{"id":41171,"date":"2019-08-18T20:48:47","date_gmt":"2019-08-18T17:48:47","guid":{"rendered":"http:\/\/omathimatikos.gr\/?p=41171"},"modified":"2019-08-04T08:28:51","modified_gmt":"2019-08-04T05:28:51","slug":"%ce%bc%ce%b9%ce%b1-%ce%b1%cf%80%cf%81%cf%8c%cf%83%ce%bc%ce%b5%ce%bd%ce%b7-%ce%b9%ce%b4%ce%b9%cf%8c%cf%84%ce%b7%cf%84%ce%b1-%cf%84%ce%bf%cf%85-%ce%ba%ce%bb%ce%ac%cf%83%ce%bc%ce%b1%cf%84%ce%bf%cf%82-1-8","status":"publish","type":"post","link":"https:\/\/omathimatikos.gr\/?p=41171","title":{"rendered":"\u039c\u03b9\u03b1 \u03b1\u03c0\u03c1\u03cc\u03c3\u03bc\u03b5\u03bd\u03b7 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c4\u03bf\u03c5 \u03ba\u03bb\u03ac\u03c3\u03bc\u03b1\u03c4\u03bf\u03c2 1\/89"},"content":{"rendered":"<p><!--more--><!--more-->\u039c\u03b9\u03b1 \u03b1\u03c0\u03cc \u03c4\u03b9\u03c2 \u03c0\u03b9\u03bf \u03b5\u03bd\u03b4\u03b9\u03b1\u03c6\u03ad\u03c1\u03bf\u03c5\u03c3\u03b5\u03c2 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b5\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd \u03c3\u03c4\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7\u00a0<strong><a href=\"https:\/\/en.wikipedia.org\/wiki\/Fibonacci_number\" target=\"_blank\" rel=\"noopener noreferrer\">\u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1 Fibonacci<\/a><\/strong>: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, \u2026<br \/>\n\u0398\u03b5\u03c9\u03c1\u03ce\u03bd\u03c4\u03b1\u03c2 \u03b5\u03be\u2019 \u03bf\u03c1\u03b9\u03c3\u03bc\u03bf\u03cd \u03c4\u03bf\u03c5\u03c2 \u03b4\u03c5\u03bf \u03c0\u03c1\u03ce\u03c4\u03bf\u03c5\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2 \u03c4\u03b7\u03c2 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1\u03c2 Fibonacci F<sub>1<\/sub>=F<sub>2<\/sub>=1, \u03c4\u03cc\u03c4\u03b5 \u03bf\u03b9 \u03b5\u03c0\u03cc\u03bc\u03b5\u03bd\u03bf\u03b9 \u03cc\u03c1\u03bf\u03b9 \u03c0\u03c1\u03bf\u03ba\u03cd\u03c0\u03c4\u03bf\u03c5\u03bd \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03b1\u03bd\u03b1\u03b4\u03c1\u03bf\u03bc\u03b9\u03ba\u03ae \u03c3\u03c7\u03ad\u03c3\u03b7: F<sub>n<\/sub>=F<sub>n-1<\/sub>+F<sub>n-2<\/sub>.<br \/>\n\u03a4\u03bf 1994 \u03bf Cody Birsner \u03cc\u03c4\u03b1\u03bd \u03ae\u03c4\u03b1\u03bd \u03c6\u03bf\u03b9\u03c4\u03b7\u03c4\u03ae\u03c2 \u03c3\u03c4\u03bf \u03c0\u03b1\u03bd\u03b5\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b9\u03bf \u03c4\u03b7\u03c2 \u039f\u03ba\u03bb\u03b1\u03c7\u03cc\u03bc\u03b1 \u03b1\u03bd\u03b1\u03ba\u03ac\u03bb\u03c5\u03c8\u03b5 \u03c4\u03b7\u03bd \u03c0\u03b1\u03c1\u03b1\u03ba\u03ac\u03c4\u03c9 \u03c3\u03c7\u03ad\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03ba\u03bb\u03ac\u03c3\u03bc\u03b1\u03c4\u03bf\u03c2 1\/89 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1 Fibonacci:<a class=\"single-image-gallery\" href=\"https:\/\/physicsgg.me\/2019\/07\/20\/%ce%bc%ce%b9%ce%b1-%ce%b1%cf%80%cf%81%cf%8c%cf%83%ce%bc%ce%b5%ce%bd%ce%b7-%ce%b9%ce%b4%ce%b9%cf%8c%cf%84%ce%b7%cf%84%ce%b1-%cf%84%ce%bf%cf%85-%ce%ba%ce%bb%ce%ac%cf%83%ce%bc%ce%b1%cf%84%ce%bf%cf%82-1-8\/fibonacci2\/\" rel=\"attachment wp-att-55172\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-55172\" src=\"https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci2.png?w=594&#038;h=96&#038;resize=594%2C96\" sizes=\"(max-width: 594px) 100vw, 594px\" srcset=\"https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci2.png?w=594&#038;h=96&#038;resize=594%2C96 594w, https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci2.png?w=150&amp;h=24 150w, https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci2.png?w=300&amp;h=48 300w, https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci2.png?w=768&amp;h=124 768w, https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci2.png 895w\" alt=\"\" width=\"594\" height=\"96\" data-attachment-id=\"55172\" data-permalink=\"https:\/\/physicsgg.me\/2019\/07\/20\/%ce%bc%ce%b9%ce%b1-%ce%b1%cf%80%cf%81%cf%8c%cf%83%ce%bc%ce%b5%ce%bd%ce%b7-%ce%b9%ce%b4%ce%b9%cf%8c%cf%84%ce%b7%cf%84%ce%b1-%cf%84%ce%bf%cf%85-%ce%ba%ce%bb%ce%ac%cf%83%ce%bc%ce%b1%cf%84%ce%bf%cf%82-1-8\/fibonacci2\/\" data-orig-file=\"https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci2.png\" data-orig-size=\"895,144\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"fibonacci2\" data-image-description=\"\" data-medium-file=\"https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci2.png?w=300\" data-large-file=\"https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci2.png?w=594\" data-recalc-dims=\"1\" \/><\/a>\u03ae \u03c0\u03b9\u03bf \u03b1\u03bd\u03b1\u03bb\u03c5\u03c4\u03b9\u03ba\u03ac:<br \/>\n<a class=\"single-image-gallery\" href=\"https:\/\/physicsgg.me\/2019\/07\/20\/%ce%bc%ce%b9%ce%b1-%ce%b1%cf%80%cf%81%cf%8c%cf%83%ce%bc%ce%b5%ce%bd%ce%b7-%ce%b9%ce%b4%ce%b9%cf%8c%cf%84%ce%b7%cf%84%ce%b1-%cf%84%ce%bf%cf%85-%ce%ba%ce%bb%ce%ac%cf%83%ce%bc%ce%b1%cf%84%ce%bf%cf%82-1-8\/fibonacci1\/\" rel=\"attachment wp-att-55173\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-55173\" src=\"https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci1.png?w=240&#038;h=350&#038;resize=240%2C350\" sizes=\"(max-width: 240px) 100vw, 240px\" srcset=\"https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci1.png?w=240&#038;h=350&#038;resize=240%2C350 240w, https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci1.png?w=103&amp;h=150 103w, https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci1.png?w=206&amp;h=300 206w, https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci1.png 393w\" alt=\"\" width=\"240\" height=\"350\" data-attachment-id=\"55173\" data-permalink=\"https:\/\/physicsgg.me\/2019\/07\/20\/%ce%bc%ce%b9%ce%b1-%ce%b1%cf%80%cf%81%cf%8c%cf%83%ce%bc%ce%b5%ce%bd%ce%b7-%ce%b9%ce%b4%ce%b9%cf%8c%cf%84%ce%b7%cf%84%ce%b1-%cf%84%ce%bf%cf%85-%ce%ba%ce%bb%ce%ac%cf%83%ce%bc%ce%b1%cf%84%ce%bf%cf%82-1-8\/fibonacci1\/\" data-orig-file=\"https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci1.png\" data-orig-size=\"393,573\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"fibonacci1\" data-image-description=\"\" data-medium-file=\"https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci1.png?w=206\" data-large-file=\"https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci1.png?w=393\" data-recalc-dims=\"1\" \/><\/a><br \/>\n\u0399\u03b4\u03bf\u03cd \u03ba\u03b1\u03b9 \u03bc\u03b9\u03b1 \u03c9\u03c1\u03b1\u03af\u03b1 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 \u03b1\u03c5\u03c4\u03ae\u03c2 \u03c4\u03b7\u03c2 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2:<a class=\"single-image-gallery\" href=\"https:\/\/physicsgg.me\/2019\/07\/20\/%ce%bc%ce%b9%ce%b1-%ce%b1%cf%80%cf%81%cf%8c%cf%83%ce%bc%ce%b5%ce%bd%ce%b7-%ce%b9%ce%b4%ce%b9%cf%8c%cf%84%ce%b7%cf%84%ce%b1-%cf%84%ce%bf%cf%85-%ce%ba%ce%bb%ce%ac%cf%83%ce%bc%ce%b1%cf%84%ce%bf%cf%82-1-8\/fibonacci\/\" rel=\"attachment wp-att-55177\"><br \/>\n<img data-attachment-id=\"55177\" data-permalink=\"https:\/\/omathimatikos.gr\/?attachment_id=55177\" data-orig-file=\"https:\/\/i0.wp.com\/omathimatikos.gr\/wp-content\/uploads\/2022\/09\/-e1662620507226.jpg?fit=628%2C418&amp;ssl=1\" data-orig-size=\"628,418\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"\u03ba\u03b1\u03b8\u03b7\u03b3\u03b7\u03c4\u03ae\u03c2\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/omathimatikos.gr\/wp-content\/uploads\/2022\/09\/-e1662620507226.jpg?fit=350%2C233&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/omathimatikos.gr\/wp-content\/uploads\/2022\/09\/-e1662620507226.jpg?fit=523%2C348&amp;ssl=1\" decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-55177\" src=\"https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci.jpg?w=594&#038;h=600&#038;resize=594%2C600\" sizes=\"(max-width: 594px) 100vw, 594px\" srcset=\"https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci.jpg?w=594&#038;h=600&#038;resize=594%2C600 594w, https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci.jpg?w=297&amp;h=300 297w, https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci.jpg 717w\" alt=\"\" width=\"594\" height=\"600\" data-attachment-id=\"55177\" data-permalink=\"https:\/\/physicsgg.me\/2019\/07\/20\/%ce%bc%ce%b9%ce%b1-%ce%b1%cf%80%cf%81%cf%8c%cf%83%ce%bc%ce%b5%ce%bd%ce%b7-%ce%b9%ce%b4%ce%b9%cf%8c%cf%84%ce%b7%cf%84%ce%b1-%cf%84%ce%bf%cf%85-%ce%ba%ce%bb%ce%ac%cf%83%ce%bc%ce%b1%cf%84%ce%bf%cf%82-1-8\/fibonacci\/\" data-orig-file=\"https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci.jpg\" data-orig-size=\"717,724\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"fibonacci\" data-image-description=\"\" data-medium-file=\"https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci.jpg?w=297\" data-large-file=\"https:\/\/physicsgg.files.wordpress.com\/2019\/07\/fibonacci.jpg?w=594\" data-recalc-dims=\"1\" \/><\/a>\u039c\u03b9\u03b1 \u03b5\u03bd\u03b1\u03bb\u03bb\u03b1\u03ba\u03c4\u03b9\u03ba\u03ae \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 \u03b8\u03b1 \u03b2\u03c1\u03b5\u03af\u03c4\u03b5\u00a0<strong><a href=\"http:\/\/www2.math.ou.edu\/~dmccullough\/teaching\/miscellanea\/miner.html\">\u0395\u0394\u03a9:<\/a><\/strong><!--more--><\/p>\n<p>\u03c0\u03b7\u03b3\u03ae<\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":0,"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":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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