{"id":35021,"date":"2013-05-08T15:01:26","date_gmt":"2013-05-08T09:31:26","guid":{"rendered":"http:\/\/www.vallamai.com\/?p=35021"},"modified":"2013-05-08T15:05:35","modified_gmt":"2013-05-08T09:35:35","slug":"%e0%ae%b5%e0%ae%bf%e0%ae%9e%e0%af%8d%e0%ae%9e%e0%ae%be%e0%ae%a9%e0%ae%95%e0%ae%a3%e0%ae%bf%e0%ae%a4-%e0%ae%ae%e0%af%87%e0%ae%a4%e0%af%88%e0%ae%95%e0%ae%b3%e0%af%8d-fibonacci","status":"publish","type":"post","link":"https:\/\/www.vallamai.com\/?p=35021","title":{"rendered":"\u0bb5\u0bbf\u0b9e\u0bcd\u0b9e\u0bbe\u0ba9,\u0b95\u0ba3\u0bbf\u0ba4 \u0bae\u0bc7\u0ba4\u0bc8\u0b95\u0bb3\u0bcd-Fibonacci"},"content":{"rendered":"<p style=\"text-align: justify\"><strong>\u0b9a\u0bc1.\u0bb0\u0bb5\u0bbf<\/strong><\/p>\n<p style=\"text-align: justify\"><span style=\"color: #993300\"><strong>LEONARDO FIBONACCI (1170-1230)<\/strong><\/span><\/p>\n<p><span style=\"color: #993300\"><strong> \u0b87\u0ba4\u0bcd\u0ba4\u0bbe\u0bb2\u0bbf\u0baf \u0ba8\u0bbe\u0b9f\u0bcd\u0b9f\u0bc8\u0b9a\u0bcd \u0b9a\u0bc7\u0bb0\u0bcd\u0ba8\u0bcd\u0ba4 \u0b95\u0ba3\u0bbf\u0ba4 \u0bae\u0bc7\u0ba4\u0bc8 \u0b83\u0baa\u0bbf\u0baa\u0bcb\u0ba9\u0bbe\u0b95\u0bcd\u0b95\u0bbf \u0ba4\u0ba8\u0bcd\u0ba4 \u0b95\u0ba3\u0b95\u0bcd\u0b95\u0bc1 \u0b87\u0ba4\u0bc1:<\/strong><\/span><\/p>\n<p><span style=\"color: #993300\"><strong>&#8221; \u0b89\u0ba9\u0bcd\u0ba9\u0bbf\u0b9f\u0bae\u0bcd \u0b92\u0bb0\u0bc1 \u0b9c\u0bcb\u0b9f\u0bbf \u0bae\u0bc1\u0baf\u0bb2\u0bcd\u0b95\u0bb3\u0bcd ( \u0b93\u0bb0\u0bcd \u0b86\u0ba3\u0bcd, \u0b92\u0bb0\u0bc1 \u0baa\u0bc6\u0ba3\u0bcd) \u0b89\u0bb3\u0bcd\u0bb3\u0ba9.<\/strong><\/span><\/p>\n<p><span style=\"color: #993300\"><strong> \u0b87\u0bb5\u0bc8 \u0b92\u0bb5\u0bcd\u0bb5\u0bca\u0bb0\u0bc1 \u0bae\u0bbe\u0ba4\u0bae\u0bc1\u0bae\u0bcd \u0b92\u0bb0\u0bc1 \u0b9c\u0bcb\u0b9f\u0bbf ( 1\u0b86\u0ba3\u0bcd, 1 \u0baa\u0bc6\u0ba3\u0bcd) \u0bae\u0bc1\u0baf\u0bb2\u0bcd\u0b95\u0bc1\u0b9f\u0bcd\u0b9f\u0bbf\u0b95\u0bb3\u0bc8 \u0b88\u0ba9\u0bc1\u0bae\u0bcd.<\/strong><\/span><br \/>\n<span style=\"color: #993300\"><strong> \u0baa\u0bbf\u0bb1\u0ba8\u0bcd\u0ba4 \u0b95\u0bc1\u0b9f\u0bcd\u0b9f\u0bbf\u0b95\u0bb3\u0bcd \u0b92\u0bb0\u0bc1 \u0bae\u0bbe\u0ba4\u0ba4\u0bcd\u0ba4\u0bbf\u0bb2\u0bcd \u0b87\u0ba9\u0baa\u0bcd\u0baa\u0bc6\u0bb0\u0bc1\u0b95\u0bcd\u0b95\u0ba4\u0bcd\u0ba4\u0bc1\u0b95\u0bcd\u0b95\u0bc1\u0ba4\u0bcd \u0ba4\u0baf\u0bbe\u0bb0\u0bbe\u0b95\u0bc1\u0bae\u0bcd. \u0b87\u0bb5\u0bc8\u0baf\u0bc1\u0bae\u0bcd 1\u0b86\u0ba3\u0bcd,1\u0baa\u0bc6\u0ba3\u0bcd \u0b95\u0bc1\u0b9f\u0bcd\u0b9f\u0bbf\u0b95\u0bb3\u0bc8<\/strong><\/span><br \/>\n<span style=\"color: #993300\"><strong> \u0b88\u0ba9\u0bc1\u0bae\u0bc6\u0ba9\u0bbf\u0bb2\u0bcd, \u0bb5\u0bb0\u0bc1\u0b9f\u0bae\u0bc1\u0b9f\u0bbf\u0bb5\u0bbf\u0bb2\u0bcd \u0b89\u0ba9\u0bcd\u0ba9\u0bbf\u0b9f\u0bae\u0bcd \u0b8e\u0ba4\u0bcd\u0ba4\u0ba9\u0bc8 \u0b9c\u0bcb\u0b9f\u0bbf \u0bae\u0bc1\u0baf\u0bb2\u0bcd\u0b95\u0bb3\u0bcd \u0b87\u0bb0\u0bc1\u0b95\u0bcd\u0b95\u0bc1\u0bae\u0bcd?<\/strong><\/span><br \/>\n<span style=\"color: #993300\"><strong>( \u0bae\u0bc1\u0baf\u0bb2\u0bcd\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0b87\u0ba9\u0baa\u0bcd\u0baa\u0bc6\u0bb0\u0bc1\u0b95\u0bcd\u0b95\u0ba4\u0bcd\u0ba4\u0bc1\u0b95\u0bcd\u0b95\u0bc1, \u0b89\u0bb1\u0bb5\u0bc1\u0bae\u0bc1\u0bb1\u0bc8\u0ba4\u0bcd \u0ba4\u0b9f\u0bc8\u0b95\u0bb3\u0bc6\u0ba4\u0bc1\u0bae\u0bcd \u0b95\u0bbf\u0b9f\u0bc8\u0baf\u0bbe\u0ba4\u0bc1; \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd, \u0b87\u0ba8\u0bcd\u0ba4 \u0b92\u0bb0\u0bc1 \u0bb5\u0bb0\u0bc1\u0b9f\u0ba4\u0bcd\u0ba4\u0bbf\u0bb2\u0bcd<\/strong><\/span><br \/>\n<span style=\"color: #993300\"><strong>\u0b8e\u0ba8\u0bcd\u0ba4 \u0bae\u0bc1\u0baf\u0bb2\u0bc1\u0bae\u0bcd \u0b87\u0bb1\u0b95\u0bcd\u0b95\u0bb5\u0bbf\u0bb2\u0bcd\u0bb2\u0bc8 \u0b8e\u0ba9\u0bcd\u0bb1\u0bc1\u0bae\u0bcd \u0b95\u0bca\u0bb3\u0bcd\u0b95).<\/strong><\/span><\/p>\n<p><span style=\"color: #993300\"><strong>\u0bae\u0bc7\u0bb1\u0bcd\u0baa\u0b9f\u0bbf \u0b95\u0ba3\u0b95\u0bcd\u0b95\u0bc8\u0baa\u0bcd \u0baa\u0bcb\u0b9f\u0bcd\u0b9f\u0bc1\u0baa\u0bcd \u0baa\u0bbe\u0bb0\u0bcd\u0b95\u0bcd\u0b95\u0bb2\u0bbe\u0bae\u0bcd:<\/strong><\/span><\/p>\n<p><a href=\"http:\/\/www.vallamai.com\/wp-content\/uploads\/2013\/05\/Microsoft-Office-Excel-Worksheet-1.jpg\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-35024\" src=\"http:\/\/www.vallamai.com\/wp-content\/uploads\/2013\/05\/Microsoft-Office-Excel-Worksheet-1.jpg\" alt=\"\" width=\"677\" height=\"69\" \/><\/a><\/p>\n<p style=\"text-align: justify\"><span style=\"color: #993300\"><strong>\u0bb5\u0bb0\u0bc1\u0b9f \u0bae\u0bc1\u0b9f\u0bbf\u0bb5\u0bbf\u0bb2\u0bcd 144 \u0b9c\u0bcb\u0b9f\u0bbf \u0bae\u0bc1\u0baf\u0bb2\u0bcd\u0b95\u0bb3\u0bcd \u0b87\u0bb0\u0bc1\u0b95\u0bcd\u0b95\u0bc1\u0bae\u0bcd.<\/strong><\/span><\/p>\n<p><span style=\"color: #993300\"><strong>\u0b92\u0bb5\u0bcd\u0bb5\u0bca\u0bb0\u0bc1 \u0bae\u0bbe\u0ba4 \u0b87\u0bb1\u0bc1\u0ba4\u0bbf\u0baf\u0bbf\u0bb2\u0bc1\u0bae\u0bcd \u0b87\u0bb0\u0bc1\u0b95\u0bcd\u0b95\u0bc1\u0bae\u0bcd \u0b8e\u0ba3\u0bcd\u0ba3\u0bbf\u0b95\u0bcd\u0b95\u0bc8\u0baf\u0bbf\u0ba9\u0bcd \u0bb5\u0bb0\u0bbf\u0b9a\u0bc8\u0baf\u0bc7 &#8220;\u0b83\u0baa\u0bbf\u0baa\u0bcb\u0ba9\u0bbe\u0b95\u0bcd\u0b95\u0bbf \u0ba8\u0bbf\u0bb0\u0bb2\u0bcd&#8221; \u0b8e\u0ba9\u0baa\u0bcd\u0baa\u0b9f\u0bc1\u0bae\u0bcd;\u0b87\u0ba8\u0bcd\u0ba4 \u0ba8\u0bbf\u0bb0\u0bb2\u0bbf\u0bb2\u0bcd \u0b85\u0bae\u0bc8\u0ba8\u0bcd\u0ba4 \u0b8e\u0ba3\u0bcd\u0b95\u0bb3\u0bcd &#8216;\u0b83\u0baa\u0bbf\u0baa\u0bcb\u0ba9\u0bbe\u0b95\u0bcd\u0b95\u0bbf \u0b8e\u0ba3\u0bcd\u0b95\u0bb3\u0bcd&#8221; \u0b8e\u0ba9\u0baa\u0bcd \u0baa\u0b9f\u0bc1\u0bae\u0bcd.<\/strong><\/span><\/p>\n<p><span style=\"color: #993300\"><strong> &#8220;1,1,2,3,5,8,13,21,34,55,89,144\u2026.&#8221;<\/strong><\/span><\/p>\n<p><span style=\"color: #993300\"><strong>\u0baa\u0bc6\u0bb0\u0bbf\u0baf \u0b86\u0b9a\u0bcd\u0b9a\u0bb0\u0bbf\u0baf\u0bae\u0bcd, \u0b87\u0baf\u0bb1\u0bcd\u0b95\u0bc8, \u0b83\u0baa\u0bbf\u0baa\u0bcb\u0ba9\u0bbe\u0b95\u0bcd\u0b95\u0bbf \u0bb5\u0bb0\u0bbf\u0b9a\u0bc8\u0baa\u0bcd\u0baa\u0b9f\u0bbf \u0baa\u0bb2 \u0b85\u0bae\u0bc8\u0baa\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bc8\u0b95\u0bcd \u0b95\u0bca\u0ba3\u0bcd\u0b9f\u0bbf\u0bb0\u0bc1\u0baa\u0bcd\u0baa\u0ba4\u0bc1- \u0b92\u0bb0\u0bc1 \u0b95\u0bbf\u0bb3\u0bc8\u0baf\u0bc8\u0b9a\u0bcd \u0b9a\u0bc1\u0bb1\u0bcd\u0bb1\u0bbf\u0baa\u0bcd \u0baa\u0b9f\u0bb0\u0bcd\u0ba8\u0bcd\u0ba4\u0bc1 \u0ba4\u0bc1\u0bb3\u0bbf\u0bb0\u0bcd\u0bb5\u0bbf\u0b9f\u0bc1\u0bae\u0bcd<\/strong><\/span><br \/>\n<span style=\"color: #993300\"><strong>\u0b87\u0bb2\u0bc8\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0b8e\u0ba3\u0bcd\u0ba3\u0bbf\u0b95\u0bcd\u0b95\u0bc8. \u0b9a\u0bc2\u0bb0\u0bbf\u0baf\u0b95\u0bbe\u0ba8\u0bcd\u0ba4\u0bbf\u0baa\u0bcd \u0baa\u0bc2\u0bb5\u0bbf\u0ba9\u0bcd \u0b85\u0bb2\u0bcd\u0bb2\u0bbf\u0bb5\u0b9f\u0bcd\u0b9f\u0ba4\u0bcd\u0ba4\u0bbf\u0bb2\u0bcd \u0bb5\u0bbf\u0ba4\u0bc8\u0b95\u0bb3\u0bcd \u0baa\u0bb0\u0bb5\u0bbf\u0baf\u0bbf\u0bb0\u0bc1\u0b95\u0bcd\u0b95\u0bc1\u0bae\u0bcd \u0b85\u0bae\u0bc8\u0baa\u0bcd\u0baa\u0bc1, \u0baa\u0bc8\u0ba9\u0bcd \u0bae\u0bb0\u0ba4\u0bcd\u0ba4\u0bbf\u0ba9\u0bcd \u0b9a\u0bc6\u0ba4\u0bbf\u0bb2\u0bcd\u0b95\u0bb3\u0bcd- \u0b87\u0bb5\u0bc8 \u0baf\u0bbe\u0bb5\u0bc1\u0bae\u0bcd<\/strong><\/span><br \/>\n<span style=\"color: #993300\"><strong>\u0b83\u0baa\u0bbf\u0baa\u0bcb\u0ba9\u0bbe\u0b95\u0bcd\u0b95\u0bbf \u0ba8\u0bbf\u0bb0\u0bb2\u0bcd \u0b9a\u0bbe\u0bb0\u0bcd\u0ba8\u0bcd\u0ba4\u0bb5\u0bc8. Cumulative Growth \u0b8e\u0ba9\u0bcd\u0baa\u0ba4\u0bc7 \u0b83\u0baa\u0bbf\u0baa\u0bcb\u0ba9\u0bbe\u0b95\u0bcd\u0b95\u0bbf \u0bb5\u0bb0\u0bbf\u0b9a\u0bc8\u0baa\u0bcd\u0baa\u0b9f\u0bbf\u0ba4\u0bbe\u0ba9\u0bcd \u0ba8\u0bbf\u0b95\u0bb4\u0bc1\u0bae\u0bcd.<\/strong><\/span><\/p>\n<p><span style=\"color: #993300\"><strong>\u0b85\u0bb0\u0bc7\u0baa\u0bbf\u0baf \u0b8e\u0ba3\u0bcd\u0b95\u0bb3\u0bc8 \u0b89\u0bb2\u0b95\u0bae\u0baf\u0bae\u0bbe\u0b95\u0bcd\u0b95\u0bbf\u0baf\u0ba4\u0bbf\u0bb2\u0bc1\u0bae\u0bcd \u0b83\u0baa\u0bbf\u0baa\u0bcb\u0ba9\u0bbe\u0b95\u0bcd\u0b95\u0bbf\u0b95\u0bcd\u0b95\u0bc1\u0baa\u0bcd \u0baa\u0bc6\u0bb0\u0bc1\u0bae\u0bcd \u0baa\u0b99\u0bcd\u0b95\u0bc1 \u0b89\u0ba3\u0bcd\u0b9f\u0bc1.<\/strong><\/span><\/p>\n<p><span style=\"color: #993300\"><strong>\u0b8e\u0ba9\u0bcd \u0b95\u0bbe\u0bb2\u0bc8 \u0ba8\u0bc7\u0bb0\u0b95\u0bcd \u0b95\u0bc8\u0bb5\u0ba3\u0bcd\u0ba3\u0ba4\u0bcd\u0ba4\u0bbf\u0bb2\u0bcd \u0b87\u0ba4\u0bcb \u0b83\u0baa\u0bbf\u0baa\u0bcb\u0ba9\u0bbe\u0b95\u0bcd\u0b95\u0bbf\u0baf\u0bbf\u0ba9\u0bcd \u0b93\u0bb5\u0bbf\u0baf\u0bae\u0bcd.<\/strong><\/span><\/p>\n<p><span style=\"color: #993300\"><strong>(\u0b87\u0ba4\u0bc8 \u0bb5\u0bb0\u0bc8\u0baf &#8216;\u0bae\u0bc1\u0baf\u0bb2\u0bcd&#8217; \u0bb5\u0ba4\u0bc1 \u0b8e\u0ba9\u0b95\u0bcd\u0b95\u0bc1 \u0b9a\u0ba8\u0bcd\u0ba4\u0bcb\u0bb7\u0ba4\u0bcd\u0ba4\u0bc8\u0b95\u0bcd \u0b95\u0bca\u0b9f\u0bc1\u0ba4\u0bcd\u0ba4\u0ba4\u0bc1!)<\/strong><\/span><\/p>\n<p style=\"text-align: justify\"><a href=\"http:\/\/www.vallamai.com\/wp-content\/uploads\/2013\/05\/Fibonacci-2.jpg\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-35022\" src=\"http:\/\/www.vallamai.com\/wp-content\/uploads\/2013\/05\/Fibonacci-2.jpg\" alt=\"\" width=\"668\" height=\"677\" srcset=\"https:\/\/www.vallamai.com\/wp-content\/uploads\/2013\/05\/Fibonacci-2.jpg 768w, https:\/\/www.vallamai.com\/wp-content\/uploads\/2013\/05\/Fibonacci-2-296x300.jpg 296w\" sizes=\"(max-width: 668px) 100vw, 668px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0b9a\u0bc1.\u0bb0\u0bb5\u0bbf LEONARDO FIBONACCI (1170-1230) \u0b87\u0ba4\u0bcd\u0ba4\u0bbe\u0bb2\u0bbf\u0baf \u0ba8\u0bbe\u0b9f\u0bcd\u0b9f\u0bc8\u0b9a\u0bcd \u0b9a\u0bc7\u0bb0\u0bcd\u0ba8\u0bcd\u0ba4 \u0b95\u0ba3\u0bbf\u0ba4 \u0bae\u0bc7\u0ba4\u0bc8 \u0b83\u0baa\u0bbf\u0baa\u0bcb\u0ba9\u0bbe\u0b95\u0bcd\u0b95\u0bbf \u0ba4\u0ba8\u0bcd\u0ba4 \u0b95\u0ba3\u0b95\u0bcd\u0b95\u0bc1 \u0b87\u0ba4\u0bc1: &#8221; \u0b89\u0ba9\u0bcd\u0ba9\u0bbf\u0b9f\u0bae\u0bcd&#8230;<\/p>\n","protected":false},"author":162,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[629,491,501],"tags":[899],"class_list":["post-35021","post","type-post","status-publish","format-standard","hentry","category-home-lit","category-paintings","category-fine-arts","tag-899"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","featured_image_urls":{"full":"","thumbnail":"","medium":"","medium_large":"","large":"","1536x1536":"","2048x2048":"","covernews-featured":"","covernews-medium":""},"author_info":{"display_name":"\u0bae\u0bc1\u0ba9\u0bc8\u0bb5\u0bb0\u0bcd \u0b87\u0bb0\u0bbe. \u0baa\u0ba9\u0bcd\u0ba9\u0bbf\u0bb0\u0bc1\u0b95\u0bc8\u0bb5\u0b9f\u0bbf\u0bb5\u0bc7\u0bb2\u0ba9\u0bcd","author_link":"https:\/\/www.vallamai.com\/?author=162"},"category_info":"<a href=\"https:\/\/www.vallamai.com\/?cat=629\" rel=\"category\">home-lit<\/a> <a href=\"https:\/\/www.vallamai.com\/?cat=491\" rel=\"category\">\u0b93\u0bb5\u0bbf\u0baf\u0b99\u0bcd\u0b95\u0bb3\u0bcd<\/a> <a href=\"https:\/\/www.vallamai.com\/?cat=501\" rel=\"category\">\u0ba8\u0bc1\u0ba3\u0bcd\u0b95\u0bb2\u0bc8\u0b95\u0bb3\u0bcd<\/a>","tag_info":"\u0ba8\u0bc1\u0ba3\u0bcd\u0b95\u0bb2\u0bc8\u0b95\u0bb3\u0bcd","comment_count":"2","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.vallamai.com\/index.php?rest_route=\/wp\/v2\/posts\/35021","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vallamai.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vallamai.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vallamai.com\/index.php?rest_route=\/wp\/v2\/users\/162"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vallamai.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=35021"}],"version-history":[{"count":0,"href":"https:\/\/www.vallamai.com\/index.php?rest_route=\/wp\/v2\/posts\/35021\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vallamai.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=35021"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vallamai.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=35021"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vallamai.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=35021"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}