{"id":3451,"date":"2026-03-18T10:03:01","date_gmt":"2026-03-18T10:03:01","guid":{"rendered":"https:\/\/npk1169-001-site1.mtempurl.com\/?p=3451"},"modified":"2026-04-19T11:15:50","modified_gmt":"2026-04-19T11:15:50","slug":"fibonacci-numbers","status":"publish","type":"post","link":"https:\/\/www.bharatwisdom.com\/hi\/mathematics\/fibonacci-numbers\/","title":{"rendered":"\u092b\u093f\u092c\u094b\u0928\u093e\u091a\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u2013 \u0924\u093e\u0932 \u0915\u093e \u092a\u0930\u094d\u0935\u0924"},"content":{"rendered":"<div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1279.2px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-0 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:0px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-text fusion-text-1\"><p id=\"p-rc_ed88986f39805c81-229\" data-path-to-node=\"54\"><span data-path-to-node=\"54,0\"><b data-path-to-node=\"54,0\" data-index-in-node=\"0\">\u0905\u0935\u0927\u093e\u0930\u0923\u093e<\/b> <\/span><span data-path-to-node=\"54,2\"><span class=\"citation-965\">\u092b\u093f\u092c\u094b\u0928\u093e\u091a\u0940 \u0905\u0928\u0941\u0915\u094d\u0930\u092e (0, 1, 1, 2, 3, 5, 8\u2026) \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0940 \u090f\u0915 \u0910\u0938\u0940 \u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0909\u0938\u0938\u0947 \u092a\u0939\u0932\u0947 \u0915\u0940 \u0926\u094b \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u093e \u092f\u094b\u0917 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"54,4\">. <\/span><span data-path-to-node=\"54,6\"><span class=\"citation-964\">\u092f\u0939 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u092a\u0930\u093f\u0935\u0947\u0936\u094b\u0902 \u092e\u0947\u0902 \u092a\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u091c\u093f\u0928\u092e\u0947\u0902 \u092a\u093e\u0907\u0928\u0915\u094b\u0928 \u0915\u093e \u0938\u0930\u094d\u092a\u093f\u0932 \u0906\u0915\u093e\u0930 \u0914\u0930 \u092b\u0942\u0932\u094b\u0902 \u0915\u0940 \u092a\u0902\u0916\u0941\u0921\u093c\u093f\u092f\u094b\u0902 \u0915\u0940 \u0935\u094d\u092f\u0935\u0938\u094d\u0925\u093e \u0936\u093e\u092e\u093f\u0932 \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"54,8\">.<\/span><\/p>\n<p id=\"p-rc_ed88986f39805c81-230\" data-path-to-node=\"55\"><span data-path-to-node=\"55,0\"><b data-path-to-node=\"55,0\" data-index-in-node=\"0\">\u0915\u0939\u093e\u0928\u0940<\/b> <\/span><span data-path-to-node=\"55,2\"><span class=\"citation-963\">\u0938\u0928\u094d 1202 \u0908\u0938\u094d\u0935\u0940 \u092e\u0947\u0902, \u0932\u093f\u092f\u094b\u0928\u093e\u0930\u094d\u0921\u094b \u092b\u093f\u092c\u094b\u0928\u093e\u091a\u0940 \u0928\u0947 \u092f\u0942\u0930\u094b\u092a \u0915\u094b \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0940 \u090f\u0915 \u0910\u0938\u0940 \u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e \u0938\u0947 \u092a\u0930\u093f\u091a\u093f\u0924 \u0915\u0930\u093e\u092f\u093e \u091c\u094b \u092a\u094d\u0930\u0915\u0943\u0924\u093f \u092e\u0947\u0902 \u0939\u0930 \u091c\u0917\u0939 \u092a\u093e\u0908 \u091c\u093e\u0924\u0940 \u0925\u0940, \u091a\u0940\u0921\u093c \u0915\u0947 \u0936\u0902\u0915\u0941\u0913\u0902 \u0938\u0947 \u0932\u0947\u0915\u0930 \u092b\u0942\u0932\u094b\u0902 \u0915\u0940 \u092a\u0902\u0916\u0941\u0921\u093c\u093f\u092f\u094b\u0902 \u0924\u0915\u0964<\/span><\/span><span data-path-to-node=\"55,4\">. <\/span><span data-path-to-node=\"55,6\"><span class=\"citation-962\">\u0932\u0947\u0915\u093f\u0928 \u092d\u093e\u0930\u0924 \u092e\u0947\u0902 \u0907\u0928\u094d\u0939\u0947\u0902 \u092b\u093f\u092c\u094b\u0928\u093e\u091a\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u0928\u0939\u0940\u0902 \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0925\u093e; \u0907\u0928\u094d\u0939\u0947\u0902 &#039;\u0939\u0947\u092e\u091a\u0902\u0926\u094d\u0930-\u0935\u093f\u0930\u0939\u093e\u0902\u0915&#039; \u0905\u0928\u0941\u0915\u094d\u0930\u092e \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0925\u093e\u0964<\/span><\/span><span data-path-to-node=\"55,8\">. <\/span><span data-path-to-node=\"55,10\"><span class=\"citation-961\">\u092d\u093e\u0930\u0924\u0940\u092f \u092d\u093e\u0937\u093e\u0935\u093f\u0926\u094b\u0902 \u0928\u0947 \u092a\u093e\u092f\u093e \u0915\u093f \u0938\u0902\u0938\u094d\u0915\u0943\u0924 \u0915\u0935\u093f\u0924\u093e \u0915\u0940 \u0938\u0941\u0902\u0926\u0930\u0924\u093e \u0932\u0902\u092c\u0940 \u0914\u0930 \u091b\u094b\u091f\u0940 \u0932\u092f \u0915\u0947 \u090f\u0915 \u0935\u093f\u0936\u093f\u0937\u094d\u091f \u092a\u0948\u091f\u0930\u094d\u0928 \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"55,12\">. <\/span><span data-path-to-node=\"55,14\"><span class=\"citation-960\">\u0915\u093e\u0935\u094d\u092f \u0915\u0940 \u0939\u0930 \u0938\u0902\u092d\u0935 \u0935\u093f\u0935\u093f\u0927\u0924\u093e \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 &#039;\u0932\u092f \u0915\u093e \u092a\u0930\u094d\u0935\u0924&#039; (\u092e\u0947\u0930\u0941 \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0930\u093e) \u092c\u0928\u093e\u092f\u093e\u0964<\/span><\/span><span data-path-to-node=\"55,16\">. <\/span><span data-path-to-node=\"55,18\"><span class=\"citation-959\">\u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 \u092e\u0939\u0938\u0942\u0938 \u0915\u093f\u092f\u093e \u0915\u093f \u092a\u0939\u093e\u0921\u093c \u0915\u0940 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0928\u0908 \u092a\u0930\u0924 \u0905\u092a\u0928\u0947 \u090a\u092a\u0930 \u0915\u0940 \u0926\u094b \u092a\u0930\u0924\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 \u092e\u093e\u0924\u094d\u0930 \u0939\u0948\u2014\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 \u092a\u0936\u094d\u091a\u093f\u092e \u0938\u0947 \u0938\u0926\u093f\u092f\u094b\u0902 \u092a\u0939\u0932\u0947 \u091c\u0948\u0935\u093f\u0915 \u0935\u093f\u0915\u093e\u0938 \u0915\u0947 \u0917\u0923\u093f\u0924\u0940\u092f \u0930\u0939\u0938\u094d\u092f \u0915\u094b \u0938\u0941\u0932\u091d\u093e \u0932\u093f\u092f\u093e\u0964<\/span><\/span><span data-path-to-node=\"55,20\">.<\/span><\/p>\n<p data-path-to-node=\"56\"><b data-path-to-node=\"56\" data-index-in-node=\"0\">\u0938\u092e\u092f\u0930\u0947\u0916\u093e<\/b><\/p>\n<table data-path-to-node=\"57\">\n<thead>\n<tr>\n<td><strong>\u092e\u0940\u0932 \u0915\u093e \u092a\u0924\u094d\u0925\u0930<\/strong><\/td>\n<td><strong>\u0935\u093f\u0935\u0930\u0923<\/strong><\/td>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><span data-path-to-node=\"57,1,0,0\"><b data-path-to-node=\"57,1,0,0\" data-index-in-node=\"0\">\u092a\u0936\u094d\u091a\u093f\u092e\u0940 \u0938\u0902\u0926\u0930\u094d\u092d.<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_ed88986f39805c81-231\" data-path-to-node=\"57,1,1,0\"><span data-path-to-node=\"57,1,1,0,1\"><span class=\"citation-958\">1202 \u0908\u0938\u094d\u0935\u0940 (\u092b\u093f\u092c\u094b\u0928\u093e\u091a\u0940) <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"57,2,0,0\"><b data-path-to-node=\"57,2,0,0\" data-index-in-node=\"0\">\u0907\u0902\u0921. \u0938\u094d\u0930\u094b\u0924<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_ed88986f39805c81-232\" data-path-to-node=\"57,2,1,0\"><span data-path-to-node=\"57,2,1,0,0\">700 \u0908\u0938\u094d\u0935\u0940 (\u0935\u093f\u0930\u093e\u0939\u0902\u0915\u093e); <\/span><span data-path-to-node=\"57,2,1,0,2\"><span class=\"citation-957\">1150 \u0908. (\u0939\u0947\u092e\u091a\u0902\u0926\u094d\u0930) <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"57,3,0,0\"><b data-path-to-node=\"57,3,0,0\" data-index-in-node=\"0\">\u0915\u093e\u0932 \u0905\u0902\u0924\u0930\u093e\u0932<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_ed88986f39805c81-233\" data-path-to-node=\"57,3,1,0\"><span data-path-to-node=\"57,3,1,0,1\"><span class=\"citation-956\">500 \u0935\u0930\u094d\u0937\u094b\u0902 \u0938\u0947 \u0905\u0927\u093f\u0915 \u0915\u0940 \u092a\u0942\u0930\u094d\u0935 \u092a\u0930\u0902\u092a\u0930\u093e <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p data-path-to-node=\"58\"><b data-path-to-node=\"58\" data-index-in-node=\"0\">\u0938\u092c\u0942\u0924<\/b><\/p>\n<blockquote data-path-to-node=\"59\">\n<p id=\"p-rc_ed88986f39805c81-234\" data-path-to-node=\"59,0\"><span data-path-to-node=\"59,0,0\"><b data-path-to-node=\"59,0,0\" data-index-in-node=\"0\">\u0938\u0902\u0938\u094d\u0915\u0943\u0924 \u0936\u094d\u0932\u094b\u0915:<\/b> \u0915\u093f\u091e\u094d\u091a\u093f\u0924\u094d \u092a\u0942\u0930\u094d\u0935\u093e\u092a\u0930\u093e\u0919\u094d\u0915\u0947\u0928 \u092e\u093f\u0936\u094d\u0930\u092f\u093f\u0924\u094d\u0935\u093e \u0926\u0932\u0947\u0928 \u091a\u0964 <\/span><span data-path-to-node=\"59,0,2\"><span class=\"citation-955\">\u0938\u094d\u0925\u093e\u092a\u092f\u0947\u0924\u094d\u0924\u0924\u094d\u0930 \u0924\u0924\u094d\u0930\u0948\u0935 \u0936\u0947\u0937\u0902 \u0936\u0947\u0937\u0902 \u092a\u094d\u0930\u0915\u0932\u094d\u092a\u092f\u0947\u0924\u094d \u0965 <\/span><\/span><span data-path-to-node=\"59,0,4\"> <b data-path-to-node=\"59,0,4\" data-index-in-node=\"1\">\u0932\u093f\u092a\u094d\u092f\u0902\u0924\u0930\u0923:<\/b> \u0915\u093f\u0902\u091a\u093f\u0924\u094d \u092a\u0942\u0930\u094d\u0935\u092a\u0930\u0902\u0915\u0947\u0923 \u092e\u093f\u0936\u094d\u0930\u092f\u093f\u0924\u094d\u0935\u093e \u0926\u0932\u0947\u0928 \u091a | \u0938\u094d\u0925\u093e\u092a\u092f\u0947\u0924\u094d\u0924\u0924\u094d\u0930 \u0924\u0924\u094d\u0930\u0948\u0935 \u0936\u0947\u0937\u0902 \u0936\u0947\u0937\u0902 \u092a\u094d\u0930\u0915\u0932\u094d\u092a\u092f\u0947\u0924\u094d || (\u0935\u093f\u0930\u093e\u0939\u0902\u0915\u093e \u0926\u094d\u0935\u093e\u0930\u093e \u0935\u0943\u0924\u094d\u0924-\u091c\u093e\u0924\u093f-\u0938\u092e\u0941\u091a\u094d\u091a\u092f) <\/span><span data-path-to-node=\"59,0,7\"> <b data-path-to-node=\"59,0,7\" data-index-in-node=\"1\">\u0905\u0930\u094d\u0925:<\/b> '\u092a\u093f\u091b\u0932\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u0909\u0938\u0938\u0947 \u092a\u0939\u0932\u0947 \u0935\u093e\u0932\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u092e\u0947\u0902 \u092e\u093f\u0932\u093e\u0915\u0930 (\u091c\u094b\u0921\u093c\u0915\u0930), \u092f\u094b\u0917 \u0915\u094b \u0935\u0939\u093e\u0902 \u0930\u0916\u0947\u0902\u0964. <\/span><span data-path-to-node=\"59,0,9\"><span class=\"citation-953\">\u0907\u0938\u0938\u0947 \u0936\u0947\u0937 \u0917\u0923\u0928\u093e\u090f\u0901 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902\u0964 (\u092f\u0939 \u0905\u0928\u0941\u0915\u094d\u0930\u092e Fn = F + F \u0915\u093e \u0935\u0930\u094d\u0923\u0928 \u0915\u0930\u0924\u093e \u0939\u0948\u0964) <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/blockquote>\n<p id=\"p-rc_ed88986f39805c81-235\" data-path-to-node=\"60\"><span data-path-to-node=\"60,0\"><b data-path-to-node=\"60,0\" data-index-in-node=\"0\">\u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0928\u0935\u093e\u091a\u093e\u0930<\/b> <\/span><span data-path-to-node=\"60,2\"><span class=\"citation-952\">\u092a\u093f\u0902\u0917\u0932\u093e \u0915\u0947 \u091b\u0902\u0926\u0936\u093e\u0938\u094d\u0924\u094d\u0930 (\u0932\u0917\u092d\u0917 2000 \u0908\u0938\u093e \u092a\u0942\u0930\u094d\u0935) \u092e\u0947\u0902 \u092e\u0947\u0930\u0941 \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0930 \u0915\u093e \u0935\u093f\u0915\u093e\u0938 \u0939\u0941\u0906, \u091c\u094b \u090f\u0915 \u0938\u0902\u092f\u094b\u091c\u0928\u093e\u0924\u094d\u092e\u0915 &#039;\u0932\u092f \u0915\u093e \u092a\u0930\u094d\u0935\u0924&#039; \u0939\u0948 \u0914\u0930 \u092a\u093e\u0938\u094d\u0915\u0932 \u0915\u0947 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0938\u0947 \u092d\u0940 \u092a\u0939\u0932\u0947 \u0915\u093e \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"60,4\">. <\/span><span data-path-to-node=\"60,6\"><span class=\"citation-951\">\u0907\u0938\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093e\u0935\u094d\u092f \u091b\u0902\u0926\u094b\u0902 \u0915\u0947 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0909\u092a\u092f\u094b\u0917\u094b\u0902 \u0915\u094b \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0925\u093e\u0964<\/span><\/span><span data-path-to-node=\"60,8\">.<\/span><\/p>\n<p id=\"p-rc_ed88986f39805c81-236\" data-path-to-node=\"61\"><span data-path-to-node=\"61,0\"><b data-path-to-node=\"61,0\" data-index-in-node=\"0\">\u0906\u0927\u0941\u0928\u093f\u0915 \u0935\u093f\u0930\u093e\u0938\u0924<\/b> <\/span><span data-path-to-node=\"61,2\"><span class=\"citation-950\">\u092f\u0947 \u0906\u0902\u0915\u0921\u093c\u0947 \u0906\u0927\u0941\u0928\u093f\u0915 \u0905\u0928\u0941\u0938\u0902\u0927\u093e\u0928 \u0915\u0940 \u0928\u0940\u0902\u0935 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0915\u093e\u0930\u094d\u092f \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0907\u0928\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u091c\u0948\u0935\u093f\u0915 \u092e\u0949\u0921\u0932\u093f\u0902\u0917, \u0935\u093f\u0924\u094d\u0924\u0940\u092f \u092c\u093e\u091c\u093e\u0930 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0914\u0930 \u0915\u0902\u092a\u094d\u092f\u0942\u091f\u0930 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u092e \u092e\u0947\u0902 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"61,4\">.<\/span><\/p>\n<\/div><\/div><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":3502,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[74],"tags":[544,543,538,539,541,542,540],"class_list":["post-3451","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics","tag-ancient-indian-mathematics","tag-combinatorics","tag-fibonacci-sequence","tag-hemachandra","tag-meru-prastara","tag-pingala","tag-virahanka"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\r\n<title>Fibonacci Numbers \u2013 The Mountain of Cadence - BharatWisdom<\/title>\r\n<meta name=\"description\" content=\"Excerpt\" \/>\r\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, 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