{"id":429,"date":"2024-12-26T13:47:32","date_gmt":"2024-12-26T11:47:32","guid":{"rendered":"https:\/\/blogs.sch.gr\/pmantzaris\/?p=429"},"modified":"2024-12-26T13:47:32","modified_gmt":"2024-12-26T11:47:32","slug":"o-arithmos-2025-ena-mathimatiko-taxidi-kai-i-gefyra-pros-ton-srinivasa-ramanujan","status":"publish","type":"post","link":"https:\/\/pmantzaris.sites.sch.gr\/?p=429","title":{"rendered":"\u039f \u0391\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 2025: \u0388\u03bd\u03b1 \u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u03a4\u03b1\u03be\u03af\u03b4\u03b9 \u03ba\u03b1\u03b9 \u03b7 \u0393\u03ad\u03c6\u03c5\u03c1\u03b1 \u03c0\u03c1\u03bf\u03c2 \u03c4\u03bf\u03bd Srinivasa Ramanujan"},"content":{"rendered":"<p>\u03a3\u03c4\u03bf\u03bd \u03ba\u03cc\u03c3\u03bc\u03bf \u03c4\u03c9\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd, \u03ba\u03ac\u03b8\u03b5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03ba\u03c1\u03cd\u03b2\u03b5\u03b9 \u03bc\u03bf\u03bd\u03b1\u03b4\u03b9\u03ba\u03ad\u03c2 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03ba\u03b1\u03b9 \u03c3\u03c5\u03bd\u03b4\u03ad\u03c3\u03b5\u03b9\u03c2. \u03a4\u03bf \u03ad\u03c4\u03bf\u03c2 <strong>2025<\/strong> \u03b5\u03af\u03bd\u03b1\u03b9 \u03ad\u03bd\u03b1 \u03c7\u03b1\u03c1\u03b1\u03ba\u03c4\u03b7\u03c1\u03b9\u03c3\u03c4\u03b9\u03ba\u03cc \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1, \u03ba\u03b1\u03b8\u03ce\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03ad\u03bd\u03b1 <strong>\u03c4\u03ad\u03bb\u03b5\u03b9\u03bf \u03c4\u03b5\u03c4\u03c1\u03ac\u03b3\u03c9\u03bd\u03bf<\/strong>. \u0397 \u03b1\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7 \u03c4\u03c9\u03bd \u03b9\u03b4\u03b9\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd \u03c4\u03bf\u03c5 \u03bc\u03b1\u03c2 \u03bf\u03b4\u03b7\u03b3\u03b5\u03af \u03c3\u03b5 \u03ad\u03bd\u03b1\u03bd \u03b1\u03c0\u03cc \u03c4\u03bf\u03c5\u03c2 \u03c0\u03b9\u03bf \u03b4\u03b9\u03ac\u03c3\u03b7\u03bc\u03bf\u03c5\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03cc\u03bb\u03c9\u03bd \u03c4\u03c9\u03bd \u03b5\u03c0\u03bf\u03c7\u03ce\u03bd, \u03c4\u03bf\u03bd <strong>Srinivasa Ramanujan<\/strong>, \u03c4\u03bf\u03c5 \u03bf\u03c0\u03bf\u03af\u03bf\u03c5 \u03b7 \u03b6\u03c9\u03ae \u03ba\u03b1\u03b9 \u03c4\u03bf \u03ad\u03c1\u03b3\u03bf \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03bf\u03cd\u03bd \u03c0\u03b7\u03b3\u03ae \u03ad\u03bc\u03c0\u03bd\u03b5\u03c5\u03c3\u03b7\u03c2 \u03b3\u03b9\u03b1 \u03cc\u03bb\u03bf\u03c5\u03c2 \u03c4\u03bf\u03c5\u03c2 \u03bb\u03ac\u03c4\u03c1\u03b5\u03b9\u03c2 \u03c4\u03c9\u03bd \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd.<\/p>\n<blockquote><p><strong>\u0399\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03c4\u03bf\u03c5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd 2025<\/strong><\/p><\/blockquote>\n<ol>\n<li><strong>\u03a4\u03ad\u03bb\u03b5\u03b9\u03bf \u03a4\u03b5\u03c4\u03c1\u03ac\u03b3\u03c9\u03bd\u03bf: <\/strong>\u03a4\u03bf <strong>2025<\/strong> \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03c4\u03b5\u03c4\u03c1\u03ac\u03b3\u03c9\u03bd\u03bf \u03c4\u03bf\u03c5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd <strong>45<\/strong>, \u03b4\u03b7\u03bb\u03b1\u03b4\u03ae: <span class=\"katex\">2025 = 45^2<\/span><\/li>\n<li><strong>\u03a0\u03b1\u03c1\u03b1\u03b3\u03bf\u03bd\u03c4\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7: <\/strong>\u039f \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 2025 \u03c0\u03b1\u03c1\u03b1\u03b3\u03bf\u03bd\u03c4\u03bf\u03c0\u03bf\u03b9\u03b5\u03af\u03c4\u03b1\u03b9 \u03c9\u03c2 \u03b5\u03be\u03ae\u03c2: <span class=\"katex\">2025=3^4\u22c55^2<\/span><\/li>\n<li><strong>\u03a8\u03b7\u03c6\u03b9\u03b1\u03ba\u03ae \u0391\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7:<\/strong>\n<ul>\n<li>\u03a4\u03bf \u03ac\u03b8\u03c1\u03bf\u03b9\u03c3\u03bc\u03b1 \u03c4\u03c9\u03bd \u03c8\u03b7\u03c6\u03af\u03c9\u03bd \u03c4\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 <strong><span class=\"katex\">2 + 0 + 2 + 5 = 9<\/span><\/strong>, \u03c0\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b5\u03c0\u03af\u03c3\u03b7\u03c2 \u03c4\u03ad\u03bb\u03b5\u03b9\u03bf \u03c4\u03b5\u03c4\u03c1\u03ac\u03b3\u03c9\u03bd\u03bf.<\/li>\n<li>\u0391\u03bd \u03b4\u03b9\u03b1\u03c7\u03c9\u03c1\u03af\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b1 \u03c8\u03b7\u03c6\u03af\u03b1 \u03c4\u03bf\u03c5 \u03c3\u03b5 <span class=\"katex\">20<\/span> \u03ba\u03b1\u03b9 <span class=\"katex\">25<\/span>, \u03c4\u03bf \u03ac\u03b8\u03c1\u03bf\u03b9\u03c3\u03bc\u03ac \u03c4\u03bf\u03c5\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 <span class=\"katex\">45<\/span>, \u03b7 \u03c4\u03b5\u03c4\u03c1\u03b1\u03b3\u03c9\u03bd\u03b9\u03ba\u03ae \u03c1\u03af\u03b6\u03b1 \u03c4\u03bf\u03c5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd.<\/li>\n<\/ul>\n<\/li>\n<li><strong>\u0398\u03ad\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd \u03c3\u03c4\u03bf \u03c0: <\/strong>\u0397 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1 \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd 2025 \u03b5\u03bc\u03c6\u03b1\u03bd\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03b3\u03b9\u03b1 \u03c0\u03c1\u03ce\u03c4\u03b7 \u03c6\u03bf\u03c1\u03ac \u03c3\u03c4\u03b1 \u03b4\u03b5\u03ba\u03b1\u03b4\u03b9\u03ba\u03ac \u03c8\u03b7\u03c6\u03af\u03b1 \u03c4\u03bf\u03c5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd <span class=\"katex\"><span class=\"katex-mathml\">\u03c0<\/span><\/span>\u00a0\u03c3\u03c4\u03b7 \u03b8\u03ad\u03c3\u03b7 33.953 (\u03b1\u03bd \u03bc\u03b5\u03c4\u03c1\u03ae\u03c3\u03bf\u03c5\u03bc\u03b5 \u03b1\u03c0\u03cc \u03c4\u03bf \u03c0\u03c1\u03ce\u03c4\u03bf \u03b4\u03b5\u03ba\u03b1\u03b4\u03b9\u03ba\u03cc \u03c8\u03b7\u03c6\u03af\u03bf).<\/li>\n<\/ol>\n<blockquote><p><strong>\u03a4\u03b1 \u03a4\u03ad\u03bb\u03b5\u03b9\u03b1 \u03a4\u03b5\u03c4\u03c1\u03ac\u03b3\u03c9\u03bd\u03b1 \u0388\u03c4\u03b7 \u03bc.\u03a7.<\/strong><\/p><\/blockquote>\n<p>\u03a3\u03c4\u03b7\u03bd \u03b9\u03c3\u03c4\u03bf\u03c1\u03af\u03b1 \u03c4\u03b7\u03c2 \u03b1\u03bd\u03b8\u03c1\u03ce\u03c0\u03b9\u03bd\u03b7\u03c2 \u03c7\u03c1\u03bf\u03bd\u03bf\u03bb\u03cc\u03b3\u03b7\u03c3\u03b7\u03c2, \u03b1\u03c1\u03ba\u03b5\u03c4\u03ac \u03ad\u03c4\u03b7 \u03bc.\u03a7. \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03ad\u03bb\u03b5\u03b9\u03b1 \u03c4\u03b5\u03c4\u03c1\u03ac\u03b3\u03c9\u03bd\u03b1. \u0391\u03c5\u03c4\u03ac \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u03c4\u03b7\u03c2 \u03bc\u03bf\u03c1\u03c6\u03ae\u03c2 <span class=\"katex\"><span class=\"katex-mathml\">n^2<\/span><\/span>, \u03cc\u03c0\u03bf\u03c5 <span class=\"katex\"><span class=\"katex-mathml\">n \u2208 N. <\/span><\/span>\u0391\u03c0\u03cc \u03c4\u03bf 1\u03bc.\u03a7. \u03ad\u03c9\u03c2 \u03c4\u03bf 2025\u03bc.\u03a7. \u03c4\u03b1 \u03c4\u03ad\u03bb\u03b5\u03b9\u03b1 \u03c4\u03b5\u03c4\u03c1\u03ac\u03b3\u03c9\u03bd\u03b1 \u03ad\u03c4\u03b7 \u03b5\u03af\u03bd\u03b1\u03b9: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025.<\/p>\n<blockquote><p><strong>\u0399\u03c3\u03c4\u03bf\u03c1\u03b9\u03ba\u03ae \u03ba\u03b1\u03b9 \u0395\u03ba\u03c0\u03b1\u03b9\u03b4\u03b5\u03c5\u03c4\u03b9\u03ba\u03ae \u03a0\u03c1\u03bf\u03c3\u03ad\u03b3\u03b3\u03b9\u03c3\u03b7<\/strong><\/p><\/blockquote>\n<p>\u0397 \u03bc\u03b5\u03bb\u03ad\u03c4\u03b7 \u03c4\u03ad\u03c4\u03bf\u03b9\u03c9\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03ad\u03c3\u03b5\u03b9 \u03ad\u03bd\u03b1\u03c5\u03c3\u03bc\u03b1 \u03b3\u03b9\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03b5\u03be\u03b5\u03c1\u03b5\u03cd\u03bd\u03b7\u03c3\u03b7 \u03c3\u03c4\u03b7\u03bd \u03c4\u03ac\u03be\u03b7:<\/p>\n<ul>\n<li><strong>\u03a3\u03cd\u03bd\u03b4\u03b5\u03c3\u03b7 \u03bc\u03b5 \u0399\u03c3\u03c4\u03bf\u03c1\u03af\u03b1<\/strong>: \u03a4\u03b9 \u03c3\u03c5\u03bd\u03ad\u03b2\u03b7 \u03c3\u03c4\u03b1 \u03c4\u03ad\u03bb\u03b5\u03b9\u03b1 \u03c4\u03b5\u03c4\u03c1\u03ac\u03b3\u03c9\u03bd\u03b1 \u03ad\u03c4\u03b7; \u03a0\u03bf\u03b9\u03b1 \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03ac \u03b3\u03b5\u03b3\u03bf\u03bd\u03cc\u03c4\u03b1 \u03b4\u03b9\u03b1\u03bc\u03cc\u03c1\u03c6\u03c9\u03c3\u03b1\u03bd \u03c4\u03b7\u03bd \u03c0\u03bf\u03c1\u03b5\u03af\u03b1 \u03c4\u03b7\u03c2 \u03b1\u03bd\u03b8\u03c1\u03c9\u03c0\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2;<\/li>\n<li><strong>\u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u0395\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ae<\/strong>: \u0391\u03bd\u03b1\u03ba\u03b1\u03bb\u03cd\u03c8\u03c4\u03b5 \u03c4\u03b9\u03c2 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03c4\u03c9\u03bd \u03c4\u03ad\u03bb\u03b5\u03b9\u03c9\u03bd \u03c4\u03b5\u03c4\u03c1\u03b1\u03b3\u03ce\u03bd\u03c9\u03bd, \u03b5\u03c3\u03c4\u03b9\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c3\u03b5 \u03c0\u03b1\u03c1\u03b1\u03b3\u03bf\u03bd\u03c4\u03bf\u03c0\u03bf\u03b9\u03ae\u03c3\u03b5\u03b9\u03c2 \u03ba\u03b1\u03b9 \u03b3\u03b5\u03c9\u03bc\u03b5\u03c4\u03c1\u03b9\u03ba\u03ad\u03c2 \u03b5\u03c1\u03bc\u03b7\u03bd\u03b5\u03af\u03b5\u03c2.<\/li>\n<li><strong>\u03a0\u03c1\u03bf\u03b2\u03bb\u03ae\u03bc\u03b1\u03c4\u03b1 \u03c0\u03c1\u03bf\u03c2 \u03b5\u03c0\u03af\u03bb\u03c5\u03c3\u03b7<\/strong>: \u03a0\u03bf\u03b9\u03bf \u03b8\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03b5\u03c0\u03cc\u03bc\u03b5\u03bd\u03bf \u03c4\u03ad\u03bb\u03b5\u03b9\u03bf \u03c4\u03b5\u03c4\u03c1\u03ac\u03b3\u03c9\u03bd\u03bf \u03ad\u03c4\u03bf\u03c2;<\/li>\n<\/ul>\n<blockquote><p><strong>\u0391\u03c0\u03cc \u03c4\u03bf 2025 \u03c3\u03c4\u03bf\u03bd Srinivasa Ramanujan<\/strong><\/p><\/blockquote>\n<p>\u0397 \u03b1\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7 \u03c4\u03bf\u03c5 2025 \u03c6\u03ad\u03c1\u03bd\u03b5\u03b9 \u03c3\u03c4\u03bf \u03c0\u03c1\u03bf\u03c3\u03ba\u03ae\u03bd\u03b9\u03bf \u03c4\u03b7\u03bd \u03ad\u03bd\u03bd\u03bf\u03b9\u03b1 \u03c4\u03b7\u03c2 \u03c0\u03b1\u03c1\u03b1\u03b3\u03bf\u03bd\u03c4\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7\u03c2, \u03c4\u03b7\u03c2 \u03c3\u03c5\u03bc\u03bc\u03b5\u03c4\u03c1\u03af\u03b1\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03b7\u03c2 \u03b1\u03b9\u03c3\u03b8\u03b7\u03c4\u03b9\u03ba\u03ae\u03c2 \u03c4\u03c9\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd. \u0391\u03c5\u03c4\u03cc \u03bc\u03b1\u03c2 \u03bf\u03b4\u03b7\u03b3\u03b5\u03af \u03c3\u03c4\u03bf\u03bd <strong>Srinivasa Ramanujan<\/strong> (1887\u20131920), \u03ad\u03bd\u03b1\u03bd \u03b1\u03c0\u03cc \u03c4\u03bf\u03c5\u03c2 \u03c0\u03b9\u03bf \u03b5\u03c0\u03b9\u03b4\u03c1\u03b1\u03c3\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03c4\u03b7\u03c2 \u03b5\u03c0\u03bf\u03c7\u03ae\u03c2 \u03c4\u03bf\u03c5, \u03bf \u03bf\u03c0\u03bf\u03af\u03bf\u03c2 \u03b5\u03af\u03c7\u03b5 \u03b2\u03b1\u03b8\u03b9\u03ac \u03b1\u03bd\u03c4\u03af\u03bb\u03b7\u03c8\u03b7 \u03b3\u03b9\u03b1 \u03c4\u03b9\u03c2 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03c4\u03c9\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd.<\/p>\n<blockquote><p><strong>\u039c\u03b9\u03b1 \u03a3\u03cd\u03bd\u03c4\u03bf\u03bc\u03b7 \u0392\u03b9\u03bf\u03b3\u03c1\u03b1\u03c6\u03af\u03b1<\/strong><\/p><\/blockquote>\n<p>\u039f Ramanujan \u03b3\u03b5\u03bd\u03bd\u03ae\u03b8\u03b7\u03ba\u03b5 \u03c3\u03c4\u03b7\u03bd \u0399\u03bd\u03b4\u03af\u03b1 \u03ba\u03b1\u03b9 \u03b1\u03bd\u03ad\u03c0\u03c4\u03c5\u03be\u03b5 \u03c4\u03bf \u03b5\u03bd\u03b4\u03b9\u03b1\u03c6\u03ad\u03c1\u03bf\u03bd \u03c4\u03bf\u03c5 \u03b3\u03b9\u03b1 \u03c4\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03c3\u03b5 \u03bd\u03b5\u03b1\u03c1\u03ae \u03b7\u03bb\u03b9\u03ba\u03af\u03b1. \u03a0\u03b1\u03c1\u03ac \u03c4\u03b7\u03bd \u03ad\u03bb\u03bb\u03b5\u03b9\u03c8\u03b7 \u03b5\u03c0\u03af\u03c3\u03b7\u03bc\u03b7\u03c2 \u03b5\u03ba\u03c0\u03b1\u03af\u03b4\u03b5\u03c5\u03c3\u03b7\u03c2, \u03ac\u03c1\u03c7\u03b9\u03c3\u03b5 \u03bd\u03b1 \u03b1\u03bd\u03b1\u03ba\u03b1\u03bb\u03cd\u03c0\u03c4\u03b5\u03b9 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ad\u03c2 \u03c3\u03c7\u03ad\u03c3\u03b5\u03b9\u03c2 \u03ba\u03b1\u03b9 \u03b8\u03b5\u03c9\u03c1\u03ae\u03bc\u03b1\u03c4\u03b1 \u03bc\u03b5 \u03b5\u03bb\u03ac\u03c7\u03b9\u03c3\u03c4\u03b1 \u03bc\u03ad\u03c3\u03b1. \u03a4\u03bf 1913, \u03b7 \u03b1\u03bb\u03bb\u03b7\u03bb\u03bf\u03b3\u03c1\u03b1\u03c6\u03af\u03b1 \u03c4\u03bf\u03c5 \u03bc\u03b5 \u03c4\u03bf\u03bd \u0392\u03c1\u03b5\u03c4\u03b1\u03bd\u03cc \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc <strong>G. H. Hardy<\/strong> \u03c4\u03bf\u03bd \u03bf\u03b4\u03ae\u03b3\u03b7\u03c3\u03b5 \u03c3\u03c4\u03bf \u03a0\u03b1\u03bd\u03b5\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b9\u03bf \u03c4\u03bf\u03c5 \u039a\u03ad\u03b9\u03bc\u03c0\u03c1\u03b9\u03c4\u03b6.<\/p>\n<blockquote><p><strong>\u03a4\u03bf \u0388\u03c1\u03b3\u03bf \u03c4\u03bf\u03c5 Ramanujan<\/strong><\/p><\/blockquote>\n<p>\u039f Ramanujan \u03c3\u03c5\u03bd\u03b5\u03b9\u03c3\u03ad\u03c6\u03b5\u03c1\u03b5 \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03ac \u03c3\u03c4\u03bf\u03c5\u03c2 \u03c0\u03b1\u03c1\u03b1\u03ba\u03ac\u03c4\u03c9 \u03c4\u03bf\u03bc\u03b5\u03af\u03c2:<\/p>\n<ol>\n<li><strong>\u0398\u03b5\u03c9\u03c1\u03af\u03b1 \u0391\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd<\/strong><br \/>\n\u039f Ramanujan \u03b1\u03bd\u03ad\u03c0\u03c4\u03c5\u03be\u03b5 \u03c0\u03c1\u03c9\u03c4\u03bf\u03c0\u03bf\u03c1\u03b9\u03b1\u03ba\u03ac \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03ad\u03c3\u03bc\u03b1\u03c4\u03b1 \u03c3\u03c7\u03b5\u03c4\u03b9\u03ba\u03ac \u03bc\u03b5 \u03c4\u03bf\u03c5\u03c2 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c5\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03b9\u03c2 \u03b4\u03b9\u03b1\u03af\u03c1\u03b5\u03c3\u03b5\u03b9\u03c2.<\/li>\n<li><strong>\u039c\u03b1\u03b3\u03b9\u03ba\u03bf\u03af \u0391\u03c1\u03b9\u03b8\u03bc\u03bf\u03af<\/strong><br \/>\n\u039c\u03af\u03b1 \u03b4\u03b9\u03ac\u03c3\u03b7\u03bc\u03b7 \u03b9\u03c3\u03c4\u03bf\u03c1\u03af\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03c3\u03c7\u03ad\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03bc\u03b5 \u03c4\u03bf\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc <strong>1729<\/strong>, \u03c4\u03bf\u03bd \u03bf\u03c0\u03bf\u03af\u03bf \u03bf\u03bd\u03cc\u03bc\u03b1\u03c3\u03b5 &#8220;\u03c4\u03bf\u03bd \u03bc\u03b9\u03ba\u03c1\u03cc\u03c4\u03b5\u03c1\u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03c0\u03bf\u03c5 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03b3\u03c1\u03b1\u03c6\u03c4\u03b5\u03af \u03c9\u03c2 \u03ac\u03b8\u03c1\u03bf\u03b9\u03c3\u03bc\u03b1 \u03b4\u03cd\u03bf \u03ba\u03cd\u03b2\u03c9\u03bd \u03bc\u03b5 \u03b4\u03cd\u03bf \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03b5\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03c4\u03c1\u03cc\u03c0\u03bf\u03c5\u03c2&#8221;:<span class=\"katex\">1729 = 1^3 + 12^3 = 9^3 + 10^3<\/span><\/li>\n<li><strong>\u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ad\u03c2 \u03a3\u03c5\u03bd\u03b1\u03c1\u03c4\u03ae\u03c3\u03b5\u03b9\u03c2<\/strong><br \/>\n\u0391\u03bd\u03ad\u03c0\u03c4\u03c5\u03be\u03b5 \u03c4\u03b9\u03c2 \u03c3\u03c5\u03bd\u03b1\u03c1\u03c4\u03ae\u03c3\u03b5\u03b9\u03c2 Ramanujan, \u03c0\u03bf\u03c5 \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03bf\u03cd\u03bd\u03c4\u03b1\u03b9 \u03b1\u03ba\u03cc\u03bc\u03b1 \u03c3\u03c4\u03b7 \u03b8\u03b5\u03c9\u03c1\u03af\u03b1 \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd \u03ba\u03b1\u03b9 \u03c3\u03c4\u03b7 \u03c6\u03c5\u03c3\u03b9\u03ba\u03ae.<\/li>\n<\/ol>\n<blockquote><p><strong>\u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u0388\u03bc\u03c0\u03bd\u03b5\u03c5\u03c3\u03b7<\/strong><\/p><\/blockquote>\n<p>\u039f Ramanujan \u03ad\u03b2\u03bb\u03b5\u03c0\u03b5 \u03c4\u03bf\u03c5\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2 \u03c9\u03c2 \u03c6\u03af\u03bb\u03bf\u03c5\u03c2 \u03bc\u03b5 \u03ba\u03c1\u03c5\u03bc\u03bc\u03ad\u03bd\u03b1 \u03bc\u03c5\u03c3\u03c4\u03b9\u03ba\u03ac. \u03a0\u03af\u03c3\u03c4\u03b5\u03c5\u03b5 \u03cc\u03c4\u03b9 \u03ba\u03ac\u03b8\u03b5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03b5\u03af\u03c7\u03b5 \u03c4\u03b7 \u03b4\u03b9\u03ba\u03ae \u03c4\u03bf\u03c5 \u03bf\u03bc\u03bf\u03c1\u03c6\u03b9\u03ac \u03ba\u03b1\u03b9 \u03b9\u03c3\u03c4\u03bf\u03c1\u03af\u03b1. \u0391\u03c5\u03c4\u03ae \u03b7 \u03c6\u03b9\u03bb\u03bf\u03c3\u03bf\u03c6\u03af\u03b1 \u03b1\u03bd\u03c4\u03b9\u03ba\u03b1\u03c4\u03bf\u03c0\u03c4\u03c1\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c3\u03c4\u03bf\u03bd \u03c4\u03c1\u03cc\u03c0\u03bf \u03c0\u03bf\u03c5 \u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u03cc\u03c0\u03c9\u03c2 \u03c4\u03bf 2025 \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03bd \u03bd\u03b1 \u03bc\u03b1\u03c2 \u03bf\u03b4\u03b7\u03b3\u03ae\u03c3\u03bf\u03c5\u03bd \u03c3\u03b5 \u03b2\u03b1\u03b8\u03cd\u03c4\u03b5\u03c1\u03b7 \u03ba\u03b1\u03c4\u03b1\u03bd\u03cc\u03b7\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae\u03c2 \u03b1\u03b9\u03c3\u03b8\u03b7\u03c4\u03b9\u03ba\u03ae\u03c2.<\/p>\n<blockquote><p><strong>\u0393\u03b9\u03b1\u03c4\u03af \u03bd\u03b1 \u0394\u03b9\u03b4\u03ac\u03be\u03bf\u03c5\u03bc\u03b5 Ramanujan \u03c3\u03c4\u03b7\u03bd \u03a4\u03ac\u03be\u03b7<\/strong><\/p><\/blockquote>\n<p>\u0397 \u03b6\u03c9\u03ae \u03ba\u03b1\u03b9 \u03c4\u03bf \u03ad\u03c1\u03b3\u03bf \u03c4\u03bf\u03c5 Ramanujan \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03bf\u03cd\u03bd \u03ad\u03bd\u03b1\u03c5\u03c3\u03bc\u03b1 \u03b3\u03b9\u03b1 \u03b5\u03ba\u03c0\u03b1\u03b9\u03b4\u03b5\u03c5\u03c4\u03b9\u03ba\u03ae \u03c3\u03c5\u03b6\u03ae\u03c4\u03b7\u03c3\u03b7:<\/p>\n<ul>\n<li><strong>\u03a3\u03cd\u03bd\u03b4\u03b5\u03c3\u03b7 \u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd \u03ba\u03b1\u03b9 \u0399\u03c3\u03c4\u03bf\u03c1\u03af\u03b1\u03c2<\/strong>: \u03a0\u03ce\u03c2 \u03ad\u03bd\u03b1\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u0399\u03bd\u03b4\u03af\u03b1 \u03ac\u03bb\u03bb\u03b1\u03be\u03b5 \u03c4\u03b7\u03bd \u03c0\u03bf\u03c1\u03b5\u03af\u03b1 \u03c4\u03b7\u03c2 \u03c0\u03b1\u03b3\u03ba\u03cc\u03c3\u03bc\u03b9\u03b1\u03c2 \u03b5\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b7\u03c2;<\/li>\n<li><strong>\u0395\u03bc\u03c0\u03bd\u03b5\u03c5\u03c3\u03bc\u03ad\u03bd\u03b5\u03c2 \u0399\u03c3\u03c4\u03bf\u03c1\u03af\u03b5\u03c2<\/strong>: \u0397 \u03c0\u03bf\u03c1\u03b5\u03af\u03b1 \u03c4\u03bf\u03c5 Ramanujan \u03b4\u03b5\u03af\u03c7\u03bd\u03b5\u03b9 \u03cc\u03c4\u03b9 \u03c4\u03bf \u03c4\u03b1\u03bb\u03ad\u03bd\u03c4\u03bf \u03ba\u03b1\u03b9 \u03c4\u03bf \u03c0\u03ac\u03b8\u03bf\u03c2 \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03bd \u03bd\u03b1 \u03be\u03b5\u03c0\u03b5\u03c1\u03ac\u03c3\u03bf\u03c5\u03bd \u03ba\u03ac\u03b8\u03b5 \u03b5\u03bc\u03c0\u03cc\u03b4\u03b9\u03bf.<\/li>\n<li><strong>\u0395\u03be\u03b5\u03c1\u03b5\u03cd\u03bd\u03b7\u03c3\u03b7 \u0391\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd<\/strong>: \u0395\u03c1\u03b3\u03b1\u03c3\u03af\u03b5\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03c0\u03b1\u03c1\u03b1\u03b3\u03bf\u03bd\u03c4\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7, \u03c4\u03b1 \u03c4\u03ad\u03bb\u03b5\u03b9\u03b1 \u03c4\u03b5\u03c4\u03c1\u03ac\u03b3\u03c9\u03bd\u03b1 \u03ba\u03b1\u03b9 \u03c4\u03bf\u03c5\u03c2 &#8220;\u03bc\u03b1\u03b3\u03b9\u03ba\u03bf\u03cd\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2&#8221;.<\/li>\n<\/ul>\n<blockquote><p><strong>\u03a3\u03c5\u03bc\u03c0\u03b5\u03c1\u03b1\u03c3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac<\/strong><\/p><\/blockquote>\n<p>\u03a4\u03bf <strong>2025<\/strong>, \u03c9\u03c2 \u03c4\u03ad\u03bb\u03b5\u03b9\u03bf \u03c4\u03b5\u03c4\u03c1\u03ac\u03b3\u03c9\u03bd\u03bf, \u03bc\u03b1\u03c2 \u03c5\u03c0\u03b5\u03bd\u03b8\u03c5\u03bc\u03af\u03b6\u03b5\u03b9 \u03cc\u03c4\u03b9 \u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03c0\u03bb\u03ce\u03c2 \u03c3\u03cd\u03bc\u03b2\u03bf\u03bb\u03b1, \u03b1\u03bb\u03bb\u03ac \u03c0\u03cd\u03bb\u03b5\u03c2 \u03c0\u03c1\u03bf\u03c2 \u03c4\u03b7 \u03b3\u03bd\u03ce\u03c3\u03b7 \u03ba\u03b1\u03b9 \u03c4\u03b7\u03bd \u03b1\u03bd\u03b1\u03ba\u03ac\u03bb\u03c5\u03c8\u03b7. \u0391\u03bd\u03b1\u03ba\u03b1\u03bb\u03cd\u03c0\u03c4\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b9\u03c2 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03ad\u03c2 \u03c4\u03bf\u03c5, \u03b2\u03bb\u03ad\u03c0\u03bf\u03c5\u03bc\u03b5 \u03c0\u03ce\u03c2 \u03c4\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03c3\u03c5\u03bd\u03b4\u03ad\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03c4\u03b7\u03bd \u0399\u03c3\u03c4\u03bf\u03c1\u03af\u03b1 \u03ba\u03b1\u03b9 \u03c4\u03b7\u03bd \u0395\u03ba\u03c0\u03b1\u03af\u03b4\u03b5\u03c5\u03c3\u03b7. \u0391\u03c0\u03bf\u03ba\u03b1\u03bb\u03cd\u03c0\u03c4\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b9\u03c2 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03ad\u03c2 \u03c4\u03bf\u03c5, \u03ba\u03ac\u03bd\u03bf\u03c5\u03bc\u03b5 \u03ad\u03bd\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u03c4\u03b1\u03be\u03af\u03b4\u03b9 \u03c0\u03bf\u03c5 \u03bc\u03b1\u03c2 \u03c3\u03c5\u03bd\u03b4\u03ad\u03b5\u03b9 \u03bc\u03b5 \u03c4\u03bf\u03bd Ramanujan \u03ba\u03b1\u03b9 \u03c4\u03bf \u03cc\u03c1\u03b1\u03bc\u03ac \u03c4\u03bf\u03c5 \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03bf\u03bc\u03bf\u03c1\u03c6\u03b9\u03ac \u03c4\u03c9\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd. \u0397 \u03bc\u03b5\u03bb\u03ad\u03c4\u03b7 \u03c4\u03bf\u03c5 \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03c0\u03bb\u03ce\u03c2 \u03ad\u03bd\u03b1 \u03bc\u03ac\u03b8\u03b7\u03bc\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd, \u03b1\u03bb\u03bb\u03ac \u03bc\u03b9\u03b1 \u03c5\u03c0\u03b5\u03bd\u03b8\u03cd\u03bc\u03b9\u03c3\u03b7 \u03b3\u03b9\u03b1 \u03c4\u03bf \u03c0\u03ce\u03c2 \u03b7 \u03b1\u03bd\u03b8\u03c1\u03ce\u03c0\u03b9\u03bd\u03b7 \u03b5\u03c5\u03c6\u03c5\u0390\u03b1 \u03ba\u03b1\u03b9 \u03c4\u03bf \u03c0\u03ac\u03b8\u03bf\u03c2 \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03bd \u03bd\u03b1 \u03b1\u03c6\u03ae\u03c3\u03bf\u03c5\u03bd \u03b1\u03bd\u03b5\u03be\u03af\u03c4\u03b7\u03bb\u03bf \u03c3\u03c4\u03af\u03b3\u03bc\u03b1.<\/p>\n<hr \/>\n<blockquote><p><strong>\u0392\u03b9\u03b2\u03bb\u03b9\u03bf\u03b3\u03c1\u03b1\u03c6\u03af\u03b1<\/strong><\/p><\/blockquote>\n<ul>\n<li>Burton, D. M. (2010).\u00a0<em>Elementary Number Theory<\/em>. McGraw-Hill Education.<\/li>\n<li>Hardy, G. H. (1940). <em>A Mathematician&#8217;s Apology<\/em>. Cambridge University Press.<\/li>\n<li>Kanigel, R. (1991). <em>The Man Who Knew Infinity: A Life of the Genius Ramanujan<\/em>. Washington Square Press.<\/li>\n<li>Niven, I., Zuckerman, H. S., &amp; Montgomery, H. L. (1991). <em>An Introduction to the Theory of Numbers<\/em>. Wiley.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u03a3\u03c4\u03bf\u03bd \u03ba\u03cc\u03c3\u03bc\u03bf \u03c4\u03c9\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd, \u03ba\u03ac\u03b8\u03b5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03ba\u03c1\u03cd\u03b2\u03b5\u03b9 \u03bc\u03bf\u03bd\u03b1\u03b4\u03b9\u03ba\u03ad\u03c2 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03ba\u03b1\u03b9 \u03c3\u03c5\u03bd\u03b4\u03ad\u03c3\u03b5\u03b9\u03c2. \u03a4\u03bf \u03ad\u03c4\u03bf\u03c2 2025 \u03b5\u03af\u03bd\u03b1\u03b9 \u03ad\u03bd\u03b1 \u03c7\u03b1\u03c1\u03b1\u03ba\u03c4\u03b7\u03c1\u03b9\u03c3\u03c4\u03b9\u03ba\u03cc \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1, \u03ba\u03b1\u03b8\u03ce\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03ad\u03bd\u03b1 \u03c4\u03ad\u03bb\u03b5\u03b9\u03bf \u03c4\u03b5\u03c4\u03c1\u03ac\u03b3\u03c9\u03bd\u03bf. \u0397 \u03b1\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7 \u03c4\u03c9\u03bd \u03b9\u03b4\u03b9\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd \u03c4\u03bf\u03c5 \u03bc\u03b1\u03c2 \u03bf\u03b4\u03b7\u03b3\u03b5\u03af \u03c3\u03b5 \u03ad\u03bd\u03b1\u03bd \u03b1\u03c0\u03cc \u03c4\u03bf\u03c5\u03c2 \u03c0\u03b9\u03bf \u03b4\u03b9\u03ac\u03c3\u03b7\u03bc\u03bf\u03c5\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03cc\u03bb\u03c9\u03bd \u03c4\u03c9\u03bd \u03b5\u03c0\u03bf\u03c7\u03ce\u03bd, \u03c4\u03bf\u03bd Srinivasa Ramanujan, \u03c4\u03bf\u03c5 \u03bf\u03c0\u03bf\u03af\u03bf\u03c5 \u03b7 \u03b6\u03c9\u03ae \u03ba\u03b1\u03b9 \u03c4\u03bf \u03ad\u03c1\u03b3\u03bf \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03bf\u03cd\u03bd \u03c0\u03b7\u03b3\u03ae \u03ad\u03bc\u03c0\u03bd\u03b5\u03c5\u03c3\u03b7\u03c2 \u03b3\u03b9\u03b1 \u03cc\u03bb\u03bf\u03c5\u03c2&#8230;<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[],"class_list":["post-429","post","type-post","status-publish","format-standard","hentry","category-arthrografia"],"_links":{"self":[{"href":"https:\/\/pmantzaris.sites.sch.gr\/index.php?rest_route=\/wp\/v2\/posts\/429","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pmantzaris.sites.sch.gr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pmantzaris.sites.sch.gr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pmantzaris.sites.sch.gr\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/pmantzaris.sites.sch.gr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=429"}],"version-history":[{"count":0,"href":"https:\/\/pmantzaris.sites.sch.gr\/index.php?rest_route=\/wp\/v2\/posts\/429\/revisions"}],"wp:attachment":[{"href":"https:\/\/pmantzaris.sites.sch.gr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=429"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pmantzaris.sites.sch.gr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=429"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pmantzaris.sites.sch.gr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=429"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}