Qua m\u1ed9t \u0111i\u1ec3m \u1edf ngo\u00e0i m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 th\u1ec3 v\u1ebd v\u00f4 s\u1ed1 \u0111\u01b0\u1eddng th\u1eb3ng kh\u00f4ng c\u1eaft nhau. C\u00e1c b\u1ea1n c\u00f3 tin kh\u00f4ng? Cho d\u00f9 \u0111\u00e2y l\u00e0 m\u1ec7nh \u0111\u1ec1 m\u00e2u thu\u1eabn v\u1edbi c\u00e1c gi\u00e1o tr\u00ecnh to\u00e1n h\u1ecdc \u1edf b\u1eadc trung h\u1ecdc, song \u0111\u00f3 l\u00e0 m\u1ed9t lo\u1ea1i h\u00ecnh h\u1ecdc kh\u00e1c, h\u00ecnh h\u1ecdc phi Euclide.<\/p>\n\n\n\n
T\u1eeb x\u01b0a \u0111\u1ebfn nay ng\u01b0\u1eddi ta cho r\u1eb1ng t\u1eeb m\u1ed9t \u0111i\u1ec3m \u1edf ngo\u00e0i \u0111\u01b0\u1eddng th\u1eb3ng ta ch\u1ec9 c\u00f3 th\u1ec3 v\u1ebd m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00f3 v\u00e0 ch\u1ec9 m\u1ed9t m\u00e0 th\u00f4i. \u0110\u00f3 l\u00e0 m\u1ec7nh \u0111\u1ec1 do Euclide, nh\u00e0 to\u00e1n h\u1ecdc c\u1ed5 Hy L\u1ea1p, \u0111\u00e3 ph\u00e1t bi\u1ec3u trong s\u00e1ch \u201cNguy\u00ean l\u00ed h\u00ecnh h\u1ecdc\u201d c\u1ee7a \u00f4ng. N\u0103m 1826, Lobasevski \u0111\u00e3 \u0111\u01b0a ra m\u1ed9t m\u00f4n h\u00ecnh h\u1ecdc m\u1edbi, trong c\u00f3 m\u1ed9t \u0111\u1ecbnh \u0111\u1ec1 g\u1ecdi l\u00e0 \u0110\u1ecbnh \u0111\u1ec1 phi Euclide: Qua m\u1ed9t \u0111i\u1ec3m \u1edf ngo\u00e0i m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng \u00edt nh\u1ea5t c\u00f3 th\u1ec3 v\u1ebd hai \u0111\u01b0\u1eddng th\u1eb3ng kh\u00f4ng c\u1eaft \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00f3. \u0110\u1ecbnh \u0111\u1ec1 n\u00e0y k\u1ebft h\u1ee3p v\u1edbi c\u00e1c \u0111\u1ecbnh \u0111\u1ec1 Euclide kh\u00e1c, ph\u00e1t tri\u1ec3n th\u00e0nh h\u00ecnh h\u1ecdc phi Euclide. \u0110\u00f3 l\u00e0 m\u1ed9t lo\u1ea1i h\u00ecnh h\u1ecdc c\u00f3 quy m\u00f4 gi\u1ed1ng nh\u01b0 h\u00ecnh h\u1ecdc Euclide v\u00e0 ch\u01b0a ph\u00e1t hi\u1ec7n ra h\u1ec7 th\u1ed1ng h\u00ecnh h\u1ecdc m\u1edbi n\u00e0o c\u00f3 m\u00e2u thu\u00e2n b\u1edfi ch\u00ednh ch\u00fang ta c\u00f3 th\u1ec3 d\u00f9ng m\u1ed9t m\u00f4 h\u00ecnh \u0111\u1ec3 gi\u1ea3i th\u00edch h\u00ecnh h\u1ecdc Lobasevski. H\u00ecnh ph\u1eb3ng trong h\u00ecnh h\u1ecdc Lobasevski c\u0169ng gi\u1ed1ng h\u00ecnh ph\u1eb3ng trong h\u00ecnh h\u1ecdc th\u01b0\u1eddng, \u0111\u1ecbnh ngh\u0129a v\u1ec1 \u0111i\u1ec3m trong hai m\u00f4n h\u00ecnh h\u1ecdc c\u0169ng ho\u00e0n to\u00e0n gi\u1ed1ng nhau. Nh\u01b0 tr\u00ean h\u00ecnh 1, v\u1edbi m\u1ed9t h\u00ecnh ph\u1eb3ng \u03b1 ta c\u00f3 th\u1ec3 d\u00f9ng m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng a chia h\u00ecnh \u0111\u00f3 l\u00e0m hai ph\u1ea7n b\u1eb1ng nhau. M\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 t\u00e2m a tr\u00ean \u0111\u01b0\u1eddng th\u1eb3ng s\u1ebd nh\u1eadn \u0111\u01b0\u1eddng th\u1eb3ng l\u00e0m \u0111\u01b0\u1eddng k\u00ednh l\u00e0 chung cho c\u1ea3 hai lo\u1ea1i h\u00ecnh h\u1ecdc. Nh\u01b0 \u1edf h\u00ecnh 2 ta ch\u1ecdn m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng AB trong h\u00ecnh h\u1ecdc Lobasevski, v\u00e0 ch\u1ecdn tu\u1ef3 \u00fd m\u1ed9t \u0111i\u1ec3m P, ta c\u00f3 th\u1ec3 v\u1ebd nhi\u1ec1u \u0111\u01b0\u1eddng th\u1eb3ng kh\u00f4ng c\u1eaft AB. B\u1edfi v\u00ec v\u1edbi v\u00f2ng tr\u00f2n c\u00f3 t\u00e2m tr\u00ean a, qua \u0111i\u1ec3m P ta c\u00f3 th\u1ec3 v\u1ebd nhi\u1ec1u n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n kh\u00f4ng c\u1eaft n\u1eeda v\u00f2ng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh AB.<\/p>\n\n\n\n
T\u1eeb khi xu\u1ea5t hi\u1ec7n h\u00ecnh h\u1ecdc Lobasevski, \u0111\u00e3 xu\u1ea5t hi\u1ec7n nhi\u1ec1u lo\u1ea1i h\u00ecnh h\u1ecdc m\u1edbi nh\u01b0 h\u00ecnh h\u1ecdc Rieman l\u00e0 m\u1ed9t lo\u1ea1i h\u00ecnh h\u1ecdc phi Euclide. H\u00ecnh h\u1ecdc phi Euclide v\u00e0 h\u00ecnh h\u1ecdc Euclide ph\u1ea3n \u00e1nh m\u1ed9t t\u1ed3n t\u1ea1i kh\u00e1ch quan, ch\u1ec9 c\u00f3 \u0111i\u1ec1u l\u00e0 ph\u1ea3n \u00e1nh hi\u1ec7n th\u1ef1c kh\u00e1ch quan kh\u00f4ng \u1edf trong c\u00f9ng m\u1ed9t ph\u1ea1m vi. V\u00ed d\u1ee5 Einstin trong h\u1ecdc thuy\u1ebft t\u01b0\u01a1ng \u0111\u1ed1i r\u1ed9ng \u0111\u00e3 d\u00f9ng h\u00ecnh h\u1ecdc Rieman l\u00e0m kh\u00f4ng gian v\u1eadt l\u00ed. \u0110\u01b0\u01a1ng nhi\u00ean l\u00e0 trong cu\u1ed9c s\u1ed1ng h\u00e0ng ng\u00e0y ch\u00fang ta to\u00e0n d\u00f9ng h\u00ecnh h\u1ecdc Euclide.<\/p>\n\n\n\n
<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
Qua m\u1ed9t \u0111i\u1ec3m \u1edf ngo\u00e0i m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 th\u1ec3 v\u1ebd v\u00f4 s\u1ed1 \u0111\u01b0\u1eddng th\u1eb3ng kh\u00f4ng c\u1eaft nhau. C\u00e1c b\u1ea1n c\u00f3 tin kh\u00f4ng? Cho d\u00f9 \u0111\u00e2y l\u00e0 m\u1ec7nh \u0111\u1ec1 m\u00e2u thu\u1eabn v\u1edbi c\u00e1c gi\u00e1o tr\u00ecnh to\u00e1n h\u1ecdc \u1edf b\u1eadc trung h\u1ecdc, song \u0111\u00f3 l\u00e0 m\u1ed9t lo\u1ea1i h\u00ecnh h\u1ecdc kh\u00e1c, h\u00ecnh h\u1ecdc phi Euclide. T\u1eeb x\u01b0a […]<\/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-7664","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\/7664","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=7664"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7664\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7664"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7664"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7664"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}