{"id":49847,"date":"2024-12-01T14:37:19","date_gmt":"2024-12-01T12:37:19","guid":{"rendered":"https:\/\/www.lecturesbureau.gr\/1\/?p=49847"},"modified":"2024-12-01T14:45:10","modified_gmt":"2024-12-01T12:45:10","slug":"mathematical-induction","status":"publish","type":"post","link":"https:\/\/www.lecturesbureau.gr\/1\/mathematical-induction\/","title":{"rendered":"\u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03b5\u03c0\u03b1\u03b3\u03c9\u03b3\u03ae – \u039c\u03af\u03b1 \u03b1\u03c0\u03bb\u03ae \u03b1\u03bb\u03bb\u03ac \u03b9\u03c3\u03c7\u03c5\u03c1\u03ae \u03ba\u03b1\u03b9 \u03b5\u03c5\u03ad\u03bb\u03b9\u03ba\u03c4\u03b7 \u00b5\u03ad\u03b8\u03bf\u03b4\u03bf\u03c2 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7\u03c2 \u03c0\u03c1\u03bf\u03c4\u03ac\u03c3\u03b5\u03c9\u03bd \u03c0\u03bf\u03c5 \u03b1\u03c6\u03bf\u03c1\u03bf\u03cd\u03bd, \u03ac\u00b5\u03b5\u03c3\u03b1 \u03ae \u03ad\u00b5\u00b5\u03b5\u03c3\u03b1, \u03b1\u03ba\u03b5\u03c1\u03b1\u03af\u03bf\u03c5\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2"},"content":{"rendered":"

\u0397 (\u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae) \u03b5\u03c0\u03b1\u03b3\u03c9\u03b3\u03ae \u03b5\u03af\u03bd\u03b1\u03b9 \u00b5\u03af\u03b1 \u03b1\u03c0\u03bb\u03ae \u03b1\u03bb\u03bb\u03ac \u03b9\u03c3\u03c7\u03c5\u03c1\u03ae \u03ba\u03b1\u03b9 \u03b5\u03c5\u03ad\u03bb\u03b9\u03ba\u03c4\u03b7 \u00b5\u03ad\u03b8\u03bf\u03b4\u03bf\u03c2 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7\u03c2 \u03c0\u03c1\u03bf\u03c4\u03ac\u03c3\u03b5\u03c9\u03bd \u03c0\u03bf\u03c5 \u03b1\u03c6\u03bf\u03c1\u03bf\u03cd\u03bd, \u03ac\u00b5\u03b5\u03c3\u03b1 \u03ae \u03ad\u00b5\u00b5\u03b5\u03c3\u03b1, \u03b1\u03ba\u03b5\u03c1\u03b1\u03af\u03bf\u03c5\u03c2. \u0388\u03c7\u03b5\u03b9 \u03c7\u03c1\u03b7\u03c3\u03b9\u00b5\u03bf\u03c0\u03bf\u03b9\u03b7\u03b8\u03b5\u03af \u00b5\u03b5 \u03b5\u03c0\u03b9\u03c4\u03c5\u03c7\u03af\u03b1 \u03c3\u03b5 \u03c3\u03c7\u03b5\u03b4\u03cc\u03bd \u03cc\u03bb\u03bf \u03c4\u03bf \u03c6\u03ac\u03c3\u00b5\u03b1 \u03c4\u03c9\u03bd \u00b5\u03b1\u03b8\u03b7\u00b5\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd: \u03c4\u03b7\u03bd \u03c3\u03c5\u03bd\u03b1\u03bd\u03c4\u03ac\u00b5\u03b5 \u03c3\u03b5 \u00b5\u03b5\u03b3\u03ac\u03bb\u03bf \u03b5\u03cd\u03c1\u03bf\u03c2 \u03ba\u03bb\u03ac\u03b4\u03c9\u03bd \u03cc\u03c0\u03c9\u03c2 \u03c3\u03c4\u03b7\u03bd \u0386\u03bb\u03b3\u03b5\u03b2\u03c1\u03b1, \u03c3\u03c4\u03b7\u03bd \u0393\u03b5\u03c9\u00b5\u03b5\u03c4\u03c1\u03af\u03b1, \u03c3\u03c4\u03b7\u03bd \u03a4\u03c1\u03b9\u03b3\u03c9\u03bd\u03bf\u00b5\u03b5\u03c4\u03c1\u03af\u03b1, \u03c3\u03c4\u03b7\u03bd \u0391\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7, \u03c3\u03c4\u03b7\u03bd \u03a3\u03c5\u03bd\u03b4\u03c5\u03b1\u03c3\u03c4\u03b9\u03ba\u03ae, \u03c3\u03c4\u03b7\u03bd \u0398\u03b5\u03c9\u03c1\u03af\u03b1 \u0393\u03c1\u03b1\u03c6\u03b7\u00b5\u03ac\u03c4\u03c9\u03bd \u03ba\u03b1\u03b9 \u03c3\u03b5 \u03c0\u03bf\u03bb\u03bb\u03bf\u03cd\u03c2 \u03ac\u03bb\u03bb\u03bf\u03c5\u03c2 \u03ba\u03bb\u03ac\u03b4\u03bf\u03c5\u03c2.<\/p>\n

\u0397 \u03b1\u03c1\u03c7\u03ae \u03c4\u03b7\u03c2 \u03b5\u03c0\u03b1\u03b3\u03c9\u03b3\u03ae\u03c2 \u03ad\u03c7\u03b5\u03b9 \u00b5\u03b1\u03ba\u03c1\u03ac \u03b9\u03c3\u03c4\u03bf\u03c1\u03af\u03b1 \u03c3\u03c4\u03b1 \u00b5\u03b1\u03b8\u03b7\u00b5\u03b1\u03c4\u03b9\u03ba\u03ac. \u039a\u03b1\u03c4\u0384 \u03b1\u03c1\u03c7\u03ac\u03c2, \u03c0\u03b1\u03c1\u2019 \u03cc\u03bb\u03bf \u03c0\u03bf\u03c5 \u03b7 \u03af\u03b4\u03b9\u03b1 \u03b7 \u03b1\u03c1\u03c7\u03ae \u03b4\u03b5\u03bd \u03b4\u03b9\u03b1\u03c4\u03c5\u03c0\u03ce\u03bd\u03b5\u03c4\u03b1\u03b9 \u00b5\u03b5 \u03c3\u03b1\u03c6\u03ae\u03bd\u03b5\u03b9\u03b1 \u03c3\u03b5 \u03ba\u03b1\u03bd\u03ad\u03bd\u03b1 \u03b1\u03c1\u03c7\u03b1\u03af\u03bf \u03b5\u03bb\u03bb\u03b7\u03bd\u03b9\u03ba\u03cc \u03ba\u03b5\u03af\u00b5\u03b5\u03bd\u03bf, \u03c5\u03c0\u03ac\u03c1\u03c7\u03bf\u03c5\u03bd \u03b1\u03c1\u03ba\u03b5\u03c4\u03ac \u03c3\u03b7\u00b5\u03b5\u03af\u03b1 \u03cc\u03c0\u03bf\u03c5 \u03b3\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c7\u03c1\u03ae\u03c3\u03b7 \u03b5\u03bd\u03cc\u03c2 \u03c0\u03c1\u03cc\u03b4\u03c1\u03bf\u00b5\u03bf\u03c5 \u03c3\u03c4\u03b1\u03b4\u03af\u03bf\u03c5 \u03c4\u03b7\u03c2. \u0386\u03bb\u03bb\u03c9\u03c3\u03c4\u03b5 \u03bf\u03c1\u03b9\u03c3\u00b5\u03ad\u03bd\u03bf\u03b9 \u03b9\u03c3\u03c4\u03bf\u03c1\u03b9\u03ba\u03bf\u03af \u03b1\u03bd\u03b1\u03b3\u03bd\u03c9\u03c1\u03af\u03b6\u03bf\u03c5\u03bd \u03c3\u03c4\u03bf \u03b1\u03ba\u03cc\u03bb\u03bf\u03c5\u03b8\u03bf \u03c7\u03c9\u03c1\u03af\u03bf \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd \u03b4\u03b9\u03ac\u03bb\u03bf\u03b3\u03bf \u03a0\u03b1\u03c1\u00b5\u03b5\u03bd\u03af\u03b4\u03b7 (\u00a7147a7-c3) \u03c4\u03bf\u03c5 \u03a0\u03bb\u03ac\u03c4\u03c9\u03bd\u03b1 (427-347 BC) \u03c9\u03c2 \u03c4\u03b7\u03bd \u03b1\u03c1\u03c7\u03b1\u03b9\u03cc\u03c4\u03b5\u03c1\u03b7 \u03c7\u03c1\u03ae\u03c3\u03b7 \u03b5\u03c0\u03b1\u03b3\u03c9\u03b3\u03b9\u03ba\u03bf\u03cd \u03c3\u03c5\u03bb\u03bb\u03bf\u03b3\u03b9\u03c3\u00b5\u03bf\u03cd:
\n\u039a\u03b1\u03b9 \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03c5\u03c0\u03ac\u03c1\u03c7\u03bf\u03c5\u03bd \u03c4\u03bf\u03c5\u03bb\u03ac\u03c7\u03b9\u03c3\u03c4\u03bf\u03bd \u03b4\u03cd\u03bf \u03cc\u03c1\u03bf\u03b9, \u03b5\u03ac\u03bd \u03c0\u03c1\u03cc\u03ba\u03b5\u03b9\u03c4\u03b1\u03b9 \u03bd\u03b1 \u03c5\u03c0\u03ac\u03c1\u03c7\u03b5\u03b9 \u03b5\u03c0\u03b1\u03c6\u03ae. \u2013 \u03a0\u03c1\u03ad\u03c0\u03b5\u03b9 \u2013 \u0395\u03ac\u03bd \u03b4\u03b5 \u03c3\u03c4\u03bf\u03c5\u03c2 \u03b4\u03cd\u03bf \u03cc\u03c1\u03bf\u03c5\u03c2 \u03c0\u03c1\u03bf\u03c3\u03c4\u03b5\u03b8\u03b5\u03af \u03c4\u03c1\u03af\u03c4\u03bf\u03c2 \u03b4\u03b9\u03b1\u03b4\u03bf\u03c7\u03b9\u03ba\u03ac, \u03c4\u03cc\u03c4\u03b5 \u03b1\u03c5\u03c4\u03bf\u03af \u00b5\u03b5\u03bd \u03b8\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03c1\u03b5\u03b9\u03c2, \u03bf\u03b9 \u03b4\u03b5 \u03b5\u03c0\u03b1\u03c6\u03ad\u03c2 \u03b4\u03cd\u03bf. \u2013 \u039d\u03b1\u03b9 \u2013 \u039a\u03b1\u03b9 \u03ad\u03c4\u03c3\u03b9 \u03b1\u03bd \u03ad\u03bd\u03b1\u03c2 \u03cc\u03c1\u03bf\u03c2 \u03c0\u03c1\u03bf\u03c3\u03c4\u03af\u03b8\u03b5\u03c4\u03b1\u03b9 \u03c3\u03c5\u03bd\u03ad\u03c7\u03b5\u03b9\u03b1, \u03ba\u03b1\u03b9 \u00b5\u03af\u03b1 \u03b5\u03c0\u03b1\u03c6\u03ae \u03b8\u03b1 \u03c0\u03c1\u03bf\u03c3\u03c4\u03af\u03b8\u03b5\u03bd\u03c4\u03b1\u03b9, \u03ba\u03b1\u03b9 \u03ad\u03c0\u03b5\u03c4\u03b1\u03b9 \u03cc\u03c4\u03b9 \u03bf\u03b9 \u03b5\u03c0\u03b1\u03c6\u03ad\u03c2 \u03b8\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u00b5\u03af\u03b1 \u03bb\u03b9\u03b3\u03cc\u03c4\u03b5\u03c1\u03b5\u03c2 \u03b1\u03c0\u03cc \u03c4\u03bf \u03c0\u03bb\u03ae\u03b8\u03bf\u03c2 \u03c4\u03c9\u03bd \u03cc\u03c1\u03c9\u03bd. \u2206\u03b9\u03cc\u03c4\u03b9 \u00b5\u03b5 \u03cc\u03c0\u03bf\u03b9\u03bf\u03bd \u03b1\u03c1\u03b9\u03b8\u00b5\u03cc \u03c4\u03b1 \u03b4\u03cd\u03bf \u03c0\u03c1\u03ce\u03c4\u03b1 \u03c5\u03c0\u03b5\u03c1\u03ad\u03c7\u03bf\u03c5\u03bd \u03c4\u03bf\u03c5 \u03c0\u03bb\u03ae\u03b8\u03bf\u03c5\u03c2 \u03c4\u03c9\u03bd \u03b5\u03c0\u03b1\u03c6\u03ce\u03bd, \u00b5\u03b5 \u03c4\u03bf \u03af\u03b4\u03b9\u03bf \u03b1\u03c1\u03b9\u03b8\u00b5\u03cc \u03c4\u03bf \u00b5\u03b5\u03c4\u03ad\u03c0\u03b5\u03b9\u03c4\u03b1 \u03c0\u03bb\u03ae\u03b8\u03bf\u03c2 \u03c4\u03c9\u03bd \u03cc\u03c1\u03c9\u03bd \u03b8\u03b1 \u03c5\u03c0\u03b5\u03c1\u03b2\u03b1\u03af\u03bd\u03b5\u03b9 \u03c4\u03bf \u03c0\u03bb\u03ae\u03b8\u03bf\u03c2 \u03c4\u03c9\u03bd \u03b5\u03c0\u03b1\u03c6\u03ce\u03bd. \u2206\u03b9\u03cc\u03c4\u03b9 \u03ba\u03b1\u03c4\u03cc\u03c0\u03b9\u03bd \u03cc\u03c4\u03b1\u03bd \u03c0\u03c1\u03bf\u03c3\u03c4\u03af\u03b8\u03b5\u03c4\u03b1\u03b9 \u03ad\u03bd\u03b1\u03c2 \u03cc\u03c1\u03bf\u03c2, \u03c0\u03c1\u03bf\u03c3\u03c4\u03af\u03b8\u03b5\u03c4\u03b1\u03b9 \u03ba\u03b1\u03b9 \u00b5\u03af\u03b1 \u03b5\u03c0\u03b1\u03c6\u03ae \u03c3\u03c4\u03bf \u03c0\u03bb\u03ae\u03b8\u03bf\u03c2 \u03c4\u03c9\u03bd \u03b5\u03c0\u03b1\u03c6\u03ce\u03bd. \u2013 \u03a3\u03c9\u03c3\u03c4\u03ac \u2013 \u038c\u03c3\u03bf \u03bb\u03bf\u03b9\u03c0\u03cc\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03c0\u03bb\u03ae\u03b8\u03bf\u03c2 \u03c4\u03c9\u03bd \u03cc\u03c1\u03c9\u03bd, \u03c0\u03ac\u03bd\u03c4\u03b1 \u03bf\u03b9 \u03b5\u03c0\u03b1\u03c6\u03ad\u03c2 \u03b8\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03ba\u03b1\u03c4\u03ac \u00b5\u03af\u03b1 \u03bb\u03b9\u03b3\u03cc\u03c4\u03b5\u03c1\u03b5\u03c2. \u2013\u03a3\u03c9\u03c3\u03c4\u03ac -.<\/em>
\n\u03a4\u03bf \u03c0\u03c1\u03bf\u03b7\u03b3\u03bf\u03cd\u00b5\u03b5\u03bd\u03bf \u03c7\u03c9\u03c1\u03af\u03bf \u03b5\u03af\u03bd\u03b1\u03b9, \u03b2\u03ad\u03b2\u03b1\u03b9\u03b1, \u03b1\u03c0\u03cc \u03c6\u03b9\u03bb\u03bf\u03c3\u03bf\u03c6\u03b9\u03ba\u03cc \u03ba\u03b5\u03af\u00b5\u03b5\u03bd\u03bf. \u03a5\u03c0\u03ac\u03c1\u03c7\u03bf\u03c5\u03bd \u03cc\u00b5\u03c9\u03c2 \u03ba\u03b1\u03b9
\n\u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03ac \u00b5\u03b1\u03b8\u03b7\u00b5\u03b1\u03c4\u03b9\u03ba\u03ac \u03ad\u03c1\u03b3\u03b1 \u03c4\u03b1 \u03bf\u03c0\u03bf\u03af\u03b1 \u03c0\u03b5\u03c1\u03b9\u03ad\u03c7\u03bf\u03c5\u03bd \u00b5\u03b9\u03b1 \u03c0\u03c1\u03ce\u03b9\u00b5\u03b7 \u00b5\u03bf\u03c1\u03c6\u03ae \u03b5\u03c0\u03b1\u03b3\u03c9\u03b3\u03b9\u03ba\u03bf\u03cd \u03c3\u03c5\u03bb\u03bb\u03bf\u03b3\u03b9\u03c3\u00b5\u03bf\u03cd. \u0388\u03bd\u03b1 \u03c4\u03ad\u03c4\u03bf\u03b9\u03bf, \u03c0\u03b1\u03c1\u03b1\u03b4\u03b5\u03af\u03b3\u00b5\u03b1\u03c4\u03bf\u03c2 \u03c7\u03ac\u03c1\u03b9\u03bd, \u03b5\u03af\u03bd\u03b1\u03b9 \u03c3\u03c4\u03b1 \u03a3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03b1 \u03c4\u03bf\u03c5 \u0395\u03c5\u03ba\u03bb\u03b5\u03af\u03b4\u03b7 (~330 \u2013 ~ 265 \u03c0.\u03a7.) \u03a0\u03c1\u03cc\u03c4\u03b1\u03c3\u03b7 31 \u03c4\u03bf\u03c5 \u03b2\u03b9\u03b2\u03bb\u03af\u03bf\u03c5 VII, \u03cc\u03c0\u03bf\u03c5 \u03b1\u03c0\u03bf\u03b4\u03b5\u03b9\u03ba\u03bd\u03cd\u03b5\u03c4\u03b1\u03b9 \u03cc\u03c4\u03b9 \u03ba\u03ac\u03b8\u03b5 \u03c6\u03c5\u03c3\u03b9\u03ba\u03cc\u03c2 \u03b1\u03c1\u03b9\u03b8\u00b5\u03cc\u03c2 \u03b5\u03af\u03c4\u03b5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03b5\u03af\u03c4\u03b5 \u03b4\u03b9\u03b1\u03b9\u03c1\u03b5\u03af\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03ba\u03ac\u03c0\u03bf\u03b9\u03bf\u03bd \u03c0\u03c1\u03ce\u03c4\u03bf. \u039c\u03af\u03b1 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 \u03ba\u03ac\u03c0\u03c9\u03c2 \u03c0\u03b9\u03bf \u03ba\u03bf\u03bd\u03c4\u03ac \u03c3\u03c4\u03b7 \u03c3\u03cd\u03b3\u03c7\u03c1\u03bf\u03bd\u03b7 \u00b5\u03bf\u03c1\u03c6\u03ae \u03c4\u03b7\u03c2 \u03b5\u03c0\u03b1\u03b3\u03c9\u03b3\u03ae\u03c2 \u03c0\u03b5\u03c1\u03b9\u03ad\u03c7\u03b5\u03c4\u03b1\u03b9 \u03c3\u03c4\u03b7\u03bd \u03a3\u03c5\u03bd\u03b1\u03b3\u03c9\u03b3\u03ae \u03c4\u03bf\u03c5 \u03a0\u03ac\u03c0\u03c0\u03bf\u03c5 (~290-~350 \u00b5.\u03a7.). \u0395\u03ba\u03b5\u03af \u03b1\u03c0\u03bf\u03b4\u03b5\u03b9\u03ba\u03bd\u03cd\u03b5\u03c4\u03b1\u03b9 \u03c4\u03bf \u03b1\u03ba\u03cc\u03bb\u03bf\u03c5\u03b8\u03bf \u03b3\u03b5\u03c9\u00b5\u03b5\u03c4\u03c1\u03b9\u03ba\u03cc \u03b8\u03b5\u03ce\u03c1\u03b7\u00b5\u03b1:
\n\u0388\u03c3\u03c4\u03c9 AB \u03ad\u03bd\u03b1 \u03b5\u03c5\u03b8\u03cd\u03b3\u03c1\u03b1\u00b5\u00b5\u03bf \u03c4\u00b5\u03ae\u00b5\u03b1 \u03ba\u03b1\u03b9 C \u03ad\u03bd\u03b1 \u03c3\u03b7\u00b5\u03b5\u03af\u03bf \u03c4\u03bf\u03c5. \u0398\u03b5\u03c9\u03c1\u03bf\u03cd\u00b5\u03b5 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03af\u03b4\u03b9\u03b1 \u03c0\u03bb\u03b5\u03c5\u03c1\u03ac \u03c4\u03bf\u03c5 AB \u03c4\u03c1\u03af\u03b1 \u03b7\u00b5\u03b9\u03ba\u03cd\u03ba\u03bb\u03b9\u03b1 \u00b5\u03b5 \u03b4\u03b9\u03b1\u00b5\u03ad\u03c4\u03c1\u03bf\u03c5\u03c2 AB, AC \u03ba\u03b1\u03b9 CB, \u03b1\u03bd\u03c4\u03af\u03c3\u03c4\u03bf\u03b9\u03c7\u03b1. \u039a\u03b1\u03c4\u03b1\u03c3\u03ba\u03b5\u03c5\u03ac\u03b6\u03bf\u03c5\u00b5\u03b5 \u03c4\u03ce\u03c1\u03b1 \u03ba\u03cd\u03ba\u03bb\u03bf\u03c5\u03c2 Cn<\/sub>\u00a0\u03c9\u03c2 \u03b5\u03be\u03ae\u03c2: \u03bf C1<\/sub>\u00a0\u03b5\u03c6\u03ac\u03c0\u03c4\u03b5\u03c4\u03b1\u03b9 \u03c4\u03c9\u03bd \u03c4\u03c1\u03b9\u03ce\u03bd \u03c0\u03b1\u03c1\u03b1\u03c0\u03ac\u03bd\u03c9 \u03b7\u00b5\u03b9\u03ba\u03c5\u03ba\u03bb\u03af\u03c9\u03bd. \u039f Cn+1<\/sub>\u00a0\u03b5\u03c6\u03ac\u03c0\u03c4\u03b5\u03c4\u03b1\u03b9 \u03c4\u03bf\u03c5 Cn<\/sub>\u00a0\u03ba\u03b1\u03b9 \u03c4\u03c9\u03bd \u03b7\u00b5\u03b9\u03ba\u03c5\u03ba\u03bb\u03af\u03c9\u03bd \u03b5\u03c0\u03af \u03c4\u03c9\u03bd AB \u03ba\u03b1\u03b9 AC. \u0391\u03bd dn<\/sub>\u00a0\u03c4\u03bf \u00b5\u03ae\u03ba\u03bf\u03c2 \u03c4\u03b7\u03c2 \u03b4\u03b9\u03b1\u00b5\u03ad\u03c4\u03c1\u03bf\u03c5 \u03c4\u03bf\u03c5 Cn \u03ba\u03b1\u03b9 hn<\/sub>\u00a0\u03b7 \u03b1\u03c0\u03cc\u03c3\u03c4\u03b1\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03ba\u03ad\u03bd\u03c4\u03c1\u03bf\u03c5 \u03c4\u03bf\u03c5 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd AB. \u03a4\u03cc\u03c4\u03b5 hn<\/sub>\u00a0= n dn<\/sub>.<\/em>
\n\u039f \u03c4\u03c1\u03cc\u03c0\u03bf\u03c2 \u00b5\u03b5 \u03c4\u03bf\u03bd \u03bf\u03c0\u03bf\u03af\u03bf \u03b1\u03c0\u03bf\u03b4\u03b5\u03b9\u03ba\u03bd\u03cd\u03b5\u03b9 \u03c4\u03bf \u03b8\u03b5\u03ce\u03c1\u03b7\u00b5\u03b1 \u03bf \u03a0\u03ac\u03c0\u03c0\u03bf\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bd\u03b1 \u03b4\u03b5\u03af\u03be\u03b5\u03b9 \u03b3\u03b5\u03c9\u00b5\u03b5\u03c4\u03c1\u03b9\u03ba\u03ac \u03c4\u03b7\u03bd \u03b1\u03bd\u03b1\u03b4\u03c1\u03bf\u00b5\u03b9\u03ba\u03ae \u03c3\u03c7\u03ad\u03c3\u03b7 hn+1<\/sub>\/dn+1<\/sub>\u00a0= (hn<\/sub>\u00a0+ dn<\/sub>)\/dn<\/sub>. \u039a\u03b1\u03c4\u03cc\u03c0\u03b9\u03bd \u03b5\u03c0\u03b9\u03ba\u03b1\u03bb\u03b5\u03af\u03c4\u03b1\u03b9 \u03ad\u03bd\u03b1 \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u00b5\u03b1 \u03c4\u03bf\u03c5 \u0391\u03c1\u03c7\u03b9\u00b5\u03ae\u03b4\u03b7 (287 \u2013 212 \u03c0.\u03a7.) \u03b1\u03c0\u03cc \u03c4\u03bf \u03ad\u03c1\u03b3\u03bf \u03c4\u03bf\u03c5 \u039b\u03ae\u00b5\u00b5\u03b1\u03c4\u03b1 (\u03a0\u03c1\u03cc\u03c4\u03b1\u03c3\u03b7 6) \u03b7 \u03bf\u03c0\u03bf\u03af\u03b1 \u03b4\u03b5\u03af\u03c7\u03bd\u03b5\u03b9 \u03c4\u03b7\u03bd \u03bf\u03c1\u03b8\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c4\u03bf\u03c5 \u03c0\u03b1\u03c1\u03b1\u03c0\u03ac\u03bd\u03c9 \u03b8\u03b5\u03c9\u03c1\u03ae\u00b5\u03b1\u03c4\u03bf\u03c2 \u03c3\u03c4\u03b7\u03bd \u03c0\u03b5\u03c1\u03af\u03c0\u03c4\u03c9\u03c3\u03b7 n=1. \u03a7\u03c1\u03b7\u03c3\u03b9\u00b5\u03bf\u03c0\u03bf\u03b9\u03ce\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b7\u03bd \u03c4\u03b5\u03bb\u03b5\u03c5\u03c4\u03b1\u03af\u03b1 \u03c3\u03b5 \u03c3\u03c5\u03bd\u03b4\u03c5\u03b1\u03c3\u00b5\u03cc \u00b5\u03b5 \u03c4\u03b7\u03bd \u03b1\u03bd\u03b1\u03b4\u03c1\u03bf\u00b5\u03b9\u03ba\u03ae \u03c3\u03c7\u03ad\u03c3\u03b7, \u03c3\u03c5\u03bd\u03ac\u03b3\u03b5\u03b9 \u03c4\u03bf \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u00b5\u03b1 \u03b3\u03b9\u03b1 \u03c4\u03bf \u03b3\u03b5\u03bd\u03b9\u03ba\u03cc n.<\/p>\n

\u03a0\u0397\u0393\u0397 : physicsgg.me<\/p>\n

EIKONA : physicsgg.me<\/p>\n","protected":false},"excerpt":{"rendered":"

\u0397 (\u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae) \u03b5\u03c0\u03b1\u03b3\u03c9\u03b3\u03ae \u03b5\u03af\u03bd\u03b1\u03b9 \u00b5\u03af\u03b1 \u03b1\u03c0\u03bb\u03ae \u03b1\u03bb\u03bb\u03ac \u03b9\u03c3\u03c7\u03c5\u03c1\u03ae \u03ba\u03b1\u03b9 \u03b5\u03c5\u03ad\u03bb\u03b9\u03ba\u03c4\u03b7 \u00b5\u03ad\u03b8\u03bf\u03b4\u03bf\u03c2 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7\u03c2 \u03c0\u03c1\u03bf\u03c4\u03ac\u03c3\u03b5\u03c9\u03bd \u03c0\u03bf\u03c5 \u03b1\u03c6\u03bf\u03c1\u03bf\u03cd\u03bd, \u03ac\u00b5\u03b5\u03c3\u03b1 \u03ae \u03ad\u00b5\u00b5\u03b5\u03c3\u03b1, \u03b1\u03ba\u03b5\u03c1\u03b1\u03af\u03bf\u03c5\u03c2. \u0388\u03c7\u03b5\u03b9 \u03c7\u03c1\u03b7\u03c3\u03b9\u00b5\u03bf\u03c0\u03bf\u03b9\u03b7\u03b8\u03b5\u03af \u00b5\u03b5 \u03b5\u03c0\u03b9\u03c4\u03c5\u03c7\u03af\u03b1 \u03c3\u03b5 \u03c3\u03c7\u03b5\u03b4\u03cc\u03bd \u03cc\u03bb\u03bf \u03c4\u03bf \u03c6\u03ac\u03c3\u00b5\u03b1 \u03c4\u03c9\u03bd \u00b5\u03b1\u03b8\u03b7\u00b5\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd: \u03c4\u03b7\u03bd \u03c3\u03c5\u03bd\u03b1\u03bd\u03c4\u03ac\u00b5\u03b5 \u03c3\u03b5 \u00b5\u03b5\u03b3\u03ac\u03bb\u03bf \u03b5\u03cd\u03c1\u03bf\u03c2 \u03ba\u03bb\u03ac\u03b4\u03c9\u03bd \u03cc\u03c0\u03c9\u03c2 \u03c3\u03c4\u03b7\u03bd \u0386\u03bb\u03b3\u03b5\u03b2\u03c1\u03b1, \u03c3\u03c4\u03b7\u03bd \u0393\u03b5\u03c9\u00b5\u03b5\u03c4\u03c1\u03af\u03b1, \u03c3\u03c4\u03b7\u03bd \u03a4\u03c1\u03b9\u03b3\u03c9\u03bd\u03bf\u00b5\u03b5\u03c4\u03c1\u03af\u03b1, \u03c3\u03c4\u03b7\u03bd \u0391\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7,…<\/p>\n","protected":false},"author":2,"featured_media":49845,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[66],"tags":[2311,975,1535,2309,2312,2093,1709,2310,2308],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?fit=500%2C530&ssl=1","rttpg_featured_image_url":{"full":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?fit=500%2C530&ssl=1",500,530,false],"landscape":["https:\/\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png",500,530,false],"portraits":["https:\/\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png",500,530,false],"thumbnail":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?resize=150%2C150&ssl=1",150,150,true],"medium":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?fit=283%2C300&ssl=1",283,300,true],"large":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?fit=500%2C530&ssl=1",500,530,true],"1536x1536":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?fit=500%2C530&ssl=1",500,530,true],"2048x2048":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?fit=500%2C530&ssl=1",500,530,true],"portfolio-square":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?resize=500%2C530&ssl=1",500,530,true],"portfolio-portrait":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?resize=500%2C530&ssl=1",500,530,true],"portfolio-landscape":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?resize=500%2C530&ssl=1",500,530,true],"menu-featured-post":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?resize=345%2C198&ssl=1",345,198,true],"qode-carousel_slider":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?resize=400%2C260&ssl=1",400,260,true],"portfolio_slider":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?resize=500%2C380&ssl=1",500,380,true],"portfolio_masonry_regular":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?resize=500%2C500&ssl=1",500,500,true],"portfolio_masonry_wide":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?resize=500%2C500&ssl=1",500,500,true],"portfolio_masonry_tall":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?resize=500%2C530&ssl=1",500,530,true],"portfolio_masonry_large":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?resize=500%2C530&ssl=1",500,530,true],"portfolio_masonry_with_space":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?fit=500%2C530&ssl=1",500,530,true],"latest_post_boxes":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?resize=500%2C303&ssl=1",500,303,true],"woocommerce_thumbnail":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?resize=300%2C300&ssl=1",300,300,true],"woocommerce_single":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?fit=500%2C530&ssl=1",500,530,true],"woocommerce_gallery_thumbnail":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2024\/12\/induction-1.png?resize=100%2C100&ssl=1",100,100,true]},"rttpg_author":{"display_name":"E M","author_link":"https:\/\/www.lecturesbureau.gr\/1\/author\/e7\/"},"rttpg_comment":0,"rttpg_category":"\u0395\u03a0\u0399\u03a3\u03a4\u0397\u039c\u0397<\/a>","rttpg_excerpt":"\u0397 (\u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae) \u03b5\u03c0\u03b1\u03b3\u03c9\u03b3\u03ae \u03b5\u03af\u03bd\u03b1\u03b9 \u00b5\u03af\u03b1 \u03b1\u03c0\u03bb\u03ae \u03b1\u03bb\u03bb\u03ac \u03b9\u03c3\u03c7\u03c5\u03c1\u03ae \u03ba\u03b1\u03b9 \u03b5\u03c5\u03ad\u03bb\u03b9\u03ba\u03c4\u03b7 \u00b5\u03ad\u03b8\u03bf\u03b4\u03bf\u03c2 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7\u03c2 \u03c0\u03c1\u03bf\u03c4\u03ac\u03c3\u03b5\u03c9\u03bd \u03c0\u03bf\u03c5 \u03b1\u03c6\u03bf\u03c1\u03bf\u03cd\u03bd, \u03ac\u00b5\u03b5\u03c3\u03b1 \u03ae \u03ad\u00b5\u00b5\u03b5\u03c3\u03b1, \u03b1\u03ba\u03b5\u03c1\u03b1\u03af\u03bf\u03c5\u03c2. \u0388\u03c7\u03b5\u03b9 \u03c7\u03c1\u03b7\u03c3\u03b9\u00b5\u03bf\u03c0\u03bf\u03b9\u03b7\u03b8\u03b5\u03af \u00b5\u03b5 \u03b5\u03c0\u03b9\u03c4\u03c5\u03c7\u03af\u03b1 \u03c3\u03b5 \u03c3\u03c7\u03b5\u03b4\u03cc\u03bd \u03cc\u03bb\u03bf \u03c4\u03bf \u03c6\u03ac\u03c3\u00b5\u03b1 \u03c4\u03c9\u03bd \u00b5\u03b1\u03b8\u03b7\u00b5\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd: \u03c4\u03b7\u03bd \u03c3\u03c5\u03bd\u03b1\u03bd\u03c4\u03ac\u00b5\u03b5 \u03c3\u03b5 \u00b5\u03b5\u03b3\u03ac\u03bb\u03bf \u03b5\u03cd\u03c1\u03bf\u03c2 \u03ba\u03bb\u03ac\u03b4\u03c9\u03bd \u03cc\u03c0\u03c9\u03c2 \u03c3\u03c4\u03b7\u03bd \u0386\u03bb\u03b3\u03b5\u03b2\u03c1\u03b1, \u03c3\u03c4\u03b7\u03bd \u0393\u03b5\u03c9\u00b5\u03b5\u03c4\u03c1\u03af\u03b1, \u03c3\u03c4\u03b7\u03bd \u03a4\u03c1\u03b9\u03b3\u03c9\u03bd\u03bf\u00b5\u03b5\u03c4\u03c1\u03af\u03b1, \u03c3\u03c4\u03b7\u03bd \u0391\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7,...","_links":{"self":[{"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/posts\/49847"}],"collection":[{"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/comments?post=49847"}],"version-history":[{"count":3,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/posts\/49847\/revisions"}],"predecessor-version":[{"id":49850,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/posts\/49847\/revisions\/49850"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/media\/49845"}],"wp:attachment":[{"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/media?parent=49847"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/categories?post=49847"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/tags?post=49847"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}