h\u1ecdc sinh<\/a> \u0111\u1eb7t ra cho Pithagore m\u1ed9t c\u00e2u h\u1ecfi: Li\u1ec7u c\u00f3 th\u1ec3 d\u00f9ng s\u1ed1 nguy\u00ean hay t\u1ec9 s\u1ed1 gi\u1eefa hai s\u1ed1 nguy\u00ean \u0111\u1ec3 bi\u1ec3u di\u1ec5n \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnh vu\u00f4ng m\u00e0 c\u1ea1nh h\u00ecnh vu\u00f4ng b\u1eb1ng 1? \u0110\u1ec3 tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi n\u00e0y c\u1ea7n ph\u1ea3i ch\u1ee9ng minh. Pithagore \u0111\u00e3 ti\u1ebfn h\u00e0nh ph\u01b0\u01a1ng ph\u00e1p ch\u1ee9ng minh nh\u01b0 sau \u0111\u00e2y:<\/p>\n\n\n\nTr\u00ean h\u00ecnh v\u1ebd tr\u00ecnh b\u00e0y h\u00ecnh vu\u00f4ng c\u1ea1nh b\u1eb1ng 1 v\u00e0 \u0111\u01b0\u1eddng ch\u00e9o gi\u1ea3 s\u1eed \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1eb1ng s\u1ed1 nguy\u00ean hay t\u1ec9 s\u1ed1 c\u1ee7a hai s\u1ed1 nguy\u00ean p\/q.<\/p>\n\n\n\n
Theo \u0111\u1ecbnh l\u00ed Pithagore ta c\u00f3: (p\/q)2 = 12 + 12 = 2 hay p2 = 2q2<\/p>\n\n\n\n
Theo k\u1ebft qu\u1ea3 tr\u00ean v\u00ec 2q2 l\u00e0 s\u1ed1 ch\u1eb5n n\u00ean p2 l\u00e0 s\u1ed1 ch\u1eb5n (p kh\u00f4ng th\u1ec3 l\u00e0 s\u1ed1 l\u1ebb v\u00ec m\u1ed9t s\u1ed1 l\u1ebb b\u1ea5t k\u00ec, v\u00ed d\u1ee5 2n + 1 khi n\u00e2ng l\u00ean b\u00ecnh ph\u01b0\u01a1ng ph\u1ea3i l\u00e0 s\u1ed1 l\u1ebb: (2n+1)2 = 4n2 + 2n2+1.<\/p>\n\n\n\n
V\u1ea3 l\u1ea1i p v\u00e0 q kh\u00f4ng c\u00f3 \u01b0\u1edbc s\u1ed1 chung n\u00ean p \u0111\u00e3 l\u00e0 s\u1ed1 ch\u1eb5n th\u00ec q ph\u1ea3i l\u00e0 s\u1ed1 l\u1ebb.<\/p>\n\n\n\n
N\u1ebfu p l\u00e0 s\u1ed1 ch\u1eb5n, ta c\u00f3 th\u1ec3 \u0111\u1eb7t p = 2a do v\u1eady p2 = 4a2 = 2q2 hay q2 = 2a2 \u0111i\u1ec1u \u0111\u00f3 ch\u1ee9ng minh q2 l\u00e0 s\u1ed1 ch\u1eb5n v\u00e0 nh\u01b0 v\u1eady q c\u0169ng ph\u1ea3i l\u00e0 s\u1ed1 ch\u1eb5n; nh\u01b0 v\u1eady tr\u00e1i v\u1edbi gi\u1ea3 thi\u1ebft \u0111\u1eb7t ra t\u1eeb ban \u0111\u1ea7u v\u00e0 xu\u1ea5t hi\u1ec7n m\u00e2u thu\u1eabn l\u00e0 q v\u1eeba l\u00e0 s\u1ed1 l\u1ebb v\u1eeba l\u00e0 s\u1ed1 ch\u1eb5n. M\u00e2u thu\u1eabn v\u1eeba n\u00eau \u0111\u00e3 \u0111\u1ea9y Pithagore v\u00e0o ch\u1ed7 b\u00ed nh\u01b0ng c\u0169ng l\u00e0m nh\u1eadn th\u1ee9c v\u1ec1 s\u1ed1 c\u1ee7a lo\u00e0i ng\u01b0\u1eddi ti\u1ebfn l\u00ean m\u1ed9t b\u01b0\u1edbc.<\/p>\n\n\n\n
Vi\u1ec7c kh\u00f4ng th\u1ec3 d\u00f9ng s\u1ed1 nguy\u00ean ho\u1eb7c ph\u00e2n s\u1ed1 \u0111\u1ec3 \u0111o \u0111\u1ed9 d\u00e0i c\u1ee7a \u0111\u01b0\u1eddng ch\u00e9o h\u00ecnh vu\u00f4ng c\u1ea1nh b\u1eb1ng 1 kh\u00f4ng c\u00f3 ngh\u0129a l\u00e0 \u0111\u1ed9 d\u00e0i c\u1ee7a \u0111\u01b0\u1eddng ch\u00e9o n\u00e0y kh\u00f4ng t\u1ed3n t\u1ea1i.<\/p>\n\n\n\n
Th\u1ef1c ra \u1ee9ng d\u1ee5ng \u0111\u1ecbnh l\u00ed Pithagore ta d\u1ec5 d\u00e0ng t\u00ecm th\u1ea5y \u0111\u1ed9 d\u00e0i c\u1ee7a \u0111\u01b0\u1eddng ch\u00e9o l\u00e0 c\u0103n s\u1ed1 b\u1eadc hai c\u1ee7a s\u1ed1 2, t\u1ee9c s\u1ed1 \u221a2 . Nh\u01b0 v\u1eady ngo\u00e0i s\u1ed1 nguy\u00ean v\u00e0 ph\u00e2n s\u1ed1 (t\u1ec9 s\u1ed1 hai s\u1ed1 nguy\u00ean) ng\u01b0\u1eddi ta ph\u00e1t hi\u1ec7n m\u1ed9t lo\u1ea1i s\u1ed1 m\u1edbi m\u00e0 th\u1eddi \u0111\u00f3 c\u00f2n ch\u01b0a bi\u1ebft. Do s\u1ed1 \u221a2 kh\u00f4ng bi\u1ec3u di\u1ec5n \u0111\u01b0\u1ee3c th\u00e0nh t\u1ec9 s\u1ed1 c\u1ee7a hai s\u1ed1 nguy\u00ean n\u00ean ng\u01b0\u1eddi x\u01b0a g\u1ecdi \u0111\u00f3 l\u00e0 s\u1ed1 v\u00f4 t\u1ec9 (kh\u00f4ng bi\u1ec3u di\u1ec5n \u0111\u01b0\u1ee3c d\u01b0\u1edbi d\u1ea1ng m\u1ed9t t\u1ec9 s\u1ed1 c\u1ee7a hai s\u1ed1 nguy\u00ean).<\/p>\n\n\n\n
T\u1eeb kho\u00e1: S\u1ed1 h\u1eefu t\u1ec9; S\u1ed1 v\u00f4 t\u1ec9.<\/p>\n\n\n\n
<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
V\u00e0o th\u1ebf k\u1ec9 th\u1ee9 VI tr\u01b0\u1edbc C\u00f4ng nguy\u00ean c\u00f3 nh\u00e0 to\u00e1n h\u1ecdc c\u1ed5 Hy L\u1ea1p l\u00e0 Pithagore, \u00f4ng cho r\u1eb1ng tr\u00ean \u0111\u1eddi ch\u1ec9 c\u00f3 lo\u1ea1i s\u1ed1 nguy\u00ean v\u00e0 t\u1ec9 s\u1ed1 gi\u1eefa hai s\u1ed1 nguy\u00ean (ph\u00e2n s\u1ed1). V\u00ed d\u1ee5 ng\u01b0\u1eddi ta c\u00f3 th\u1ec3 d\u00f9ng s\u1ed1 nguy\u00ean ho\u1eb7c t\u1ec9 s\u1ed1 gi\u1eefa hai s\u1ed1 nguy\u00ean \u0111\u1ec3 bi\u1ec3u di\u1ec5n […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[15,9],"tags":[],"class_list":["post-7519","post","type-post","status-publish","format-standard","hentry","category-hoi-dap-khoa-hoc","category-toan-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7519","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=7519"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7519\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7519"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7519"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7519"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}