp;<\/b>\u03ae<b>&nbsp;\u03a7\u03c1\u03c5\u03c3\u03ae \u03b1\u03bd\u03b1\u03bb\u03bf\u03b3\u03af\u03b1,&nbsp;<\/b>\u03ae&nbsp;<b>\u0391\u03c1\u03b9\u03b8\u03bc\u03cc<\/b>&nbsp;<b>\u03c6 =<\/b>1.618033989.<br \/>\n\u039f \u03b1\u03bd\u03c4\u03af\u03c3\u03c4\u03c1\u03bf\u03c6\u03bf\u03c2 \u03c4\u03b7\u03c2 \u03a7\u03c1\u03c5\u03c3\u03ae\u03c2 \u03a4\u03bf\u03bc\u03ae\u03c2 1\/\u03c6= 0.618033989, \u03bc\u03b5 \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03bd\u03b1 \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9: 1\/\u03c6=\u03c6-1.<\/p>\n<div><sup><i><b>\u039f \u03bc\u03b1\u03b8\u03b7\u03bc\u03ac\u03b3\u03bf\u03c2 \u0386\u03c1\u03b8\u03bf\u03c5\u03c1 \u039c\u03c0\u03ad\u03bd\u03c4\u03b6\u03b1\u03bc\u03b9\u03bd \u03bc\u03b9\u03bb\u03ac\u03b5\u03b9 \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1 \u03a6\u03b9\u03bc\u03c0\u03bf\u03bd\u03ac\u03c4\u03c3\u03b9&nbsp;<\/b><\/i><\/sup><\/div>\n<div><\/div>\n<div class=\"separator\"><\/div>\n<p><iframe loading=\"lazy\" class=\"YOUTUBE-iframe-video\" src=\"https:\/\/www.youtube.com\/embed\/SjSHVDfXHQ4?feature=player_embedded\" width=\"280\" height=\"210\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\" data-thumbnail-src=\"https:\/\/i.ytimg.com\/vi\/SjSHVDfXHQ4\/0.jpg\" data-mce-fragment=\"1\"><\/iframe><\/p>\n<div><\/div>\n<p>\u0388\u03bd\u03b1 \u03bf\u03c1\u03b8\u03bf\u03b3\u03ce\u03bd\u03b9\u03bf \u03c4\u03b5\u03c4\u03c1\u03ac\u03c0\u03bb\u03b5\u03c5\u03c1\u03bf \u03c4\u03bf\u03c5 \u03bf\u03c0\u03bf\u03af\u03bf\u03c5 \u03bf \u03bb\u03cc\u03b3\u03bf\u03c2 \u03c4\u03c9\u03bd \u03c0\u03bb\u03b5\u03c5\u03c1\u03ce\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03af\u03c3\u03bf\u03c2 \u03bc\u03b5 1\/\u03c6 \u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9&nbsp;<b>\u03a7\u03c1\u03c5\u03c3\u03cc \u039f\u03c1\u03b8\u03bf\u03b3\u03ce\u03bd\u03b9\u03bf<\/b>.<br \/>\n\u0397 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1 Fibonacci \u03c0\u03b1\u03c1\u03ac\u03b3\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03b7 \u03c3\u03c7\u03ad\u03c3\u03b7 f(1) = f(2) = 1 , f(n+1) = f(n) + f(n-1), \u03ba\u03b1\u03b9 \u03b1\u03c0\u03b1\u03bd\u03c4\u03ac\u03c4\u03b1\u03b9 \u03c3\u03c5\u03c7\u03bd\u03ac \u03c3\u03b5 \u03c0\u03bf\u03bb\u03bb\u03bf\u03cd\u03c2 \u03c4\u03bf\u03bc\u03b5\u03af\u03c2 \u03c4\u03c9\u03bd \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd \u03ba\u03b1\u03b9 \u03c4\u03c9\u03bd \u03ac\u03bb\u03bb\u03c9\u03bd \u03b5\u03c0\u03b9\u03c3\u03c4\u03b7\u03bc\u03ce\u03bd. \u0395\u03af\u03bd\u03b1\u03b9 \u03cc\u03bc\u03c9\u03c2 \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03cc \u03ba\u03b1\u03b9 \u03c4\u03bf \u03c0\u03cc\u03c3\u03bf \u03c3\u03c5\u03c7\u03bd\u03ac \u03c3\u03c5\u03bd\u03b1\u03bd\u03c4\u03ac\u03c4\u03b1\u03b9 \u03c3\u03c4\u03b7 \u03c6\u03cd\u03c3\u03b7, \u03c3\u03b5 \u03bc\u03bf\u03c4\u03af\u03b2\u03b1 \u03cc\u03c0\u03c9\u03c2 \u03c4\u03b1 \u03bb\u03bf\u03c5\u03bb\u03bf\u03cd\u03b4\u03b9\u03b1 \u03ae \u03c4\u03b1 \u03c6\u03cd\u03bb\u03bb\u03b1 \u03c4\u03c9\u03bd \u03c6\u03c5\u03c4\u03ce\u03bd.<br \/>\n<a name=\"more\"><\/a><\/p>\n<blockquote><p><sup><i>\u039f\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af Fibonacci \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03b9\u03ba\u03cc \u03c3\u03cd\u03c3\u03c4\u03b7\u03bc\u03b1 \u03c4\u03b7\u03c2 \u03c6\u03cd\u03c3\u03b7\u03c2. \u0395\u03bc\u03c6\u03b1\u03bd\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c0\u03b1\u03bd\u03c4\u03bf\u03cd \u03c3\u03c4\u03b7 \u03c6\u03cd\u03c3\u03b7, \u03b1\u03c0\u03cc \u03c4\u03b7 \u03b4\u03b9\u03ac\u03c4\u03b1\u03be\u03b7 \u03c4\u03c9\u03bd \u03c6\u03cd\u03bb\u03bb\u03c9\u03bd \u03c3\u03c4\u03b1 \u03c6\u03c5\u03c4\u03ac \u03bc\u03ad\u03c7\u03c1\u03b9 \u03c4\u03bf \u03bc\u03bf\u03c4\u03af\u03b2\u03bf \u03c4\u03c9\u03bd \u03c0\u03b5\u03c4\u03ac\u03bb\u03c9\u03bd \u03c3\u03c4\u03b1 \u03bb\u03bf\u03c5\u03bb\u03bf\u03cd\u03b4\u03b9\u03b1, \u03c4\u03b9\u03c2 \u03c0\u03b5\u03c5\u03ba\u03bf\u03b2\u03b5\u03bb\u03cc\u03bd\u03b5\u03c2, \u03ae \u03c4\u03b1 \u03c3\u03c4\u03c1\u03ce\u03bc\u03b1\u03c4\u03b1 \u03c4\u03bf\u03c5 \u03c6\u03bb\u03bf\u03b9\u03bf\u03cd \u03b5\u03bd\u03cc\u03c2 \u03b1\u03bd\u03b1\u03bd\u03ac. \u03a6\u03b1\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c0\u03ce\u03c2 \u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af Fibonacci \u03c3\u03c7\u03b5\u03c4\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03b1\u03bd\u03ac\u03c0\u03c4\u03c5\u03be\u03b7 \u03ba\u03ac\u03b8\u03b5 \u03b6\u03c9\u03bd\u03c4\u03b1\u03bd\u03bf\u03cd \u03bf\u03c1\u03b3\u03b1\u03bd\u03b9\u03c3\u03bc\u03bf\u03cd, \u03b5\u03bd\u03cc\u03c2 \u03ba\u03c5\u03c4\u03c4\u03ac\u03c1\u03bf\u03c5, \u03b5\u03bd\u03cc\u03c2 \u03c3\u03c0\u03c5\u03c1\u03b9\u03bf\u03cd \u03c3\u03c4\u03b1\u03c1\u03b9\u03bf\u03cd, \u03bc\u03b9\u03b1\u03c2 \u03ba\u03c5\u03c8\u03ad\u03bb\u03b7\u03c2 \u03bc\u03b5\u03bb\u03b9\u03c3\u03c3\u03ce\u03bd, \u03b1\u03ba\u03cc\u03bc\u03b1 \u03c4\u03b7\u03c2 \u03af\u03b4\u03b9\u03b1\u03c2 \u03c4\u03b7\u03c2 \u03b1\u03bd\u03b8\u03c1\u03c9\u03c0\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2.&nbsp;<b>Stan Grist<\/b><\/i><\/sup><\/p><\/blockquote>\n<div>\n<div><b>\u0399\u03c3\u03c4\u03bf\u03c1\u03af\u03b1<\/b><br \/>\n\u039f Fibonacci \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 \u03ce\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 \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. \u0386\u03b3\u03b1\u03bb\u03bc\u03ac \u03c4\u03bf\u03c5 \u03c5\u03c0\u03ac\u03c1\u03c7\u03b5\u03b9 \u03c3\u03c4\u03bf \u03bd\u03b5\u03ba\u03c1\u03bf\u03c4\u03b1\u03c6\u03b5\u03af\u03bf, \u03b4\u03af\u03c0\u03bb\u03b1 \u03c3\u03c4\u03bf\u03bd \u039a\u03b1\u03b8\u03b5\u03b4\u03c1\u03b9\u03ba\u03cc \u039d\u03b1\u03cc \u03c4\u03b7\u03c2 Pisa, \u03ba\u03bf\u03bd\u03c4\u03ac \u03c3\u03c4\u03bf\u03bd \u03c0\u03b5\u03c1\u03af\u03c6\u03b7\u03bc\u03bf \u03c0\u03cd\u03c1\u03b3\u03bf. \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 Pisa \u03ba\u03b1\u03b9 \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 (\u03b3\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. \u039f \u03c0\u03b1\u03c4\u03ad\u03c1\u03b1\u03c2 \u03c4\u03bf\u03c5 Leonardo, Guglielmo Bonacci, \u03ae\u03c4\u03b1\u03bd \u03c4\u03b5\u03bb\u03c9\u03bd\u03b5\u03b9\u03b1\u03ba\u03cc\u03c2 \u03c5\u03c0\u03ac\u03bb\u03bb\u03b7\u03bb\u03bf\u03c2 \u03c3\u03c4\u03b7 \u0392\u03bf\u03c1\u03b5\u03b9\u03bf\u03b1\u03c6\u03c1\u03b9\u03ba\u03b1\u03bd\u03b9\u03ba\u03ae \u03c0\u03cc\u03bb\u03b7 Bugia. \u039f Fibonacci \u03bc\u03b5\u03b3\u03ac\u03bb\u03c9\u03c3\u03b5 \u03b5\u03ba\u03b5\u03af \u03ba\u03b1\u03b9 \u03b7 \u03b5\u03ba\u03c0\u03b1\u03af\u03b4\u03b5\u03c5\u03c3\u03ae \u03c4\u03bf\u03c5 \u03b5\u03c0\u03b7\u03c1\u03b5\u03ac\u03c3\u03c4\u03b7\u03ba\u03b5 \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03ac \u03b1\u03c0\u03cc \u03c4\u03bf\u03c5\u03c2 \u039c\u03b1\u03c5\u03c1\u03b9\u03c4\u03b1\u03bd\u03bf\u03cd\u03c2 \u03b1\u03bb\u03bb\u03ac \u03ba\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03b1 \u03c4\u03b1\u03be\u03af\u03b4\u03b9\u03b1 \u03c0\u03bf\u03c5 \u03ad\u03ba\u03b1\u03bd\u03b5 \u03b1\u03c1\u03b3\u03cc\u03c4\u03b5\u03c1\u03b1 \u03c3\u03b5 \u03cc\u03bb\u03bf \u03c4\u03bf \u03bc\u03ae\u03ba\u03bf\u03c2 \u03c4\u03b7\u03c2 \u039c\u03b5\u03c3\u03bf\u03b3\u03b5\u03b9\u03b1\u03ba\u03ae\u03c2 \u03b1\u03ba\u03c4\u03ae\u03c2. \u0388\u03c4\u03c3\u03b9 \u03b3\u03bd\u03ce\u03c1\u03b9\u03c3\u03b5 \u03c0\u03bf\u03bb\u03bb\u03bf\u03cd\u03c2 \u03b5\u03bc\u03c0\u03cc\u03c1\u03bf\u03c5\u03c2 \u03ba\u03b1\u03b9 \u03ad\u03bc\u03b1\u03b8\u03b5 \u03c4\u03b1 \u03b1\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03b9\u03ba\u03ac \u03c3\u03c5\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1 \u03c0\u03bf\u03c5 \u03b1\u03c5\u03c4\u03bf\u03af \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03bf\u03cd\u03c3\u03b1\u03bd \u03b3\u03b9\u03b1 \u03c4\u03b9\u03c2 \u03c3\u03c5\u03bd\u03b1\u03bb\u03bb\u03b1\u03b3\u03ad\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03bf\u03c5\u03c2 \u03bb\u03bf\u03b3\u03b1\u03c1\u03b9\u03b1\u03c3\u03bc\u03bf\u03cd\u03c2 \u03c4\u03bf\u03c5\u03c2. \u03a3\u03cd\u03bd\u03c4\u03bf\u03bc\u03b1 \u03b4\u03b9\u03b1\u03c0\u03af\u03c3\u03c4\u03c9\u03c3\u03b5 \u03c4\u03b1 \u03c0\u03bb\u03b5\u03bf\u03bd\u03b5\u03ba\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1 \u03c4\u03bf\u03c5 \u00ab\u0399\u03bd\u03b4\u03bf\u03b1\u03c1\u03b1\u03b2\u03b9\u03ba\u03bf\u03cd\u00bb \u03b1\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03b9\u03ba\u03bf\u03cd \u03c3\u03c5\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u03ba\u03b1\u03b9 \u03ad\u03b3\u03b9\u03bd\u03b5 \u03b1\u03c0\u03cc \u03c4\u03bf\u03c5\u03c2 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c5\u03c2 \u03c0\u03bf\u03c5 \u03c4\u03bf \u03b5\u03b9\u03c3\u03ae\u03b3\u03b1\u03b3\u03b1\u03bd \u03c3\u03c4\u03b7\u03bd \u0395\u03c5\u03c1\u03ce\u03c0\u03b7. \u03a0\u03c1\u03cc\u03ba\u03b5\u03b9\u03c4\u03b1\u03b9 \u03b3\u03b9\u03b1 \u03c4\u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03b9\u03ba\u03cc \u03c3\u03cd\u03c3\u03c4\u03b7\u03bc\u03b1 \u03c0\u03bf\u03c5 \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03b5\u03af\u03c4\u03b1\u03b9 \u03ba\u03b1\u03b9 \u03c3\u03ae\u03bc\u03b5\u03c1\u03b1, \u03bc\u03b5 \u03b4\u03ad\u03ba\u03b1 \u03c8\u03b7\u03c6\u03af\u03b1, \u03ad\u03bd\u03b1 \u03b5\u03ba \u03c4\u03c9\u03bd \u03bf\u03c0\u03bf\u03af\u03c9\u03bd \u03c4\u03bf \u03bc\u03b7\u03b4\u03ad\u03bd, \u03ba\u03b1\u03b9 \u03c4\u03b7\u03bd \u03c5\u03c0\u03bf\u03b4\u03b9\u03b1\u03c3\u03c4\u03bf\u03bb\u03ae.<br \/>\n\u03a4\u03bf \u03b2\u03b9\u03b2\u03bb\u03af\u03bf \u03c4\u03bf\u03c5 Liber abbaci (\u03b2\u03b9\u03b2\u03bb\u03af\u03bf \u03c4\u03c9\u03bd \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03ce\u03bd) \u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03bf\u03bb\u03bf\u03ba\u03bb\u03b7\u03c1\u03ce\u03b8\u03b7\u03ba\u03b5 \u03c4\u03bf 1202 \u03ad\u03c0\u03b5\u03b9\u03c3\u03b5 \u03b1\u03c1\u03ba\u03b5\u03c4\u03bf\u03cd\u03c2 \u0395\u03c5\u03c1\u03c9\u03c0\u03b1\u03af\u03bf\u03c5\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03bd\u03b1 \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03ae\u03c3\u03bf\u03c5\u03bd \u03c4\u03bf \u00ab\u03bd\u03ad\u03bf\u00bb \u03c3\u03cd\u03c3\u03c4\u03b7\u03bc\u03b1. \u03a4\u03bf \u03b2\u03b9\u03b2\u03bb\u03af\u03bf, \u03b3\u03c1\u03b1\u03bc\u03bc\u03ad\u03bd\u03bf \u03c3\u03c4\u03b1 \u03bb\u03b1\u03c4\u03b9\u03bd\u03b9\u03ba\u03ac, \u03c0\u03b5\u03c1\u03b9\u03b3\u03c1\u03ac\u03c6\u03b5\u03b9 \u03bc\u03b5 \u03bb\u03b5\u03c0\u03c4\u03bf\u03bc\u03ad\u03c1\u03b5\u03b9\u03b1 \u03c4\u03bf\u03c5\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03ba\u03b1\u03bd\u03cc\u03bd\u03b5\u03c2 \u03c0\u03bf\u03c5 \u03c3\u03ae\u03bc\u03b5\u03c1\u03b1 \u03b4\u03b9\u03b4\u03ac\u03c3\u03ba\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c3\u03c4\u03bf \u03b4\u03b7\u03bc\u03bf\u03c4\u03b9\u03ba\u03cc \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03c0\u03c1\u03cc\u03c3\u03b8\u03b5\u03c3\u03b7, \u03c4\u03b7\u03bd \u03b1\u03c6\u03b1\u03af\u03c1\u03b5\u03c3\u03b7, \u03c4\u03bf\u03bd \u03c0\u03bf\u03bb\u03bb\u03b1\u03c0\u03bb\u03b1\u03c3\u03b9\u03b1\u03c3\u03bc\u03cc \u03ba\u03b1\u03b9 \u03c4\u03b7 \u03b4\u03b9\u03b1\u03af\u03c1\u03b5\u03c3\u03b7 \u03ba\u03b1\u03b9 \u03c0\u03b5\u03c1\u03b9\u03ad\u03c7\u03b5\u03b9 \u03c0\u03bf\u03bb\u03bb\u03ad\u03c2 \u03b1\u03c3\u03ba\u03ae\u03c3\u03b5\u03b9\u03c2-\u03c0\u03b1\u03c1\u03b1\u03b4\u03b5\u03af\u03b3\u03bc\u03b1\u03c4\u03b1 \u03bc\u03b5 \u03bb\u03b5\u03c0\u03c4\u03bf\u03bc\u03ad\u03c1\u03b5\u03b9\u03b5\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ae \u03b1\u03c5\u03c4\u03ce\u03bd \u03c4\u03c9\u03bd \u03ba\u03b1\u03bd\u03cc\u03bd\u03c9\u03bd.<\/p>\n<p><b>\u0397 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1 Fibonacci \u03ba\u03b1\u03b9 \u03b7 \u03c6\u03cd\u03c3\u03b7<\/b><br \/>\n\u03a4\u03b1 \u03c6\u03c5\u03c4\u03ac \u03b4\u03b5 \u03b3\u03bd\u03c9\u03c1\u03af\u03b6\u03bf\u03c5\u03bd \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1 Fibonacci, \u03b1\u03c0\u03bb\u03ac \u03bc\u03b5\u03b3\u03b1\u03bb\u03ce\u03bd\u03bf\u03c5\u03bd \u03bc\u03b5 \u03c4\u03bf\u03bd \u03c0\u03b9\u03bf \u03c0\u03c1\u03cc\u03c3\u03c6\u03bf\u03c1\u03bf \u03ba\u03b1\u03b9 \u03b1\u03c0\u03bf\u03b4\u03bf\u03c4\u03b9\u03ba\u03cc \u03c4\u03cc\u03c0\u03bf. \u038c\u03bc\u03c9\u03c2 \u03b7 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1 \u03ba\u03ac\u03bd\u03b5\u03b9 \u03c4\u03b7\u03bd \u03b5\u03bc\u03c6\u03ac\u03bd\u03b9\u03c3\u03ae \u03c4\u03b7\u03c2 \u03c3\u03c4\u03b7 \u03b4\u03b9\u03ac\u03c4\u03b1\u03be\u03b7 \u03c4\u03c9\u03bd \u03c6\u03cd\u03bb\u03c9\u03bd \u03b3\u03cd\u03c1\u03c9 \u03b1\u03c0\u03cc \u03c4\u03bf \u03bc\u03af\u03c3\u03c7\u03bf. \u0395\u03bc\u03c6\u03b1\u03bd\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03b5\u03c0\u03af\u03c3\u03b7\u03c2 \u03c3\u03c4\u03b7\u03bd \u03b1\u03bd\u03ac\u03c0\u03c4\u03c5\u03be\u03b7 \u03c4\u03c9\u03bd \u03b2\u03b5\u03bb\u03cc\u03bd\u03c9\u03bd \u03b1\u03c1\u03ba\u03b5\u03c4\u03ce\u03bd \u03b5\u03b9\u03b4\u03ce\u03bd \u03b5\u03bb\u03ac\u03c4\u03bf\u03c5, \u03ba\u03b1\u03b8\u03ce\u03c2 \u03b5\u03c0\u03af\u03c3\u03b7\u03c2 \u03ba\u03b1\u03b9 \u03c3\u03c4\u03b7 \u03b4\u03b9\u03ac\u03c4\u03b1\u03be\u03b7 \u03c4\u03c9\u03bd \u03c0\u03b5\u03c4\u03ac\u03bb\u03c9\u03bd \u03c3\u03c4\u03b9\u03c2 \u03bc\u03b1\u03c1\u03b3\u03b1\u03c1\u03af\u03c4\u03b5\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03b1 \u03b7\u03bb\u03b9\u03bf\u03c4\u03c1\u03cc\u03c0\u03b9\u03b1. \u039c\u03b5\u03c1\u03b9\u03ba\u03ac 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\u03bf\u03c1\u03b8\u03bf\u03b3\u03ce\u03bd\u03b9\u03bf. \u03a4\u03bf 1995 \u03bf \u03ba\u03b1\u03b8\u03b7\u03b3\u03b7\u03c4\u03ae\u03c2 Christopher Green \u03c4\u03bf\u03c5 \u03a0\u03b1\u03bd\u03b5\u03c0\u03b9\u03c3\u03c4\u03b7\u03bc\u03af\u03bf\u03c5 York \u03c3\u03c4\u03bf Toronto, \u03c3\u03b5 \u03ad\u03bd\u03b1 \u03ac\u03c1\u03b8\u03c1\u03bf \u03c4\u03bf\u03c5 \u03c3\u03c4\u03bf \u03c0\u03b5\u03c1\u03b9\u03bf\u03b4\u03b9\u03ba\u03cc Perception \u03c0\u03b1\u03c1\u03bf\u03c5\u03c3\u03b9\u03ac\u03b6\u03b5\u03b9 \u03c4\u03b1 \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03ad\u03c3\u03bc\u03b1\u03c4\u03b1 \u03bc\u03b9\u03b1\u03c2 \u03c3\u03b5\u03b9\u03c1\u03ac\u03c2 \u03c0\u03b5\u03b9\u03c1\u03b1\u03bc\u03ac\u03c4\u03c9\u03bd \u03c0\u03bf\u03c5 \u03b4\u03b5\u03bd \u03ad\u03b4\u03b5\u03b9\u03be\u03b1\u03bd \u03ba\u03ac\u03c0\u03bf\u03b9\u03b1 \u03bc\u03b5\u03c4\u03c1\u03ae\u03c3\u03b9\u03bc\u03b7 \u03c0\u03c1\u03bf\u03c4\u03af\u03bc\u03b7\u03c3\u03b7 \u03b3\u03b9\u03b1 \u03c4\u03bf 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