{"id":167,"date":"2025-11-12T12:47:28","date_gmt":"2025-11-12T12:47:28","guid":{"rendered":"https:\/\/maths4u.gr\/wordpress\/?p=167"},"modified":"2025-11-26T12:50:42","modified_gmt":"2025-11-26T12:50:42","slug":"pythagora","status":"publish","type":"post","link":"https:\/\/maths4u.gr\/index.php\/2025\/11\/12\/pythagora\/","title":{"rendered":"\u03a0\u03c5\u03b8\u03b1\u03b3\u03cc\u03c1\u03b5\u03b9\u03b1&#8230;"},"content":{"rendered":"\r\n<p class=\"has-medium-font-size wp-block-paragraph\">\u039c\u03b9\u03b1 \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03ae \u0394\u03b9\u03bf\u03c6\u03b1\u03bd\u03c4\u03b9\u03ba\u03ae \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03b5\u03af\u03bd\u03b1\u03b9 \u03ba\u03b1\u03b9 \u03b7 \\(x^n+y^n=z^n\\), \u03cc\u03c0\u03bf\u03c5 \\(x, y, z\\) \u03bf\u03b9 \u03ac\u03b3\u03bd\u03c9\u03c3\u03c4\u03bf\u03b9 \u03ba\u03b1\u03b9 \\(n\\) \u03c6\u03c5\u03c3\u03b9\u03ba\u03cc\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 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\u0388\u03bb\u03bb\u03b7\u03bd\u03b5\u03c2. \u0389\u03b4\u03b7 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03b5\u03c0\u03bf\u03c7\u03ae \u03b5\u03ba\u03b5\u03af\u03bd\u03b7 \u03ae\u03c4\u03b1\u03bd \u03b3\u03bd\u03c9\u03c3\u03c4\u03ae \u03b7 \u03bc\u03ad\u03b8\u03bf\u03b4\u03bf\u03c2 \u03b5\u03cd\u03c1\u03b5\u03c3\u03b7\u03c2 \u03c4\u03c9\u03bd \u03c4\u03c1\u03b9\u03ac\u03b4\u03c9\u03bd \u03b1\u03c5\u03c4\u03ce\u03bd \u03b3\u03b9\u03b1 \u03c4\u03bf\u03c5\u03c2 \u03a0\u03c5\u03b8\u03b1\u03b3\u03cc\u03c1\u03b1, \u0395\u03c5\u03ba\u03bb\u03b5\u03af\u03b4\u03b7, \u0394\u03b9\u03cc\u03c6\u03b1\u03bd\u03c4\u03bf \u03ba\u03b1\u03b9 \u03ac\u03bb\u03bb\u03bf\u03c5\u03c2.<br \/>\u03a3\u03cd\u03bc\u03c6\u03c9\u03bd\u03b1 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03b1\u03c0\u03bb\u03ae \u03b1\u03c5\u03c4\u03ae \u03bc\u03ad\u03b8\u03bf\u03b4\u03bf, \u03c0\u03b1\u03af\u03c1\u03bd\u03bf\u03c5\u03bc\u03b5 \u03b4\u03c5\u03cc \u03b8\u03b5\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03b1\u03ba\u03ad\u03c1\u03b1\u03b9\u03bf\u03c5\u03c2 \\(a, b\\) \u03bc\u03b5 \\(a &gt;b\\), \u03ba\u03b1\u03b9 \\((a,b)=1\\), \u03b4\u03b7\u03bb\u03b1\u03b4\u03ae \u03c0\u03c1\u03ce\u03c4\u03bf\u03c5\u03c2 \u03c0\u03c1\u03bf\u03c2 \u03b1\u03bb\u03bb\u03ae\u03bb\u03bf\u03c5\u03c2 \u03ba\u03b1\u03b9 \u03c6\u03ad\u03c1\u03bd\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b7\u03bd \u03b5\u03c5\u03b8\u03b5\u03af\u03b1 \u03b3\u03c1\u03b1\u03bc\u03bc\u03ae \u03b1\u03c0\u03cc \u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \\((-1,0)\\) \u03bc\u03b5 \u03ba\u03bb\u03af\u03c3\u03b7 \\(b\/a\\), \u03c0\u03bf\u03c5 \u03c4\u03ad\u03bc\u03bd\u03b5\u03b9 \u03c4\u03bf\u03bd \u03bc\u03bf\u03bd\u03b1\u03b4\u03b9\u03b1\u03af\u03bf \u03ba\u03cd\u03ba\u03bb\u03bf \u03ba\u03ad\u03bd\u03c4\u03c1\u03bf\u03c5 \\((0,0)\\), \u03c3\u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \\((u,v)\\). \u0395\u03af\u03bd\u03b1\u03b9 \u03b5\u03cd\u03ba\u03bf\u03bb\u03bf \u03bd\u03b1 \u03b4\u03b5\u03af\u03be\u03bf\u03c5\u03bc\u03b5 \u03cc\u03c4\u03b9 \\[u=\\dfrac{a^2-b^2}{a^2+b^2},\\quad v=\\dfrac{2ab}{a^2+b^2}.\\] <br \/>\u0395\u03af\u03bd\u03b1\u03b9 \u03c0\u03c1\u03bf\u03c6\u03b1\u03bd\u03ad\u03c2 \u03cc\u03c4\u03b9 \u03bf\u03b9 \u03b1\u03ba\u03ad\u03c1\u03b1\u03b9\u03bf\u03b9 \\(x=a^2-b^2, y=2ab, z=a^2+b^2\\) \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03bf\u03cd\u03bd \u03bc\u03b9\u03b1 \u03a0\u03c5\u03b8\u03b1\u03b3\u03cc\u03c1\u03b5\u03b9\u03b1 \u03c4\u03c1\u03b9\u03ac\u03b4\u03b1, \u03b1\u03c6\u03bf\u03cd \\(u^2+v^2=1.\\) (\u03a3\u03c7\u03ae\u03bc\u03b1).<br \/>\u039f\u03b9 \u03c0\u03c1\u03c9\u03c4\u03bf\u03b3\u03b5\u03bd\u03b5\u03af\u03c2 \u03a0\u03c5\u03b8\u03b1\u03b3\u03cc\u03c1\u03b5\u03b9\u03b5\u03c2 \u03c4\u03c1\u03b9\u03ac\u03b4\u03b5\u03c2 \u03ad\u03c7\u03bf\u03c5\u03bd \u03bc\u03ad\u03b3\u03b9\u03c3\u03c4\u03bf \u03ba\u03bf\u03b9\u03bd\u03cc \u03b4\u03b9\u03b1\u03b9\u03c1\u03ad\u03c4\u03b7 \u03c4\u03bf \\(1\\), \u03b5\u03af\u03bd\u03b1\u03b9 \u03b4\u03b7\u03bb\u03b1\u03b4\u03ae \u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u03c4\u03c9\u03bd \u03c4\u03c1\u03b9\u03ac\u03b4\u03c9\u03bd \u03b1\u03c5\u03c4\u03ce\u03bd, \u03c0\u03c1\u03ce\u03c4\u03bf\u03b9 \u03c0\u03c1\u03bf\u03c2 \u03b1\u03bb\u03bb\u03ae\u03bb\u03bf\u03c5\u03c2.<br \/><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-304\" src=\"https:\/\/maths4u.gr\/wp-content\/uploads\/2025\/11\/\u03ba\u03c5\u03ba\u03bb\u03bf\u03c2-289x300.jpg\" alt=\"\" width=\"289\" height=\"300\" srcset=\"https:\/\/maths4u.gr\/wp-content\/uploads\/2025\/11\/\u03ba\u03c5\u03ba\u03bb\u03bf\u03c2-289x300.jpg 289w, https:\/\/maths4u.gr\/wp-content\/uploads\/2025\/11\/\u03ba\u03c5\u03ba\u03bb\u03bf\u03c2-400x415.jpg 400w, https:\/\/maths4u.gr\/wp-content\/uploads\/2025\/11\/\u03ba\u03c5\u03ba\u03bb\u03bf\u03c2-988x1024.jpg 988w, https:\/\/maths4u.gr\/wp-content\/uploads\/2025\/11\/\u03ba\u03c5\u03ba\u03bb\u03bf\u03c2-768x796.jpg 768w, https:\/\/maths4u.gr\/wp-content\/uploads\/2025\/11\/\u03ba\u03c5\u03ba\u03bb\u03bf\u03c2.jpg 1096w\" sizes=\"auto, (max-width: 289px) 85vw, 289px\" \/><br \/>\u0392\u03bb\u03ad\u03c0\u03bf\u03c5\u03bc\u03b5 \u03bb\u03bf\u03b9\u03c0\u03cc\u03bd \u03cc\u03c4\u03b9 \u03b2\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03c2 \u03b8\u03b5\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03b1\u03ba\u03ad\u03c1\u03b1\u03b9\u03bf\u03c5\u03c2 \u03c3\u03b1\u03bd \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03c9\u03bd \\(a\\) \u03ba\u03b1\u03b9 \\(b\\) \u03c0\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03b9 \u03c0\u03c1\u03bf\u03c2 \u03b1\u03bb\u03bb\u03ae\u03bb\u03bf\u03c5\u03c2, \u03c0\u03b1\u03af\u03c1\u03bd\u03bf\u03c5\u03bc\u03b5 \u03cc\u03bb\u03b5\u03c2 \u03c4\u03b9\u03c2 \u03b4\u03c5\u03bd\u03b1\u03c4\u03ad\u03c2 \u03c0\u03c1\u03c9\u03c4\u03bf\u03b3\u03b5\u03bd\u03b5\u03af\u03c2 \u03a0\u03c5\u03b8\u03b1\u03b3\u03cc\u03c1\u03b5\u03b9\u03b5\u03c2 \u03c4\u03c1\u03b9\u03ac\u03b4\u03b5\u03c2.<\/p>\r\n<p class=\"has-medium-font-size\"><\/p>","protected":false},"excerpt":{"rendered":"<p>\u039c\u03b9\u03b1 \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03ae \u0394\u03b9\u03bf\u03c6\u03b1\u03bd\u03c4\u03b9\u03ba\u03ae \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03b5\u03af\u03bd\u03b1\u03b9 \u03ba\u03b1\u03b9 \u03b7 \\(x^n+y^n=z^n\\), \u03cc\u03c0\u03bf\u03c5 \\(x, y, z\\) \u03bf\u03b9 \u03ac\u03b3\u03bd\u03c9\u03c3\u03c4\u03bf\u03b9 \u03ba\u03b1\u03b9 \\(n\\) \u03c6\u03c5\u03c3\u03b9\u03ba\u03cc\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf\u03c2 \u03c4\u03bf\u03c5 1. \u03a4\u03b7\u03bd \u03bb\u03ad\u03bc\u03b5 \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03ae, \u03b3\u03b9\u03b1\u03c4\u03af \u03b5\u03bd\u03ce \u03b3\u03b9\u03b1 \\(n=2\\) \u03ad\u03c7\u03b5\u03b9 \u03ac\u03c0\u03b5\u03b9\u03c1\u03b5\u03c2 \u03bb\u03cd\u03c3\u03b7\u03c2 \u03c3\u03c4\u03bf\u03c5\u03c2 \u03c1\u03b7\u03c4\u03bf\u03cd\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2, \u03b1\u03c6\u03bf\u03cd \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03c0\u03bf\u03c5 \u03b4\u03b9\u03ad\u03c0\u03b5\u03b9 \u03c4\u03b9\u03c2 \u03c0\u03bb\u03b5\u03c5\u03c1\u03ad\u03c2 \u03bf\u03c1\u03b8\u03bf\u03b3\u03c9\u03bd\u03af\u03bf\u03c5 \u03c4\u03c1\u03b9\u03b3\u03ce\u03bd\u03bf\u03c5 (\u03a0\u03c5\u03b8\u03b1\u03b3\u03cc\u03c1\u03b5\u03b9\u03bf \u03b8\u03b5\u03ce\u03c1\u03b7\u03bc\u03b1), \u03b3\u03b9\u03b1 \\(n&gt;2\\), \u03bf\u03b9 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03af \u03ad\u03c7\u03c5\u03c3\u03b1\u03bd \u03c0\u03bf\u03bb\u03cd \u03bc\u03b5\u03bb\u03ac\u03bd\u03b9 \u03b1\u03bb\u03bb\u03ac \u03ba\u03b1\u03b9 &hellip; <a href=\"https:\/\/maths4u.gr\/index.php\/2025\/11\/12\/pythagora\/\" class=\"more-link\">\u0394\u03b9\u03b1\u03b2\u03ac\u03c3\u03c4\u03b5 \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03b1<span class=\"screen-reader-text\"> &#8220;\u03a0\u03c5\u03b8\u03b1\u03b3\u03cc\u03c1\u03b5\u03b9\u03b1&#8230;&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-167","post","type-post","status-publish","format-standard","hentry","category-history"],"_links":{"self":[{"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/posts\/167","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/comments?post=167"}],"version-history":[{"count":9,"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/posts\/167\/revisions"}],"predecessor-version":[{"id":309,"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/posts\/167\/revisions\/309"}],"wp:attachment":[{"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/media?parent=167"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/categories?post=167"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/tags?post=167"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}