{"id":19330,"date":"2016-10-01T23:58:22","date_gmt":"2016-10-01T20:58:22","guid":{"rendered":"http:\/\/www.lecturesbureau.gr\/1\/?p=19330"},"modified":"2016-10-01T23:24:48","modified_gmt":"2016-10-01T20:24:48","slug":"the-multifarious-e","status":"publish","type":"post","link":"https:\/\/www.lecturesbureau.gr\/1\/the-multifarious-e\/","title":{"rendered":"\u039f \u03c0\u03bf\u03bb\u03c5\u03c3\u03c7\u03b9\u03b4\u03ae\u03c2 e"},"content":{"rendered":"<p>\u039f \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 <strong>e<\/strong> \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03b9\u03b1 \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03ae \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac \u03c0\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03b2\u03ac\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03c6\u03c5\u03c3\u03b9\u03ba\u03bf\u03cd \u03bb\u03bf\u03b3\u03b1\u03c1\u03af\u03b8\u03bc\u03bf\u03c5. \u0395\u03af\u03bd\u03b1\u03b9 \u03c0\u03b5\u03c1\u03af\u03c0\u03bf\u03c5 \u03af\u03c3\u03b7 \u03bc\u03b5 <strong>2,71828<\/strong> \u03ba\u03b1\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03cc\u03c1\u03b9\u03bf \u03c4\u03b7\u03c2 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1\u03c2 \u00a0<strong>(1 + 1\/<i>n<\/i>)<\/strong><sup><i><strong>n<\/strong>\u00a0<\/i><\/sup> \u03cc\u03c3\u03bf \u03c4\u03bf n \u03c0\u03bb\u03b7\u03c3\u03b9\u03ac\u03b6\u03b5\u03b9 \u03c4\u03bf \u03ac\u03c0\u03b5\u03b9\u03c1\u03bf, \u03bc\u03b9\u03b1 \u03ad\u03ba\u03c6\u03c1\u03b1\u03c3\u03b7 \u03c0\u03bf\u03c5 \u03c0\u03c1\u03bf\u03ba\u03cd\u03c0\u03c4\u03b5\u03b9 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03bc\u03b5\u03bb\u03ad\u03c4\u03b7 \u03c4\u03c9\u03bd \u03c3\u03cd\u03bd\u03b8\u03b5\u03c4\u03c9\u03bd \u03c4\u03cc\u03ba\u03c9\u03bd. \u039c\u03c0\u03bf\u03c1\u03b5\u03af \u03b5\u03c0\u03af\u03c3\u03b7\u03c2 \u03bd\u03b1 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03c4\u03b5\u03af \u03c9\u03c2 \u03c4\u03bf \u03ac\u03b8\u03c1\u03bf\u03b9\u03c3\u03bc\u03b1 \u03c4\u03b7\u03c2 \u03ac\u03c0\u03b5\u03b9\u03c1\u03b7\u03c2 \u03c3\u03b5\u03b9\u03c1\u03ac\u03c2<\/p>\n<p>\u0391\u03c0\u03bf\u03ba\u03b1\u03bb\u03bf\u03cd\u03bc\u03b5\u03bd\u03bf\u03c2 \u03bc\u03b5\u03c1\u03b9\u03ba\u03ad\u03c2 \u03c6\u03bf\u03c1\u03ad\u03c2 \u03c9\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u038c\u03b9\u03bb\u03b5\u03c1 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd \u0395\u03bb\u03b2\u03b5\u03c4\u03cc \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u039b\u03ad\u03bf\u03bd\u03b1\u03c1\u03bd\u03c4 \u038c\u03b9\u03bb\u03b5\u03c1. \u039f \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 e \u03b5\u03af\u03bd\u03b1\u03b9 \u03b5\u03c0\u03af\u03c3\u03b7\u03c2 \u03b3\u03bd\u03c9\u03c3\u03c4\u03cc\u03c2 \u03c9\u03c2 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac \u03c4\u03bf\u03c5 Napier, \u03b1\u03bb\u03bb\u03ac \u03b7 \u03b5\u03c0\u03b9\u03bb\u03bf\u03b3\u03ae \u03c4\u03bf\u03c5 Euler \u03c4\u03bf\u03c5 \u03c3\u03c5\u03bc\u03b2\u03cc\u03bb\u03bf\u03c5 e \u03bb\u03ad\u03b3\u03b5\u03c4\u03b1\u03b9 \u03cc\u03c4\u03b9 \u03ad\u03c7\u03b5\u03b9 \u03b4\u03b9\u03b1\u03c4\u03b7\u03c1\u03b7\u03b8\u03b5\u03af \u03c0\u03c1\u03bf\u03c2 \u03c4\u03b9\u03bc\u03ae\u03bd \u03c4\u03bf\u03c5. \u039f <strong>e<\/strong> \u03b1\u03bd\u03b1\u03ba\u03b1\u03bb\u03cd\u03c6\u03b8\u03b7\u03ba\u03b5 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd \u0395\u03bb\u03b2\u03b5\u03c4\u03cc \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u0393\u03b9\u03b1\u03ba\u03cc\u03bc\u03c0 \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9 \u03cc\u03c4\u03b1\u03bd \u03bc\u03b5\u03bb\u03b5\u03c4\u03bf\u03cd\u03c3\u03b5 \u03c3\u03cd\u03bd\u03b8\u03b5\u03c4\u03bf\u03c5\u03c2 \u03c4\u03cc\u03ba\u03bf\u03c5\u03c2.<br \/>\n\u0397 \u03b5\u03ba\u03b8\u03b5\u03c4\u03b9\u03ba\u03ae \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7, <strong><span style=\"color: #000000;\"><span style=\"font-family: 'Times New Roman',serif;\"><span style=\"font-size: medium;\"><i>f<\/i><\/span><\/span><\/span><span style=\"color: #000000;\"><span style=\"font-family: 'Times New Roman',serif;\"><span style=\"font-size: medium;\">(<\/span><\/span><\/span><span style=\"color: #000000;\"><span style=\"font-family: 'Times New Roman',serif;\"><span style=\"font-size: medium;\"><i>x<\/i><\/span><\/span><\/span><span style=\"color: #000000;\"><span style=\"font-family: 'Times New Roman',serif;\"><span style=\"font-size: medium;\">) = <\/span><\/span><\/span><span style=\"color: #000000;\"><span style=\"font-family: 'Times New Roman',serif;\"><span style=\"font-size: medium;\"><i>e<\/i><\/span><\/span><\/span><\/strong><span style=\"color: #000000;\"><sup><span style=\"font-family: 'Times New Roman', serif;\"><span style=\"font-size: medium;\"><i><strong>x<\/strong>\u00a0<\/i><\/span><\/span><\/sup><\/span>\u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03c3\u03c4\u03b9\u03b3\u03bc\u03ae \u03c4\u03bf\u03c5 \u03bf\u03c1\u03b9\u03c3\u03bc\u03bf\u03cd \u03c4\u03b7\u03c2 \u03ad\u03b3\u03b9\u03bd\u03b5 \u03bc\u03af\u03b1 \u03b1\u03c0\u03cc \u03c4\u03b9\u03c2 \u03b4\u03b9\u03b1\u03c3\u03b7\u03bc\u03cc\u03c4\u03b5\u03c1\u03b5\u03c2 (\u03b1\u03bd \u03cc\u03c7\u03b9 \u03b7 \u03b4\u03b9\u03b1\u03c3\u03b7\u03bc\u03cc\u03c4\u03b5\u03c1\u03b7) \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7. \u0397 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7 \u03b1\u03c5\u03c4\u03ae \u03ad\u03c7\u03b5\u03b9 \u03c4\u03b7\u03bd \u03b5\u03be\u03b1\u03b9\u03c1\u03b5\u03c4\u03b9\u03ba\u03ae \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1 \u03bd\u03b1 \u03b9\u03c3\u03bf\u03cd\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03c0\u03b1\u03c1\u03ac\u03b3\u03c9\u03b3\u03bf \u03c4\u03b7\u03c2. \u0391\u03c5\u03c4\u03cc \u03c3\u03b7\u03bc\u03b1\u03af\u03bd\u03b5\u03b9 \u03cc\u03c4\u03b9 \u03ad\u03c7\u03b5\u03b9 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03cc \u03c1\u03c5\u03b8\u03bc\u03cc \u03bc\u03b5\u03c4\u03b1\u03b2\u03bf\u03bb\u03ae\u03c2 (\u03ae \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ae \u03ad\u03bd\u03c4\u03b1\u03c3\u03b7) \u03ba\u03ac\u03c4\u03b9 \u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03c3\u03c5\u03bd\u03b1\u03bd\u03c4\u03ac\u03bc\u03b5 \u03c3\u03b5 \u03c0\u03ac\u03c1\u03b1 \u03c0\u03bf\u03bb\u03bb\u03ad\u03c2 \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ad\u03c2 \u03c9\u03c2 \u03c4\u03bf \u03c0\u03c1\u03ce\u03c4\u03bf \u03b2\u03ae\u03bc\u03b1 \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03bf\u03bc\u03ae\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c0\u03b9\u03bf \u03c0\u03bf\u03bb\u03cd\u03c0\u03bb\u03bf\u03ba\u03b1 \u03bc\u03bf\u03bd\u03c4\u03ad\u03bb\u03b1.<\/p>\n<p>&nbsp;<\/p>\n<p>\u0397 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7<strong> <span style=\"color: #000000;\"><span style=\"font-family: 'Times New Roman',serif;\"><span style=\"font-size: medium;\"><i>f<\/i><\/span><\/span><\/span><span style=\"color: #000000;\"><span style=\"font-family: 'Times New Roman',serif;\"><span style=\"font-size: medium;\">(<\/span><\/span><\/span><span style=\"color: #000000;\"><span style=\"font-family: 'Times New Roman',serif;\"><span style=\"font-size: medium;\"><i>x<\/i><\/span><\/span><\/span><span style=\"color: #000000;\"><span style=\"font-family: 'Times New Roman',serif;\"><span style=\"font-size: medium;\">) = <\/span><\/span><\/span><span style=\"color: #000000;\"><span style=\"font-family: 'Times New Roman',serif;\"><span style=\"font-size: medium;\"><i>e<\/i><\/span><\/span><\/span><span style=\"color: #000000;\"><sup><span style=\"font-family: 'Times New Roman',serif;\"><span style=\"font-size: medium;\"><i>x <\/i><\/span><\/span><\/sup><\/span><\/strong>\u03c0\u03c1\u03bf\u03c3\u03b5\u03b3\u03b3\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03bc\u03ad\u03c3\u03c9 \u03c4\u03bf\u03c5 \u03b1\u03bd\u03b1\u03c0\u03c4\u03cd\u03b3\u03bc\u03b1\u03c4\u03bf\u03c2 \u03c4\u03b7\u03c2 \u03c3\u03b5\u03b9\u03c1\u03ac\u03c2<\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/e1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-19340 aligncenter\" src=\"https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/e1.png?resize=87%2C81\" alt=\"e1\" width=\"87\" height=\"81\" data-recalc-dims=\"1\" \/><\/a><\/p>\n<p>\u039f \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 <strong>e<\/strong> \u03b5\u03af\u03bd\u03b1\u03b9 \u03b5\u03be\u03ad\u03c7\u03bf\u03c5\u03c3\u03b1\u03c2 \u03c3\u03b7\u03bc\u03b1\u03c3\u03af\u03b1\u03c2 \u03c3\u03c4\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac, \u03bc\u03b1\u03b6\u03af \u03bc\u03b5 \u03c4\u03bf <strong>0<\/strong>, \u03c4\u03bf <strong>1<\/strong>, \u03c4\u03bf <strong>\u03c0<\/strong> \u03ba\u03b1\u03b9 \u03c4\u03bf <strong>i<\/strong>. \u039a\u03b1\u03b9 \u03bf\u03b9 \u03c0\u03ad\u03bd\u03c4\u03b5 \u03b1\u03c0\u03cc \u03b1\u03c5\u03c4\u03bf\u03cd\u03c2 \u03c4\u03bf\u03c5\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2 \u03c0\u03b1\u03af\u03b6\u03bf\u03c5\u03bd \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03cc \u03ba\u03b1\u03b9 \u03b5\u03c0\u03b1\u03bd\u03b1\u03bb\u03b1\u03bc\u03b2\u03b1\u03bd\u03cc\u03bc\u03b5\u03bd\u03bf \u03c1\u03cc\u03bb\u03bf \u03c3\u03c4\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03ba\u03b1\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03c0\u03ad\u03bd\u03c4\u03b5 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ad\u03c2 \u03c0\u03bf\u03c5 \u03b5\u03bc\u03c6\u03b1\u03bd\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c3\u03b5 \u03bc\u03af\u03b1 \u03b4\u03b9\u03b1\u03c4\u03cd\u03c0\u03c9\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03c4\u03b1\u03c5\u03c4\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2 \u03c4\u03bf\u03c5 \u038c\u03b9\u03bb\u03b5\u03c1.<br \/>\n\u039f Euler \u03ba\u03b1\u03c4\u03b5\u03bb\u03ae\u03be\u03b5 \u03c3\u03c4\u03b7\u03bd \u03c0\u03b1\u03c1\u03b1\u03ba\u03ac\u03bd\u03c9 \u03c3\u03c7\u03ad\u03c3\u03b7 \u03b3\u03b9\u03b1 \u03ad\u03bd\u03b1\u03bd \u03c6\u03b1\u03bd\u03c4\u03b1\u03c3\u03c4\u03b9\u03ba\u03cc \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc:<\/p>\n<p style=\"text-align: center;\"><strong><span style=\"color: #000000;\"><span style=\"font-family: 'Times New Roman',serif;\"><span style=\"font-size: medium;\"><i>e<\/i><\/span><\/span><sup><span style=\"font-family: 'Times New Roman',serif;\"><span style=\"font-size: medium;\"><i>ix<\/i><\/span><\/span><\/sup><span style=\"font-family: 'Times New Roman',serif;\"><span style=\"font-size: medium;\"> = cos<\/span><\/span><span style=\"font-family: 'Times New Roman',serif;\"><span style=\"font-size: medium;\"><i>x<\/i><\/span><\/span><span style=\"font-family: 'Times New Roman',serif;\"><span style=\"font-size: medium;\"> + <\/span><\/span><span style=\"font-family: 'Times New Roman',serif;\"><span style=\"font-size: medium;\"><i>i<\/i><\/span><\/span><span style=\"font-family: 'Times New Roman',serif;\"><span style=\"font-size: medium;\">sin<\/span><\/span><span style=\"font-family: 'Times New Roman',serif;\"><span style=\"font-size: medium;\"><i>x<\/i><\/span><\/span> <\/span><\/strong><\/p>\n<p>\u0391\u03bd \u03b8\u03ad\u03c3\u03bf\u03c5\u03bc\u03b5 <strong>x = \u03c0<\/strong> \u03c0\u03b1\u03af\u03c1\u03bd\u03bf\u03c5\u03bc\u03b5:<\/p>\n<p><a href=\"https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/e2.png\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-19341 aligncenter\" src=\"https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/e2.png?resize=279%2C27\" alt=\"e2\" width=\"279\" height=\"27\" data-recalc-dims=\"1\" \/><\/a><\/p>\n<p>\u0397 \u03c4\u03b5\u03bb\u03b5\u03c5\u03c4\u03b1\u03af\u03b1 \u03c3\u03c7\u03ad\u03c3\u03b7 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b3\u03bd\u03c9\u03c3\u03c4\u03ae \u03c9\u03c2 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03c4\u03bf\u03c5 Euler \u03ba\u03b1\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03af\u03b1 \u03b1\u03c0\u03cc \u03c4\u03b9\u03c2 \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03cc\u03c4\u03b5\u03c1\u03b5\u03c2 \u03c3\u03c4\u03b7\u03bd \u03c6\u03b9\u03bb\u03bf\u03c3\u03bf\u03c6\u03af\u03b1 \u03c4\u03c9\u03bd \u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd. \u03a3\u03c5\u03bd\u03b4\u03ad\u03b5\u03b9 \u03c4\u03b9\u03c2 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ad\u03c2 <strong>e<\/strong>,<strong>\u03c0<\/strong>,<strong>i<\/strong> \u03bc\u03b5 \u03c4\u03b7\u03bd \u03bc\u03bf\u03bd\u03ac\u03b4\u03b1 \u03ba\u03b1\u03b9 \u03c4\u03bf \u03bc\u03b7\u03b4\u03ad\u03bd! \u03a0\u03ad\u03c1\u03b1 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03c6\u03b9\u03bb\u03bf\u03c3\u03bf\u03c6\u03af\u03b1, \u03b7 \u03c3\u03c7\u03ad\u03c3\u03b7 \u03b1\u03c5\u03c4\u03ae \u03bc\u03b1\u03c2 \u03ad\u03b4\u03c9\u03c3\u03b5 \u03ba\u03b1\u03b9 \u03ba\u03ac\u03c4\u03b9 \u03c0\u03b1\u03c1\u03b1\u03c0\u03ac\u03bd\u03c9.<br \/>\n\u03a7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03ae\u03b8\u03b7\u03ba\u03b5 \u03c3\u03c4\u03b7\u03bd \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 \u03cc\u03c4\u03b9 \u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 <strong>\u03c0<\/strong> \u03b5\u03af\u03bd\u03b1\u03b9 \u03c5\u03c0\u03b5\u03c1\u03b2\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2, \u03b4\u03b7\u03bb\u03b1\u03b4\u03ae \u03cc\u03c4\u03b9 \u03b4\u03b5\u03bd \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03b5\u03af \u03bb\u03cd\u03c3\u03b7 \u03ba\u03ac\u03c0\u03bf\u03b9\u03b1\u03c2 \u03c0\u03bf\u03bb\u03c5\u03c9\u03bd\u03c5\u03bc\u03b9\u03ba\u03ae\u03c2 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7\u03c2.\u03a4\u03ad\u03c4\u03bf\u03b9\u03bf\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03ba\u03b1\u03b9 \u03bf <strong>e<\/strong>.<\/p>\n<p>&nbsp;<\/p>\n<p>\u038c\u03c0\u03c9\u03c2 \u03ba\u03b1\u03b9 \u03b7 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac <strong>\u03c0<\/strong>, \u03c4\u03bf <strong>e<\/strong> \u03b5\u03af\u03bd\u03b1\u03b9 \u03ac\u03c1\u03c1\u03b7\u03c4\u03bf\u03c2, \u03b4\u03b7\u03bb. \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03bb\u03cc\u03b3\u03bf\u03c2 \u03b1\u03ba\u03b5\u03c1\u03b1\u03af\u03c9\u03bd, \u03ba\u03b1\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c5\u03c0\u03b5\u03c1\u03b2\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2, \u03b4\u03b7\u03bb. \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03c1\u03af\u03b6\u03b1 \u03ba\u03ac\u03b8\u03b5 \u03bc\u03b7-\u03bc\u03b7\u03b4\u03b5\u03bd\u03b9\u03ba\u03bf\u03cd \u03c0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03bf\u03c5 \u03bc\u03b5 \u03c1\u03b7\u03c4\u03bf\u03cd\u03c2 \u03c3\u03c5\u03bd\u03c4\u03b5\u03bb\u03b5\u03c3\u03c4\u03ad\u03c2. \u0397 \u03b1\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03b9\u03ba\u03ae \u03b1\u03be\u03af\u03b1 \u03c4\u03bf\u03c5 <strong>e<\/strong> \u03bc\u03ad\u03c7\u03c1\u03b9 \u03c4\u03b1 50 \u03b4\u03b5\u03ba\u03b1\u03b4\u03b9\u03ba\u03ac \u03c8\u03b7\u03c6\u03af\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 <strong>2,71828182845904523536028747135266249775724709369995<\/strong>&#8230;<\/p>\n<p>&nbsp;<\/p>\n<p>\u03a4\u03bf \u03cc\u03c4\u03b9 \u03bf \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 <strong>e<\/strong> \u03b5\u03af\u03bd\u03b1\u03b9 \u03ac\u03c1\u03c1\u03b7\u03c4\u03bf\u03c2 \u03b1\u03c0\u03b5\u03b4\u03b5\u03af\u03c7\u03b8\u03b7 \u00a0\u03b1\u03c0\u03cc \u03c4\u03bf\u03bd Euler \u03c0\u03bf\u03c5 \u03ad\u03b4\u03b5\u03b9\u03be\u03b5 \u03cc\u03c4\u03b9 \u03b7 \u03b1\u03c0\u03bb\u03ae \u03c3\u03c5\u03bd\u03ad\u03c7\u03b9\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03b5\u03c0\u03ad\u03ba\u03c4\u03b1\u03c3\u03b7\u03c2 \u03c4\u03bf\u03c5 \u03ba\u03bb\u03ac\u03c3\u03bc\u03b1\u03c4\u03bf\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03ac\u03c0\u03b5\u03b9\u03c1\u03b7.<br \/>\n\u0395\u03c0\u03b9\u03c0\u03bb\u03ad\u03bf\u03bd, \u03b1\u03c0\u03cc \u03c4\u03bf \u03b8\u03b5\u03ce\u03c1\u03b7\u03bc\u03b1 Lindemann-Weierstrass, \u03c4\u03bf <strong>e<\/strong> \u03b5\u03af\u03bd\u03b1\u03b9 \u03c5\u03c0\u03b5\u03c1\u03b2\u03b1\u03c4\u03b9\u03ba\u03cc, \u03c0\u03c1\u03ac\u03b3\u03bc\u03b1 \u03c0\u03bf\u03c5 \u03c3\u03b7\u03bc\u03b1\u03af\u03bd\u03b5\u03b9 \u03cc\u03c4\u03b9 \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03b9\u03b1 \u03bb\u03cd\u03c3\u03b7 \u03bc\u03b9\u03b1\u03c2 \u03bf\u03c0\u03bf\u03b9\u03b1\u03c3\u03b4\u03ae\u03c0\u03bf\u03c4\u03b5 \u03c0\u03bf\u03bb\u03c5\u03c9\u03bd\u03c5\u03bc\u03b9\u03ba\u03ae\u03c2 \u03bc\u03b7 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ae\u03c2 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7\u03c2 \u03bc\u03b5 \u03b1\u03ba\u03ad\u03c1\u03b1\u03b9\u03bf\u03c5\u03c2 \u03c3\u03c5\u03bd\u03c4\u03b5\u03bb\u03b5\u03c3\u03c4\u03ad\u03c2. \u0389\u03c4\u03b1\u03bd \u03bf \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03c0\u03bf\u03c5 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03c7\u03b8\u03b7\u03ba\u03b5 \u03cc\u03c4\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c5\u03c0\u03b5\u03c1\u03b2\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2 \u03c7\u03c9\u03c1\u03af\u03c2 \u03bd\u03b1 \u03ad\u03c7\u03b5\u03b9 \u03ba\u03b1\u03c4\u03b1\u03c3\u03ba\u03b5\u03c5\u03b1\u03c3\u03c4\u03b5\u03af \u03b5\u03b9\u03b4\u03b9\u03ba\u03ac \u03b3\u03b9\u03b1 \u03c4\u03bf \u03c3\u03ba\u03bf\u03c0\u03cc \u03b1\u03c5\u03c4\u03cc (\u03c3\u03b5 \u03c3\u03cd\u03b3\u03ba\u03c1\u03b9\u03c3\u03b7 \u03bc\u03b5 \u03c4\u03bf\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc Liouville). \u0397 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 \u03b4\u03cc\u03b8\u03b7\u03ba\u03b5 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd Charles Hermite \u03c4\u03bf 1873.<br \/>\n\u0395\u03b9\u03ba\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03cc\u03c4\u03b9 \u03c4\u03bf e \u03b5\u03af\u03bd\u03b1\u03b9 \u03ba\u03b1\u03bd\u03bf\u03bd\u03b9\u03ba\u03cc\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2, \u03b3\u03b5\u03b3\u03bf\u03bd\u03cc\u03c2 \u03c0\u03bf\u03c5 \u03c3\u03b7\u03bc\u03b1\u03af\u03bd\u03b5\u03b9 \u03cc\u03c4\u03b9 \u03cc\u03c4\u03b1\u03bd \u03c4\u03bf <strong>e<\/strong> \u03b5\u03ba\u03c6\u03c1\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c3\u03b5 \u03bf\u03c0\u03bf\u03b9\u03b1\u03b4\u03ae\u03c0\u03bf\u03c4\u03b5 \u03b2\u03ac\u03c3\u03b7 \u03c4\u03b1 \u03c0\u03b9\u03b8\u03b1\u03bd\u03ac \u03c8\u03b7\u03c6\u03af\u03b1 \u03c3\u03c4\u03b7\u03bd \u03b5\u03bd \u03bb\u03cc\u03b3\u03c9 \u03b2\u03ac\u03c3\u03b7 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03bc\u03bf\u03b9\u03cc\u03bc\u03bf\u03c1\u03c6\u03b1 \u03ba\u03b1\u03c4\u03b1\u03bd\u03b5\u03bc\u03b7\u03bc\u03ad\u03bd\u03b1 (\u03b5\u03bc\u03c6\u03b1\u03bd\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03b9\u03c3\u03bf\u03c0\u03af\u03b8\u03b1\u03bd\u03b1 \u03c3\u03b5 \u03bf\u03c0\u03bf\u03b9\u03b1\u03b4\u03ae\u03c0\u03bf\u03c4\u03b5 \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03b7 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1 \u03c0\u03b5\u03c0\u03b5\u03c1\u03b1\u03c3\u03bc\u03ad\u03bd\u03bf\u03c5 \u03bc\u03ae\u03ba\u03bf\u03c5\u03c2).<br \/>\n\u039f\u03b9 \u03c0\u03c1\u03ce\u03c4\u03b5\u03c2 \u03b1\u03bd\u03b1\u03c6\u03bf\u03c1\u03ad\u03c2 \u03c3\u03c4\u03b7 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac <strong>e<\/strong> \u03b4\u03b7\u03bc\u03bf\u03c3\u03b9\u03b5\u03cd\u03b8\u03b7\u03ba\u03b1\u03bd \u03c4\u03bf 1618 \u03c3\u03c4\u03bf\u03bd \u03c0\u03af\u03bd\u03b1\u03ba\u03b1 \u03c4\u03bf\u03c5 \u03c0\u03c1\u03bf\u03c3\u03b1\u03c1\u03c4\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u03b5\u03bd\u03cc\u03c2 \u03ad\u03c1\u03b3\u03bf \u03b3\u03b9\u03b1 \u03bb\u03bf\u03b3\u03b1\u03c1\u03af\u03b8\u03bc\u03bf\u03c5\u03c2 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd \u03a4\u03b6\u03bf\u03bd \u039d\u03ac\u03c0\u03b9\u03b5\u03c1 (John Napier). \u03a9\u03c3\u03c4\u03cc\u03c3\u03bf \u03b1\u03c5\u03c4\u03cc \u03b4\u03b5\u03bd \u03c0\u03b5\u03c1\u03b9\u03bb\u03b1\u03bc\u03b2\u03ac\u03bd\u03b5\u03b9 \u03c4\u03b7\u03bd \u03af\u03b4\u03b9\u03b1 \u03c4\u03b7 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac, \u03b1\u03bb\u03bb\u03ac \u03b1\u03c0\u03bb\u03bf\u03cd\u03c3\u03c4\u03b5\u03c1\u03b1 \u03bc\u03b9\u03b1 \u03bb\u03af\u03c3\u03c4\u03b1 \u03b1\u03c0\u03cc \u03bb\u03bf\u03b3\u03b1\u03c1\u03af\u03b8\u03bc\u03bf\u03c5\u03c2 \u03c0\u03bf\u03c5 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03b7 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac. \u03a5\u03c0\u03bf\u03c3\u03c4\u03b7\u03c1\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03cc\u03c4\u03b9 \u03bf \u03c0\u03af\u03bd\u03b1\u03ba\u03b1\u03c2 \u03b3\u03c1\u03ac\u03c6\u03c4\u03b7\u03ba\u03b5 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd William Oughtred. \u0397 \u03b1\u03bd\u03b1\u03ba\u03ac\u03bb\u03c5\u03c8\u03b7 \u03c4\u03b7\u03c2 \u03af\u03b4\u03b9\u03b1\u03c2 \u03c4\u03b7\u03c2 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac\u03c2 \u03c0\u03b9\u03c3\u03c4\u03ce\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c3\u03c4\u03bf\u03bd \u0393\u03b9\u03b1\u03ba\u03cc\u03bc\u03c0 \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9 (Jacob Bernoulli).<br \/>\n\u0397 \u03c0\u03c1\u03ce\u03c4\u03b7 \u03b3\u03bd\u03c9\u03c3\u03c4\u03ae \u03c7\u03c1\u03ae\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac\u03c2, \u03c0\u03bf\u03c5 \u03b1\u03bd\u03c4\u03b9\u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af \u03c3\u03c4\u03bf \u03b3\u03c1\u03ac\u03bc\u03bc\u03b1 \u00a0<strong>b<\/strong>, \u03ae\u03c4\u03b1\u03bd \u03c3\u03b5 \u03b1\u03bd\u03c4\u03b9\u03c3\u03c4\u03bf\u03b9\u03c7\u03af\u03b1 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd \u0393\u03ba\u03cc\u03c4\u03c6\u03c1\u03b9\u03bd\u03c4 \u0392\u03af\u03bb\u03c7\u03b5\u03bb\u03bc \u039b\u03ac\u03b9\u03bc\u03c0\u03bd\u03b9\u03c4\u03c2 (Gottfried Leibniz) \u03c3\u03c4\u03bf\u03bd \u039a\u03c1\u03af\u03c3\u03c4\u03b9\u03b1\u03bd \u03a7\u03cc\u03c5\u03c7\u03b5\u03bd\u03c2 (Christiaan Huygens) \u03c4\u03bf\u00a0 1690 \u03ba\u03b1\u03b9 \u03c4\u03bf 1691. \u039f \u039b\u03ad\u03bf\u03bd\u03b1\u03c1\u03bd\u03c4 \u038c\u03b9\u03bb\u03b5\u03c1 (Leonhard Euler) \u03b5\u03b9\u03c3\u03ae\u03b3\u03b1\u03b3\u03b5 \u03c4\u03bf \u03b3\u03c1\u03ac\u03bc\u03bc\u03b1 e \u03c9\u03c2 \u03c3\u03c4\u03b7 \u03b2\u03ac\u03c3\u03b7 \u03b3\u03b9\u03b1 \u03c6\u03c5\u03c3\u03b9\u03ba\u03bf\u03cd\u03c2 \u03bb\u03bf\u03b3\u03b1\u03c1\u03af\u03b8\u03bc\u03bf\u03c5\u03c2, \u03b3\u03c1\u03ac\u03c6\u03bf\u03bd\u03c4\u03ac\u03c2 \u03c4\u03bf \u03c3\u03b5 \u03b5\u03c0\u03b9\u03c3\u03c4\u03bf\u03bb\u03ae \u03c4\u03bf\u03c5 \u03c3\u03c4\u03bf\u03bd Christian Goldbach \u00a0\u03c3\u03c4\u03b9\u03c2 25 \u039d\u03bf\u03b5\u03bc\u03b2\u03c1\u03af\u03bf\u03c5 \u03c4\u03bf\u03c5 1731. \u039f Euler \u03be\u03b5\u03ba\u03af\u03bd\u03b7\u03c3\u03b5 \u03bd\u03b1 \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03b5\u03af \u03c4\u03bf \u03b3\u03c1\u03ac\u03bc\u03bc\u03b1 e \u03c9\u03c2 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac \u03c4\u03bf 1727 \u03ae \u03c4\u03bf 1728, \u03c3\u03b5 \u03ad\u03bd\u03b1 \u03b1\u03b4\u03b7\u03bc\u03bf\u03c3\u03af\u03b5\u03c5\u03c4\u03bf \u03ad\u03b3\u03b3\u03c1\u03b1\u03c6\u03bf \u03c3\u03c7\u03b5\u03c4\u03b9\u03ba\u03ac \u03bc\u03b5 \u03c4\u03b9\u03c2 \u03b5\u03ba\u03c1\u03b7\u03ba\u03c4\u03b9\u03ba\u03ad\u03c2 \u03b4\u03c5\u03bd\u03ac\u03bc\u03b5\u03b9\u03c2 \u03c3\u03b5 \u03ba\u03b1\u03bd\u03cc\u03bd\u03b9\u03b1, \u03ba\u03b1\u03b9 \u03b7 \u03c0\u03c1\u03ce\u03c4\u03b7 \u03b5\u03bc\u03c6\u03ac\u03bd\u03b9\u03c3\u03b7 \u03c4\u03bf\u03c5 e \u03c3\u03b5 \u03bc\u03b9\u03b1 \u03b4\u03b7\u03bc\u03bf\u03c3\u03af\u03b5\u03c5\u03c3\u03b7 \u03ae\u03c4\u03b1\u03bd \u03c4\u03bf\u03c5 Euler Mechanica (1736).<\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u03a4\u03cc\u03ba\u03bf\u03c2 \u03b1\u03bd\u03b1\u03c4\u03bf\u03ba\u03b9\u03c3\u03bc\u03bf\u03cd<\/strong><br \/>\nO Jacob Bernoulli \u03b1\u03bd\u03b1\u03ba\u03ac\u03bb\u03c5\u03c8\u03b5 \u03b1\u03c5\u03c4\u03ae \u03c4\u03b7 \u00a0\u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac \u03bc\u03b5\u03bb\u03b5\u03c4\u03ce\u03bd\u03c4\u03b1\u03c2 \u03bc\u03b9\u03b1 \u03b5\u03c1\u03ce\u03c4\u03b7\u03c3\u03b7 \u03c3\u03c7\u03b5\u03c4\u03b9\u03ba\u03ac \u03bc\u03b5 \u03c4\u03bf\u03c5\u03c2 \u03c4\u03cc\u03ba\u03bf\u03c5\u03c2 \u03b1\u03bd\u03b1\u03c4\u03bf\u03ba\u03b9\u03c3\u03bc\u03bf\u03cd:<br \/>\n\u0388\u03bd\u03b1\u03c2 \u03bb\u03bf\u03b3\u03b1\u03c1\u03b9\u03b1\u03c3\u03bc\u03cc\u03c2 \u03be\u03b5\u03ba\u03b9\u03bd\u03ac \u03bc\u03b5 $ 1.00 \u03ba\u03b1\u03b9 \u03c0\u03bb\u03b7\u03c1\u03ce\u03bd\u03b5\u03b9 100 \u00a0\u03c4\u03bf\u03b9\u03c2 \u03b5\u03ba\u03b1\u03c4\u03cc \u03c4\u03cc\u03ba\u03bf \u00a0\u03b1\u03bd\u03ac \u03ad\u03c4\u03bf\u03c2. \u0395\u03ac\u03bd \u03bf \u03c4\u03cc\u03ba\u03bf\u03c2 \u03c0\u03b9\u03c3\u03c4\u03ce\u03bd\u03b5\u03c4\u03b1\u03b9 \u03bc\u03b9\u03b1 \u03c6\u03bf\u03c1\u03ac \u03b7 \u03b1\u03be\u03af\u03b1 \u03c4\u03bf\u03c5 \u03bb\u03bf\u03b3\u03b1\u03c1\u03b9\u03b1\u03c3\u03bc\u03bf\u03cd \u03c3\u03c4\u03bf \u03c4\u03ad\u03bb\u03bf\u03c2 \u03c4\u03bf\u03c5 \u03ad\u03c4\u03bf\u03c5\u03c2 \u03b8\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 $ 2,00. \u03a4\u03b9 \u03c3\u03c5\u03bc\u03b2\u03b1\u03af\u03bd\u03b5\u03b9\u00a0 \u03b1\u03bd \u03bf \u03c4\u03cc\u03ba\u03bf\u03c2 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03c4\u03b5\u03af \u03ba\u03b1\u03b9 \u03c0\u03b9\u03c3\u03c4\u03c9\u03b8\u03b5\u03af \u03c0\u03b9\u03bf \u03c3\u03c5\u03c7\u03bd\u03ac \u03ba\u03b1\u03c4\u03ac \u03c4\u03b7 \u03b4\u03b9\u03ac\u03c1\u03ba\u03b5\u03b9\u03b1 \u03c4\u03bf\u03c5 \u03ad\u03c4\u03bf\u03c5\u03c2;<br \/>\n\u0391\u03bd \u03bf \u03c4\u03cc\u03ba\u03bf\u03c2 \u03c0\u03b9\u03c3\u03c4\u03c9\u03b8\u03b5\u03af \u03b4\u03cd\u03bf \u03c6\u03bf\u03c1\u03ad\u03c2 \u03c4\u03bf \u03ad\u03c4\u03bf\u03c2, \u03c4\u03bf \u03b5\u03c0\u03b9\u03c4\u03cc\u03ba\u03b9\u03bf \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5 6 \u03bc\u03ae\u03bd\u03b5\u03c2 \u03b8\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 <strong>50%<\/strong>, \u03bf\u03c0\u03cc\u03c4\u03b5 \u03c4\u03bf \u03b1\u03c1\u03c7\u03b9\u03ba\u03cc \u00a0<strong>$ 1<\/strong> \u03c0\u03bf\u03bb\u03bb\u03b1\u03c0\u03bb\u03b1\u03c3\u03b9\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03ba\u03b1\u03c4\u03ac 1,5 \u03c6\u03bf\u03c1\u03ad\u03c2, \u03b1\u03c0\u03bf\u03b4\u03af\u03b4\u03bf\u03bd\u03c4\u03b1\u03c2 <strong>$ 1.00 \u00d7 1.52 = 2,25 $<\/strong> \u00a0\u03c3\u03c4\u03bf \u03c4\u03ad\u03bb\u03bf\u03c2 \u03c4\u03bf\u03c5 \u03ad\u03c4\u03bf\u03c5\u03c2. \u03a5\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b9\u03c2 \u00a0\u03c4\u03c1\u03b9\u03bc\u03b7\u03bd\u03b9\u03b1\u03af\u03b5\u03c2 \u03b1\u03c0\u03bf\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u00a0\u03b5\u03af\u03bd\u03b1\u03b9 <strong>$ 1,00 \u00d7 1.254 = 2,4414<\/strong> \u03b4\u03bf\u03bb\u03ac\u03c1\u03b9\u03b1 &#8230; \u03ba\u03b1\u03b9 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03bf\u03c5 \u03ba\u03ac\u03b8\u03b5 \u03bc\u03ae\u03bd\u03b1 \u03c4\u03b9\u03c2 \u03b1\u03c0\u03bf\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 <strong>$ 1,00 \u00d7 (1 + 1\/12) 12 = 2,613035<\/strong> \u03b4\u03bf\u03bb\u03ac\u03c1\u03b9\u03b1 &#8230; \u0391\u03bd \u03c5\u03c0\u03ac\u03c1\u03c7\u03bf\u03c5\u03bd n \u03c3\u03c5\u03bc\u03bc\u03b9\u03b3\u03ae \u00a0\u03b4\u03b9\u03b1\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1, \u03c4\u03bf \u03b5\u03bd\u03b4\u03b9\u03b1\u03c6\u03ad\u03c1\u03bf\u03bd \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5 \u03b4\u03b9\u03ac\u03c3\u03c4\u03b7\u03bc\u03b1 \u03b8\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 <strong>100%<\/strong> \/ n \u03ba\u03b1\u03b9 \u03b7 \u03b1\u03be\u03af\u03b1 \u03c4\u03bf \u03c4\u03ad\u03bb\u03bf\u03c2 \u03c4\u03bf\u03c5 \u03ad\u03c4\u03bf\u03c5\u03c2 \u03b8\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 <strong>1,00 \u20ac \u00d7 (1 + 1 \/ n) n.<\/strong><br \/>\n\u039f Bernoulli \u03c0\u03b1\u03c1\u03b1\u03c4\u03ae\u03c1\u03b7\u03c3\u03b5 \u03cc\u03c4\u03b9 \u03b1\u03c5\u03c4\u03ae \u03b7 \u03b1\u03bb\u03bb\u03b7\u03bb\u03bf\u03c5\u03c7\u03af\u03b1 \u03c0\u03bb\u03b7\u03c3\u03b9\u03ac\u03b6\u03b5\u03b9 \u03c4\u03bf \u03cc\u03c1\u03b9\u03bf (\u03c4\u03b7 \u03b4\u03cd\u03bd\u03b1\u03bc\u03b7 \u03c4\u03bf\u03c5 \u03b5\u03bd\u03b4\u03b9\u03b1\u03c6\u03ad\u03c1\u03bf\u03bd\u03c4\u03bf\u03c2) \u03bc\u03b5 \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03b1 n \u03ba\u03b1\u03b9, \u03c9\u03c2 \u03b5\u03ba \u03c4\u03bf\u03cd\u03c4\u03bf\u03c5, \u03c4\u03b1 \u03bc\u03b9\u03ba\u03c1\u03cc\u03c4\u03b5\u03c1\u03b1 \u03b4\u03b9\u03b1\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1 \u03c3\u03cd\u03bd\u03b8\u03b5\u03c3\u03b7\u03c2. \u03a5\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03c2 \u00a0\u03c4\u03b7\u03bd \u03b5\u03b2\u03b4\u03bf\u03bc\u03ac\u03b4\u03b1 (n = 52) \u03b1\u03c0\u03bf\u03b4\u03af\u03b4\u03b5\u03b9 2,692597 \u03b4\u03bf\u03bb\u03ac\u03c1\u03b9\u03b1 &#8230;, \u03b5\u03bd\u03ce \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03c2 \u03b7\u03bc\u03b5\u03c1\u03b7\u03c3\u03af\u03c9\u03c2 (n = 365) \u03b1\u03c0\u03bf\u03b4\u03af\u03b4\u03b5\u03b9 2,714567 \u03b4\u03bf\u03bb\u03ac\u03c1\u03b9\u03b1 &#8230;, \u03bc\u03cc\u03bb\u03b9\u03c2 \u03b4\u03cd\u03bf \u03bb\u03b5\u03c0\u03c4\u03ac \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03bf. \u03a4\u03bf \u03cc\u03c1\u03b9\u03bf \u03ba\u03b1\u03b8\u03ce\u03c2 \u03c4\u03bf n \u03bc\u03b5\u03b3\u03b1\u03bb\u03ce\u03bd\u03b5\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03c0\u03bf\u03c5 \u03ad\u03b3\u03b9\u03bd\u03b5 \u03b3\u03bd\u03c9\u03c3\u03c4\u03cc\u03c2\u00a0 \u03c9\u03c2 <strong>e<\/strong>! M\u03b5 \u03c3\u03c5\u03bd\u03b5\u03c7\u03ae \u03c3\u03cd\u03bd\u03b8\u03b5\u03c3\u03b7, \u03b7 \u03b1\u03be\u03af\u03b1 \u03c4\u03bf\u03c5 \u03bb\u03bf\u03b3\u03b1\u03c1\u03b9\u03b1\u03c3\u03bc\u03bf\u03cd \u03b8\u03b1 \u03c6\u03c4\u03ac\u03c3\u03b5\u03b9 \u03c4\u03b1 $ 2.7182818 &#8230;. \u0393\u03b5\u03bd\u03b9\u03ba\u03cc\u03c4\u03b5\u03c1\u03b1, \u03ad\u03bd\u03b1\u03c2 \u03bb\u03bf\u03b3\u03b1\u03c1\u03b9\u03b1\u03c3\u03bc\u03cc\u03c2 \u03c0\u03bf\u03c5 \u03be\u03b5\u03ba\u03b9\u03bd\u03ac\u03b5\u03b9 \u03b1\u03c0\u03cc $ 1 \u03ba\u03b1\u03b9 \u03c0\u03c1\u03bf\u03c3\u03c6\u03ad\u03c1\u03b5\u03b9 \u03b5\u03c4\u03ae\u03c3\u03b9\u03bf \u03b5\u03c0\u03b9\u03c4\u03cc\u03ba\u03b9\u03bf<strong> R<\/strong>, \u03bc\u03b5\u03c4\u03ac \u03b1\u03c0\u03cc <strong>t<\/strong> \u03ad\u03c4\u03b7, \u03b8\u03b1 \u03b1\u03c0\u03bf\u03b4\u03af\u03b4\u03b5\u03b9 <strong>eRt<\/strong> \u03b4\u03bf\u03bb\u03ac\u03c1\u03b9\u03b1 \u03bc\u03b5 \u03c3\u03c5\u03bd\u03b5\u03c7\u03b5\u03af\u03c2 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03bf\u03cd\u03c2. (\u0395\u03b4\u03ce \u03c4\u03bf R \u03b5\u03af\u03bd\u03b1\u03b9 \u03ad\u03bd\u03b1 \u03ba\u03bb\u03ac\u03c3\u03bc\u03b1, \u03ad\u03c4\u03c3\u03b9 \u03b3\u03b9\u03b1 \u03c4\u03bf \u03b5\u03c0\u03b9\u03c4\u03cc\u03ba\u03b9\u03bf 5%, R = 5\/100 =0,05)<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><em><strong>e: \u0397 \u0399\u03c3\u03c4\u03bf\u03c1\u03af\u03b1 \u03b5\u03bd\u03cc\u03c2 \u0391\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd<\/strong><\/em><br \/>\n<em><strong>Eli Maor\u00a0<\/strong><\/em><\/p>\n<p><em><strong>\u0392\u03b9\u03ba\u03b9\u03c0\u03b1\u03af\u03b4\u03b5\u03b9\u03b1<\/strong><\/em><\/p>\n<p>&nbsp;<\/p>\n<p>\u0395\u03b9\u03ba\u03cc\u03bd\u03b1: http:\/\/www.gogeometry.com\/software\/word_cloud_e_euler.gif<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u039f \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 e \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03b9\u03b1 \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03ae \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac \u03c0\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03b2\u03ac\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03c6\u03c5\u03c3\u03b9\u03ba\u03bf\u03cd \u03bb\u03bf\u03b3\u03b1\u03c1\u03af\u03b8\u03bc\u03bf\u03c5. \u0395\u03af\u03bd\u03b1\u03b9 \u03c0\u03b5\u03c1\u03af\u03c0\u03bf\u03c5 \u03af\u03c3\u03b7 \u03bc\u03b5 2,71828 \u03ba\u03b1\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03cc\u03c1\u03b9\u03bf \u03c4\u03b7\u03c2 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1\u03c2 \u00a0(1 + 1\/n)n\u00a0 \u03cc\u03c3\u03bf \u03c4\u03bf n \u03c0\u03bb\u03b7\u03c3\u03b9\u03ac\u03b6\u03b5\u03b9 \u03c4\u03bf \u03ac\u03c0\u03b5\u03b9\u03c1\u03bf, \u03bc\u03b9\u03b1 \u03ad\u03ba\u03c6\u03c1\u03b1\u03c3\u03b7 \u03c0\u03bf\u03c5 \u03c0\u03c1\u03bf\u03ba\u03cd\u03c0\u03c4\u03b5\u03b9 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03bc\u03b5\u03bb\u03ad\u03c4\u03b7 \u03c4\u03c9\u03bd \u03c3\u03cd\u03bd\u03b8\u03b5\u03c4\u03c9\u03bd \u03c4\u03cc\u03ba\u03c9\u03bd&#8230;.<\/p>\n","protected":false},"author":1,"featured_media":19338,"comment_status":"open","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":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?fit=900%2C609&ssl=1","rttpg_featured_image_url":{"full":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?fit=900%2C609&ssl=1",900,609,false],"landscape":["https:\/\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg",900,609,false],"portraits":["https:\/\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg",900,609,false],"thumbnail":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?resize=150%2C150&ssl=1",150,150,true],"medium":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?fit=300%2C203&ssl=1",300,203,true],"large":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?fit=900%2C609&ssl=1",900,609,true],"1536x1536":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?fit=900%2C609&ssl=1",900,609,true],"2048x2048":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?fit=900%2C609&ssl=1",900,609,true],"portfolio-square":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?resize=570%2C570&ssl=1",570,570,true],"portfolio-portrait":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?resize=600%2C609&ssl=1",600,609,true],"portfolio-landscape":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?resize=800%2C600&ssl=1",800,600,true],"menu-featured-post":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?resize=345%2C198&ssl=1",345,198,true],"qode-carousel_slider":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?resize=400%2C260&ssl=1",400,260,true],"portfolio_slider":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?resize=500%2C380&ssl=1",500,380,true],"portfolio_masonry_regular":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?resize=500%2C500&ssl=1",500,500,true],"portfolio_masonry_wide":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?resize=900%2C500&ssl=1",900,500,true],"portfolio_masonry_tall":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?resize=500%2C609&ssl=1",500,609,true],"portfolio_masonry_large":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?resize=900%2C609&ssl=1",900,609,true],"portfolio_masonry_with_space":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?fit=700%2C474&ssl=1",700,474,true],"latest_post_boxes":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?resize=539%2C303&ssl=1",539,303,true],"woocommerce_thumbnail":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?resize=300%2C300&ssl=1",300,300,true],"woocommerce_single":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?fit=600%2C406&ssl=1",600,406,true],"woocommerce_gallery_thumbnail":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2016\/10\/post-460.jpg?resize=100%2C100&ssl=1",100,100,true]},"rttpg_author":{"display_name":"admin","author_link":"https:\/\/www.lecturesbureau.gr\/1\/author\/admin\/"},"rttpg_comment":0,"rttpg_category":"<a href=\"https:\/\/www.lecturesbureau.gr\/1\/category\/science\/\" rel=\"category tag\">\u0395\u03a0\u0399\u03a3\u03a4\u0397\u039c\u0397<\/a>","rttpg_excerpt":"\u039f \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 e \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03b9\u03b1 \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03ae \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac \u03c0\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03b2\u03ac\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03c6\u03c5\u03c3\u03b9\u03ba\u03bf\u03cd \u03bb\u03bf\u03b3\u03b1\u03c1\u03af\u03b8\u03bc\u03bf\u03c5. \u0395\u03af\u03bd\u03b1\u03b9 \u03c0\u03b5\u03c1\u03af\u03c0\u03bf\u03c5 \u03af\u03c3\u03b7 \u03bc\u03b5 2,71828 \u03ba\u03b1\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03cc\u03c1\u03b9\u03bf \u03c4\u03b7\u03c2 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03af\u03b1\u03c2 \u00a0(1 + 1\/n)n\u00a0 \u03cc\u03c3\u03bf \u03c4\u03bf n 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\u03c4\u03cc\u03ba\u03c9\u03bd....","_links":{"self":[{"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/posts\/19330"}],"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\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/comments?post=19330"}],"version-history":[{"count":7,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/posts\/19330\/revisions"}],"predecessor-version":[{"id":19344,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/posts\/19330\/revisions\/19344"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/media\/19338"}],"wp:attachment":[{"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/media?parent=19330"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/categories?post=19330"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/tags?post=19330"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}