{"id":5,"date":"2025-11-19T09:22:49","date_gmt":"2025-11-19T09:22:49","guid":{"rendered":"https:\/\/maths4u.gr\/?p=5"},"modified":"2025-11-27T16:47:05","modified_gmt":"2025-11-27T16:47:05","slug":"fibonacci","status":"publish","type":"post","link":"https:\/\/maths4u.gr\/index.php\/2025\/11\/19\/fibonacci\/","title":{"rendered":"\u0397 \u03c3\u03b5\u03b9\u03c1\u03ac \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd \u03c4\u03bf\u03c5 Fibonacci."},"content":{"rendered":"\r\n<p class=\"wp-block-paragraph\">\u0397 \u03c3\u03b5\u03b9\u03c1\u03ac Fibonacci \u03ba\u03b1\u03c4\u03b1\u03c3\u03ba\u03b5\u03c5\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03b1\u03bd \u03c0\u03ac\u03c1\u03bf\u03c5\u03bc\u03b5 \u03c3\u03b1\u03bd \u03c0\u03c1\u03ce\u03c4\u03bf \u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03bf \u03c4\u03b7\u03c2 \u03c4\u03bf \u03bc\u03b7\u03b4\u03ad\u03bd, \u03b4\u03b5\u03cd\u03c4\u03b5\u03c1\u03bf \u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03bf \u03c4\u03bf \u03ad\u03bd\u03b1, \u03ba\u03b1\u03b9 \u03b1\u03c0\u03bf \u03ba\u03b5\u03b9 \u03ba\u03b1\u03b9 \u03c0\u03ad\u03c1\u03b1 \u03c4\u03bf \u03ba\u03ac\u03b8\u03b5 \u03b5\u03c0\u03cc\u03bc\u03b5\u03bd\u03bf \u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03bf, \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. \u0388\u03c4\u03c3\u03b9 \u03b1\u03bd \u03b2\u03b1\u03c6\u03c4\u03af\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c4\u03bf\u03c5\u03c2 \u03cc\u03c1\u03bf\u03c5\u03c2 \u03c4\u03b7\u03c2 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1\u03c2 \u03bc\u03b5 \\(F_n\\) \u03cc\u03c0\u03bf\u03c5 \u03c4\u03bf \\(n\\) \u03c0\u03b1\u03af\u03c1\u03bd\u03b5\u03b9 \u03c4\u03b9\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \\(0,1,2,3&#8230;\\) \u03c4\u03c9\u03bd \u03c6\u03c5\u03c3\u03b9\u03ba\u03ce\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd, \u03b8\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \\[F_0=0, F_1=1, F_2=0+1=1, F_3=1+1=2, F_4=2+1=3 &#8230; \u03ba.\u03bf.\u03ba\\]\u00a0<br \/>\u0397 \u03c3\u03b5\u03b9\u03c1\u03ac \u03b1\u03c5\u03c4\u03ae \u03ad\u03c7\u03b5\u03b9 \u03c0\u03bf\u03bb\u03bb\u03ad\u03c2 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03c0\u03bf\u03c5 \u03c4\u03b7\u03bd \u03ba\u03ac\u03bd\u03bf\u03c5\u03bd \u03c0\u03bf\u03bb\u03cd \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03ae, \u03c0\u03b1\u03c1\u03ac \u03c4\u03bf \u03cc\u03c4\u03b9 \u03b4\u03b5\u03bd \u03c4\u03b7\u03c2 \u03c6\u03b1\u03af\u03bd\u03b5\u03c4\u03b1\u03b9. \u0397 \u03c6\u03ae\u03bc\u03b7 \u03c4\u03b7\u03c2 \u03c0\u03b1\u03c1\u03ac \u03c4\u03bf \u03cc\u03c4\u03b9 \u03bf Fibonacci \u03c4\u03b7\u03bd \u03cc\u03c1\u03b9\u03c3\u03b5 \u03c4\u03bf\u03bd 13\u03bf \u03b1\u03b9\u03ce\u03bd\u03b1, \u03ac\u03c1\u03c7\u03b9\u03c3\u03b5 3 \u03b1\u03b9\u03ce\u03bd\u03b5\u03c2 \u03bc\u03b5\u03c4\u03ac, \u03cc\u03c4\u03b1\u03bd \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03bf \u039a\u03ad\u03c0\u03bb\u03b5\u03c1 \u03ad\u03b3\u03c1\u03b1\u03c8\u03b5 \u03c4\u03bf 1611 \u03c3\u03b5 \u03bc\u03b9\u03b1 \u03b4\u03b7\u03bc\u03bf\u03c3\u03af\u03b5\u03c5\u03c3\u03b7 \u03c4\u03bf\u03c5, \u03cc\u03c4\u03b9 <strong>&#8220;\u03c3\u03c7\u03b5\u03b4\u03cc\u03bd \u03bf \u03bb\u03cc\u03b3\u03bf\u03c2 \u03c4\u03bf\u03c5 5 \u03bc\u03b5 \u03c4\u03bf 8, \u03b5\u03af\u03bd\u03b1\u03b9 \u03af\u03b4\u03b9\u03bf\u03c2 \u03bc\u03b5 \u03c4\u03bf \u03bb\u03cc\u03b3\u03bf \u03c4\u03bf\u03c5 8 \u03bc\u03b5 \u03c4\u03bf 13 \u03ba\u03b1\u03b9 \u03bf \u03af\u03b4\u03b9\u03bf\u03c2 \u03bc\u03b5 \u03c4\u03bf\u03c5 13 \u03bc\u03b5 \u03c4\u03bf 21&#8221;<\/strong>.<\/p>\r\n<p>\u03a4\u03bf\u03bd 18\u03bf \u03b1\u03b9\u03ce\u03bd\u03b1 \u03ad\u03bd\u03b1\u03c2 \u0393\u03ac\u03bb\u03bb\u03bf\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2, \u03bf Jacques-Philippe Mari Binet \u03b2\u03c1\u03ae\u03ba\u03b5 \u03ad\u03bd\u03b1\u03bd \u03c4\u03cd\u03c0\u03bf \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03bf\u03cd \u03bf\u03c0\u03bf\u03b9\u03bf\u03c5\u03b4\u03ae\u03c0\u03bf\u03c4\u03b5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd Fibonacci, \u03b1\u03bd \u03b3\u03bd\u03c9\u03c1\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b7 \u03b8\u03ad\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03c3\u03c4\u03b7\u03bd \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1. \u0391\u03c5\u03c4\u03cc \u03ba\u03b1\u03b9 \u03ac\u03bb\u03bb\u03b5\u03c2 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03c4\u03b7\u03c2 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1\u03c2 \u03b1\u03c5\u03c4\u03ae\u03c2 \u03b8\u03b1 \u03b1\u03bd\u03b1\u03bb\u03cd\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c3\u03b5 \u03b5\u03c0\u03cc\u03bc\u03b5\u03bd\u03b5\u03c2 \u03b4\u03b7\u03bc\u03bf\u03c3\u03b9\u03b5\u03cd\u03c3\u03b5\u03b9\u03c2. \u0395\u03b4\u03ce \u03b8\u03b1 \u03b1\u03c1\u03ba\u03b5\u03c3\u03c4\u03bf\u03cd\u03bc\u03b5 \u03c3\u03b5 \u03bc\u03b9\u03b1 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c0\u03bf\u03c5 \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03b5\u03cd\u03b5\u03b9 \u03c3\u03c4\u03b7\u03bd \u03ba\u03b1\u03c4\u03b1\u03c3\u03ba\u03b5\u03c5\u03ae \u03b1\u03bd\u03c4\u03b9\u03ba\u03b5\u03b9\u03bc\u03ad\u03bd\u03c9\u03bd \u03c0\u03bf\u03c5 \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03bf\u03cd\u03bc\u03b5 \u03ba\u03b1\u03b8\u03b7\u03bc\u03b5\u03c1\u03b9\u03bd\u03ac \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b3\u03af\u03bd\u03bf\u03c5\u03bd \u03c0\u03b9\u03bf \u03b5\u03bb\u03ba\u03c5\u03c3\u03c4\u03b9\u03ba\u03ac \u03c3\u03c4\u03bf \u03bc\u03ac\u03c4\u03b9 \u03bc\u03b1\u03c2.<\/p>\r\n<p>\u03a6\u03b1\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03cc\u03c4\u03b9 \u03c5\u03c0\u03ac\u03c1\u03c7\u03b5\u03b9 \u03bc\u03b9\u03b1 \u03bf\u03c0\u03c4\u03b9\u03ba\u03ac \u03b5\u03c5\u03c7\u03ac\u03c1\u03b9\u03c3\u03c4\u03b7 \u03b1\u03af\u03c3\u03b8\u03b7\u03c3\u03b7 \u03c3\u03c4\u03bf \u03b1\u03bc\u03b8\u03c1\u03ce\u03c0\u03b9\u03bd\u03bf \u03bc\u03ac\u03c4\u03b9, \u03cc\u03c4\u03b1\u03bd \u03bf\u03b9 \u03b4\u03b9\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03b9\u03c2 \u03b5\u03bd\u03cc\u03c2 \u03b1\u03bd\u03c4\u03b9\u03ba\u03b5\u03b9\u03bc\u03ad\u03bd\u03bf\u03c5, \u03cc\u03c0\u03c9\u03c2 \u03c0.\u03c7. \u03bf\u03b9 \u03b5\u03c0\u03b1\u03b3\u03b3\u03b5\u03bb\u03bc\u03b1\u03c4\u03b9\u03ba\u03ad\u03c2 \u03ba\u03ac\u03c1\u03c4\u03b5\u03c2, \u03ad\u03c7\u03bf\u03c5\u03bd \u03b4\u03b9\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03b9\u03c2 3 \u03c0\u03c1\u03bf\u03c2 5, \u03ae \u03c4\u03b1 \u03b4\u03b9\u03b1\u03c6\u03b7\u03bc\u03b9\u03c3\u03c4\u03b9\u03ba\u03ac \u03c6\u03c5\u03bb\u03bb\u03ac\u03b4\u03b9\u03b1 5 \u03c0\u03c1\u03bf\u03c2 8. \u0391\u03bd\u03c4\u03af\u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03c2 \u03b1\u03bd\u03b1\u03bb\u03bf\u03b3\u03af\u03b5\u03c2 \u03ad\u03c7\u03bf\u03c5\u03bd \u03c4\u03b1 \u03c7\u03b1\u03c1\u03c4\u03b9\u03ac \u03c4\u03b7\u03c2 \u03c4\u03c1\u03ac\u03c0\u03bf\u03c5\u03bb\u03b1\u03c2, \u03c4\u03b1 \u03c4\u03b5\u03c4\u03c1\u03ac\u03b4\u03b9\u03b1, \u03c4\u03b1 \u03c0\u03b1\u03c1\u03ac\u03b8\u03c5\u03c1\u03b1 \u03c4\u03c9\u03bd \u03c3\u03c0\u03b9\u03c4\u03b9\u03ce\u03bd, \u03c0\u03b9\u03c3\u03c4\u03c9\u03c4\u03b9\u03ba\u03ad\u03c2 \u03ba\u03b1\u03b9 \u03c7\u03c1\u03b5\u03c9\u03c3\u03c4\u03b9\u03ba\u03ad\u03c2 \u03ba\u03ac\u03c1\u03c4\u03b5\u03c2, \u03ba\u03b9\u03bd\u03b7\u03c4\u03ac \u03c4\u03b7\u03bb\u03ad\u03c6\u03c9\u03bd\u03b1 \u03ba\u03b1\u03b9 \u03c7\u03b9\u03bb\u03b9\u03ac\u03b4\u03b5\u03c2 \u03b1\u03bd\u03c4\u03b9\u03ba\u03b5\u03af\u03bc\u03b5\u03bd\u03b1 \u03c0\u03bf\u03c5 \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03bf\u03cd\u03bc\u03b5 \u03ba\u03b1\u03b8\u03b7\u03bc\u03b5\u03c1\u03b9\u03bd\u03ac.<\/p>\r\n<p>\u039f\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u03c4\u03b7\u03c2 \u03c3\u03b5\u03b9\u03c1\u03ac\u03c2 Fibonacci \u03c0\u03b1\u03c1\u03bf\u03c5\u03c3\u03b9\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c3\u03b5 \u03c0\u03bf\u03bb\u03bb\u03ac \u03ba\u03b1\u03b8\u03b7\u03bc\u03b5\u03c1\u03b9\u03bd\u03ac \u03b1\u03bd\u03c4\u03b9\u03ba\u03b5\u03af\u03bc\u03b5\u03bd\u03b1, \u03c4\u03bf\u00a0 \u03b1\u03bd\u03b8\u03c1\u03ce\u03c0\u03b9\u03bd\u03bf \u03c3\u03ce\u03bc\u03b1, \u03bf \u03c3\u03c4\u03b1\u03c5\u03c1\u03cc\u03c2 \u03c0\u03bf\u03c5 \u03c6\u03bf\u03c1\u03ac\u03bc\u03b1\u03b9 \u03c3\u03b1\u03bd \u03ba\u03cc\u03c3\u03bc\u03b7\u03bc\u03b1, \u03c4\u03bf \u03c0\u03c1\u03cc\u03c3\u03c9\u03c0\u03bf \u03bc\u03b1\u03c2, \u03c4\u03bf \u03c7\u03ad\u03c1\u03b9 \u03bc\u03b1\u03c2, \u03b8\u03ad\u03bc\u03b1\u03c4\u03b1 \u03c0\u03bf\u03c5 \u03b1\u03bd\u03ad\u03bb\u03c5\u03c3\u03b5 \u03bf \u03b1\u03c1\u03c7\u03b9\u03c4\u03ad\u03ba\u03c4\u03bf\u03bd\u03b1\u03c2 \\(Le Corbusier\\), \u03c0\u03af\u03bd\u03b1\u03ba\u03b5\u03c2 \u03bc\u03b5\u03b3\u03ac\u03bb\u03c9\u03bd \u03b6\u03c9\u03b3\u03c1\u03ac\u03c6\u03c9\u03bd \u03ba\u03bb\u03c0.<\/p>\r\n<p>\u0391\u03bd \u03c0\u03ac\u03c1\u03bf\u03c5\u03bc\u03b5 \u03c4\u03bf\u03bd \u03bb\u03cc\u03b3\u03bf \u03b4\u03cd\u03bf \u03c3\u03c5\u03bd\u03b5\u03c7\u03cc\u03bc\u03b5\u03bd\u03c9\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd \u03c4\u03b7\u03c2 \u03c3\u03b5\u03b9\u03c1\u03ac\u03c2, \u03bc\u03b5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03ae \u03c4\u03bf\u03bd \u03bc\u03b9\u03ba\u03c1\u03cc\u03c4\u03b5\u03c1\u03bf \u03ba\u03b1\u03b9 \u03c0\u03b1\u03c1\u03bf\u03bd\u03bf\u03bc\u03b1\u03c3\u03c4\u03ae \u03c4\u03bf\u03bd \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf, \u03b8\u03b1 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03ad\u03bd\u03b1\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03c0\u03bf\u03c5 \u03cc\u03c3\u03bf \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03cc\u03c1\u03bf\u03b9 \u03c4\u03cc\u03c3\u03bf \u03c0\u03c1\u03bf\u03c3\u03b5\u03b3\u03b3\u03af\u03b6\u03bf\u03c5\u03bd \u03ac\u03bd\u03c9, \u03ba\u03ac\u03c4\u03c9, \u03c3\u03c4\u03bf\u03bd \u03c7\u03c1\u03c5\u03c3\u03cc \u03bb\u03cc\u03b3\u03bf. \\[\\dfrac{2}{3}=0,666 \\quad \\dfrac{5}{8}=0,625 \\quad \\dfrac{8}{13}=0,615 \\quad \\dfrac{13}{21}=0,619&#8230;\\]<\/p>\r\n<p>\u039f \u03c7\u03c1\u03c5\u03c3\u03cc\u03c2 \u03bb\u03cc\u03b3\u03bf\u03c2 \\(x\\) \u03b4\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03b1\u03bd\u03b1\u03bb\u03bf\u03b3\u03af\u03b1 \\[\\dfrac{x}{1}=\\dfrac{1}{x+1} \\Rightarrow x(x+1)=1\\Rightarrow x^2+x-1=0\\Rightarrow x=\\dfrac{\\sqrt{5}-1}{2}=0,618.\\] \u03cc\u03c0\u03bf\u03c5 \u03b7 \u03b1\u03c1\u03bd\u03b7\u03c4\u03b9\u03ba\u03ae \u03c1\u03af\u03b6\u03b1 \u03b1\u03c0\u03bf\u03c1\u03c1\u03af\u03c0\u03c4\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c6\u03bf\u03cd \u03bc\u03b9\u03bb\u03ac\u03bc\u03b5 \u03b3\u03b9\u03b1 \u03b8\u03b5\u03c4\u03b9\u03ba\u03ad\u03c2 \u03b1\u03c0\u03bf\u03c3\u03c4\u03ac\u03c3\u03b5\u03b9\u03c2.<\/p>\r\n<p>\u0391\u03bd \u03b8\u03ad\u03bb\u03bf\u03c5\u03bc\u03b5 \u03bd\u03b1 \u03ba\u03b1\u03c4\u03b1\u03c3\u03ba\u03b5\u03c5\u03ac\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c4\u03bf \u03c7\u03c1\u03c5\u03c3\u03cc \u03bf\u03c1\u03b8\u03bf\u03b3\u03ce\u03bd\u03b9\u03bf, \u03c4\u03cc\u03c4\u03b5 \u03b7 \u03bc\u03b9\u03ba\u03c1\u03ae \u03c0\u03bb\u03b5\u03c5\u03c1\u03ac \u03c4\u03bf\u03c5 \u03bf\u03c1\u03b8\u03bf\u03b3\u03c9\u03bd\u03af\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03ae\u03ba\u03bf\u03c5\u03c2 \\(s\\) \u03ba\u03b1\u03b9 \u03b7 \u03bc\u03b5\u03b3\u03ac\u03bb\u03b7 \u03c0\u03bb\u03b5\u03c5\u03c1\u03ac \\(L\\), \u03b7 \u03b1\u03bd\u03b1\u03bb\u03bf\u03b3\u03af\u03b1 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03c0\u03b1\u03c1\u03b1\u03c3\u03c4\u03b1\u03b8\u03b5\u03af \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03c9\u03c2 \u03b5\u03be\u03ae\u03c2: \\(\\dfrac{s}{L}=\\dfrac{L}{s+L}\\) . \u0391\u03bd \u03b1\u03c5\u03c4\u03cc \u03c3\u03b1\u03c2 \u03b8\u03c5\u03bc\u03af\u03b6\u03b5\u03b9 \u03ba\u03ac\u03c4\u03b9, \u03b5\u03af\u03bd\u03b1\u03b9 \u03b2\u03ad\u03b2\u03b1\u03b9\u03bf \u03cc\u03c4\u03b9 \u03bf\u03b9 \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03bf\u03b9 \u03bc\u03b5\u03b3\u03ac\u03bb\u03bf\u03b9 \u03b6\u03c9\u03b3\u03c1\u03ac\u03c6\u03bf\u03b9 \u03ba\u03b1\u03b9 \u03b1\u03c1\u03c7\u03b9\u03c4\u03ad\u03ba\u03c4\u03bf\u03bd\u03b5\u03c2 \u03b4\u03bf\u03cd\u03bb\u03b5\u03c5\u03b1\u03bd \u03c0\u03ac\u03bd\u03c9 \u03c3&#8217; \u03b1\u03c5\u03c4\u03ae\u03bd \u03c4\u03b7\u03bd \u03b1\u03bd\u03b1\u03bb\u03bf\u03b3\u03af\u03b1&#8230;<\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>\u0397 \u03c3\u03b5\u03b9\u03c1\u03ac Fibonacci \u03ba\u03b1\u03c4\u03b1\u03c3\u03ba\u03b5\u03c5\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03b1\u03bd \u03c0\u03ac\u03c1\u03bf\u03c5\u03bc\u03b5 \u03c3\u03b1\u03bd \u03c0\u03c1\u03ce\u03c4\u03bf \u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03bf \u03c4\u03b7\u03c2 \u03c4\u03bf \u03bc\u03b7\u03b4\u03ad\u03bd, \u03b4\u03b5\u03cd\u03c4\u03b5\u03c1\u03bf \u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03bf \u03c4\u03bf \u03ad\u03bd\u03b1, \u03ba\u03b1\u03b9 \u03b1\u03c0\u03bf \u03ba\u03b5\u03b9 \u03ba\u03b1\u03b9 \u03c0\u03ad\u03c1\u03b1 \u03c4\u03bf \u03ba\u03ac\u03b8\u03b5 \u03b5\u03c0\u03cc\u03bc\u03b5\u03bd\u03bf \u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03bf, \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. \u0388\u03c4\u03c3\u03b9 \u03b1\u03bd \u03b2\u03b1\u03c6\u03c4\u03af\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c4\u03bf\u03c5\u03c2 \u03cc\u03c1\u03bf\u03c5\u03c2 \u03c4\u03b7\u03c2 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1\u03c2 \u03bc\u03b5 \\(F_n\\) \u03cc\u03c0\u03bf\u03c5 \u03c4\u03bf \\(n\\) \u03c0\u03b1\u03af\u03c1\u03bd\u03b5\u03b9 \u03c4\u03b9\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \\(0,1,2,3&#8230;\\) \u03c4\u03c9\u03bd \u03c6\u03c5\u03c3\u03b9\u03ba\u03ce\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd, \u03b8\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \\[F_0=0, F_1=1, F_2=0+1=1, &hellip; <a href=\"https:\/\/maths4u.gr\/index.php\/2025\/11\/19\/fibonacci\/\" class=\"more-link\">\u0394\u03b9\u03b1\u03b2\u03ac\u03c3\u03c4\u03b5 \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03b1<span class=\"screen-reader-text\"> &#8220;\u0397 \u03c3\u03b5\u03b9\u03c1\u03ac \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd \u03c4\u03bf\u03c5 Fibonacci.&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-5","post","type-post","status-publish","format-standard","hentry","category-maths"],"_links":{"self":[{"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/posts\/5","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/comments?post=5"}],"version-history":[{"count":17,"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/posts\/5\/revisions"}],"predecessor-version":[{"id":317,"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/posts\/5\/revisions\/317"}],"wp:attachment":[{"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/media?parent=5"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/categories?post=5"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/tags?post=5"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}